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BEGIN:VEVENT
SUMMARY:Lucien Hardy (Perimeter Institute)
DTSTART;VALUE=DATE-TIME:20211101T170000Z
DTEND;VALUE=DATE-TIME:20211101T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/1
DESCRIPTION:Title: Combining the radical aspects of Gravity and Quantum:
The causaloid framework.\nby Lucien Hardy (Perimeter Institute) as par
t of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nGeneral Relat
ivity and Quantum Theory are each conservative and radical in complementar
y respects. In General Relativity quantities take definite values but the
theory has dynamical causal structure. Quantum Theory has fixed causal s
tructure but it has the property of indefiniteness (quantities do not take
definite values). Most likely\, a theory of Quantum Gravity will combine
the radical aspects - that is it will have indefinite causal structure.
In 2005 I set up a probabilistic framework capable of accommodating theori
es with indefinite causal structure which I called the causaloid framework
. In this seminar I will present this framework along with some recent de
velopments in the quest for a foundationally inspired approach to Quantum
Gravity.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Pachol (Queen Mary London)
DTSTART;VALUE=DATE-TIME:20211115T170000Z
DTEND;VALUE=DATE-TIME:20211115T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/2
DESCRIPTION:Title: Digital quantum geometry\nby Anna Pachol (Queen Ma
ry London) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstra
ct\nNoncommutative geometry\, as the generalised notion of geometry\, allo
ws us to model the quantum gravity effects in an effective description wit
hout full knowledge of quantum gravity itself. On a curved space one must
use the methods of Riemannian geometry - but in their quantum version\, in
cluding quantum differentials\, quantum metrics and quantum connections.\n
\n \n\nIn this seminar I will provide the introduction to the general fram
ework of quantum Riemannian geometry involving noncommutative differential
graded algebra and bimodule connections. This framework is then applied t
o studying quantum Riemannian geometries over the field F2 of two elements
as the extreme case of a finite-field adaptation of noncommutative geomet
ric methods for physics. The choice of the finite field in this framework
proposes a new kind of 'discretisation scheme'\, which we called the 'digi
tal geometry'.\n\n \n\nAs a result\, we classify all possible digital quan
tum Riemannian geometries over the field F2 on unital algebras of vector s
pace dimension n<4 and find explicit forms for quantum Levi-Civita connect
ions and Riemann\, Ricci and Einstein tensors. When the quantum metrics ad
mit quantum Levi-Civita connections\, each pair produces `digital quantum
Riemannian geometry' of which most turn out to be not flat in the sense of
non-zero Riemann curvature. We find a rich moduli of examples for n=3 and
top form degree 2 (providing a landscape of all reasonable up to 2D quant
um geometries)\, including many which are not flat. Their coordinate algeb
ras are commutative\, but their differentials are not.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Shadi Tahvildar-Zadeh (Rutgers University)
DTSTART;VALUE=DATE-TIME:20211129T170000Z
DTEND;VALUE=DATE-TIME:20211129T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/3
DESCRIPTION:Title: Bohmian mechanics\nby A. Shadi Tahvildar-Zadeh (Ru
tgers University) as part of Algebra\, Particles\, and Quantum theory\n\n\
nAbstract\nIn this talk I will briefly explain what Bohmian Mechanics is\,
and what it is not. In particular\, I will argue that it is currently the
most straightforward ontological formulation of non-relativistic quantum
mechanics\, and that it does not suffer from the shortcomings that it is r
umored to suffer from. I will then talk about recent results on a relativ
istic extension of Bohmian Mechanics via multi-time wave functions and hyp
ersurface Bohm-Dirac theory\, one that my group at Rutgers has been develo
ping for the past few years. I will explain how two-sided actions on Clif
ford algebras can provide a unifying framework for a particle ontology tha
t can be extended to cover bosons as well as fermions\, and use that frame
work to study interacting electron-photon systems and Compton scattering i
n one space dimension\, in such a way that both the electron and the photo
n enter the story as point particles.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Howard Barnum
DTSTART;VALUE=DATE-TIME:20211213T170000Z
DTEND;VALUE=DATE-TIME:20211213T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/4
DESCRIPTION:Title: Euclidean Jordan Algebras and Quantum Theory\nby H
oward Barnum as part of Algebra\, Particles\, and Quantum theory\n\n\nAbst
ract\nThis talk will focus on the mathematical properties of Euclidean Jor
dan Algebras (EJAs) viewed as potential models for the state and observabl
e spaces of physical systems\, and two new characterizations of these alge
bras in terms of such properties\, by myself and collaborators. \n\nEJAs
were introduced and investigated early in the development of quantum theor
y\,\nas abstractions of the algebra of Hermitian operators on a Hilbert sp
ace\, initially in finite dimension. \nJordan\, von Neumann\, and Wigner
classified them: they are real\, complex\, and quaternionic quantum theory
\, systems whose state spaces are balls (``spin factors")\, and one except
ional case (which may be thought of as three-state octonionic quantum theo
ry).\n\nThe "general probabilistic theories" (GPT) framework formulates po
tential physical theories in terms of systems having convex\, compact stat
e spaces\, on which the probabilities of measurement\noutcomes are given b
y affine functionals. Dynamics and composite systems are also described i
n the framework. A major part of the GPT research program has been to fin
d principles\, mathematically natural\, of physical or information-process
ing significance\, or\nall three\, that narrow down the very wide landscap
e of possibilities available in the GPT framework\nto the familiar spaces
of quantum density matrices (states) and POVM elements (measurement outcom
es).\n\nSuch characterizations often proceed by first characterizing the f
inite-dimensional EJAs. After\nsummarizing important mathematical propert
ies of the EJAs\, I will describe\nseveral such characterizations\, includ
ing the Koecher-Vinberg system relating EJAs to homogeneous self-dual cone
s (which can be interpreted as ``unnormalized states"\, the positive semid
efinite Hermitian matrices being an example)\, but focusing on two new re
sults. Joachim Hilgert and I [1\,2]\ncharacterized EJAs by two properties
: a generalized spectral decomposability formulated entirely in terms of\n
convexity\, and a ``strong symmetry" property of the state space\, also fo
rmulated in convex terms: transitive\naction of the symmetry group on sets
of simultaneously perfectly distinguishable pure states. Work of HB\nwit
h C. Ududec [4] characterizes them via homogeneity of their cones of unnor
malized states (whose mathematical\, physical\, and information-processing
significance I will discuss) and transitive action of the symmetry group
on pure states. Further physical principles characterizing the usual\, co
mplex\, quantum systems within the class of EJAs will be described: tomog
raphic locality\, or energy observability [3]\nmeaning that the generators
of continuous symmetries of the state space [3\, but close to ideas of Co
nnes\n(orientation) and of Alfsen and Shultz (dynamical correspondence)]:
the generators of continuous symmetries of the state space are observables
.\n\nIf time permits\, I will also discuss the possibilities for forming c
omposites of such systems\, focusing on my work with Matthew Graydon and A
lex Wilce [5]. \n\n[1] H. Barnum and J. Hilgert\, "Strongly symmetric spe
ctral convex bodies are Jordan algebra state spaces"\, https://arxiv.org/a
bs/1904.03753\n[2] H. Barnum and J. Hilgert\, "Spectral properties of conv
ex sets"\, Journal of Lie Theory 30 (2020) 315-344.\nPreprint close to thi
s available at: https://winephysicssong.com/2021/09/01/strongly-symmetric-
spectral-convex-sets-are-jordan-algebra-state-spaces/\n[3] H. Barnum\, M.
Mueller and C. Ududec\, "Higher-order interference and single-system postu
lates characterizing quantum theory"\, New Journal of Physics 16 (2014) 12
3029. arXiv:1403.4147\n[4] H. Barnum and C. Ududec\, in preparation.\n[5]
Composites and Categories of Euclidean Jordan Algebras\, Quantum 4\, 359
(2020).\nhttps://arxiv.org/abs/1606.09331\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahn Majid (Queen Mary London)
DTSTART;VALUE=DATE-TIME:20220131T170000Z
DTEND;VALUE=DATE-TIME:20220131T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/6
DESCRIPTION:Title: Octonions as a quasiassociative algebra\nby Shahn
Majid (Queen Mary London) as part of Algebra\, Particles\, and Quantum the
ory\n\n\nAbstract\nThis will be a gentle introduction to an old result of
H. Albuquerque and myself about how to think of the Octonions as an associ
ative algebra\, but in a certain monoidal category of Z_2^3 -graded vector
spaces. The associator here is given by a coboundary 3-cocycle on the gro
up Z_2^3 of 3-vectors with entries 0\,1. Mac Lane’s theorem says that al
l constructions in the category can be done as if associative\, simply ins
erting the associator as needed for brackets to make sense (different ways
to do this will all give the same answer). The same construction for Z_2^
2 gives the quaternions while for Z_2^4 it's an interesting open problem a
s to what\nyou get. In the Octonion case\, one application is to think of
these as the coordinate algebra of a finite but nonassociative geometry. I
will indicate a couple of possible points of contact with physics.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Trautner (Max Planck Institute)
DTSTART;VALUE=DATE-TIME:20220228T170000Z
DTEND;VALUE=DATE-TIME:20220228T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/7
DESCRIPTION:Title: Symmetries of symmetries in particle physics\nby A
ndreas Trautner (Max Planck Institute) as part of Algebra\, Particles\, an
d Quantum theory\n\n\nAbstract\nThe plan of this seminar is to introduce y
ou to outer automorphisms ("symmetries of symmetries")\nof quantum field t
heories and their potential relevance for puzzles in our understanding of
Nature\nbased on the Standard Model of particle physics. We will see how t
he combined parity (P) and charge\nconjugation transformation (C) is one v
ery special kind of outer automorphism. This will lead us to a\nnew classi
fication of finite groups and the discovery that some symmetry groups do p
reclude the existence\nof CP transformations altogether\, in which case CP
can be violated by quantized\, calculable phases.\nFinally\, we will have
a look at outer automorphisms beyond the well-known C\,P\, or T transform
ations.\nBased on instructive examples\, I will discuss the general import
ance of outer automorphisms for the\ncomputation of stationary points and
emergent symmetries\, for spotting physical degeneracies in the\nparameter
space of a theory\, as well as to determine the boundaries of the renorma
lization group\nflow and RGE fixed points.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Woit (Columbia University)
DTSTART;VALUE=DATE-TIME:20220214T170000Z
DTEND;VALUE=DATE-TIME:20220214T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/8
DESCRIPTION:Title: Euclidean Twistor Unification and the Twistor P^1\
nby Peter Woit (Columbia University) as part of Algebra\, Particles\, and
Quantum theory\n\n\nAbstract\nIf one Wick rotates and works with twistors
in Euclidean\nrather than Minkowski space-time\, the way symmetries work c
hanges\nsignificantly. I'll argue that in the Euclidean context the symme
tries\nof twistor theory match well the symmetries of the Standard Model a
s\nwell as a chiral formulation of general relativity\, providing a\npromi
sing new basis for a unified theory.\n\n From the twistor perspective\, a
space-time point is described by a\nsphere with its antipodal map\, known
to mathematicians as the twistor\nP^1. Remarkably\, this same structure sh
ows up in recent advances in\nnumber theory\, and I'll say a bit about tha
t story (for more\, see\nhttps://www.math.columbia.edu/~woit/twistorp1.pdf
).\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Zanelli (CECS)
DTSTART;VALUE=DATE-TIME:20220314T170000Z
DTEND;VALUE=DATE-TIME:20220314T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/9
DESCRIPTION:Title: Local unconventional SUSY\nby Jorge Zanelli (CECS)
as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nFifty
years ago\, the discovery of supersymmetry (SUSY) allowed to combine inter
nal\nand spacetime symmetries. This required extending the Lie algebra of
those symmetries into a\ngraded Lie algebra. The additional supersymmetry
generators turned bosons into fermions and\nvice versa and\, in its simple
st form called for systems with equal number of bosons and\nfermions. SUSY
led to hopes of new physics and the resolution of many riddles\, from the
origin\nof energy hierarchies in the Standard Model to the nature of dark
matter. However\, the search\nfor supersymmetry over the past five decade
s has never found SUSY pairs and has only\nprovided higher and higher lowe
r limits for the SUSY breaking energy scale.\n\nWe argue that SUSY can be
realized in a different manner\, unifying spacetime and local internal sym
metries\, with spin-1 gauge fields and spin-1/2 fermions in a single Lie s
uperalgebra-valued connection. In this representation\, states do not come
in Bose-Fermi pairs and\, if the local\nsymmetry contains the Lorentz gro
up\, gravity is inevitably included but without spin-3/2 (or\nhigher spin)
fundamental fields. The resulting systems are remarkably simple\, closely
\nresembling a standard quantum field theory and SUSY still emerges\, alth
ough not as a\nsymmetry of the action but as a feature of the vacuum/groun
d states. Thus\, local SUSY is a\ncontingent symmetry\, like Poincaré or
AdS invariances that depend on the nature of the\nspacetime background.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Müller (Inst. for quantum optics and quantum information)
DTSTART;VALUE=DATE-TIME:20220523T160000Z
DTEND;VALUE=DATE-TIME:20220523T173000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/10
DESCRIPTION:Title: Quantum theory and Jordan algebras from simple princi
ples\nby Markus Müller (Inst. for quantum optics and quantum informat
ion) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nQu
antum theory is one of our most successful physical theories\, but its\nst
andard textbook formulation is mysterious. For example\, why are states\nd
escribed by complex vectors in a Hilbert space\, and why do observables\nc
orrespond to self-adjoint operators? In this talk\, I describe how the\nHi
lbert space formalism of quantum theory (and its Jordan-algebraic\ngeneral
izations) can be reconstructed from simple physical or\ninformation-theore
tic principles\, without presupposing any of the usual\nmathematical machi
nery. This is conceptually similar to the derivation\nof the Lorentz trans
formations from the principles of relativity and the\nconstancy of the spe
ed of light. To this end\, I introduce the framework\nof “generalized pr
obabilistic theories” which generalizes both classical\nand quantum prob
ability theory and which describes all possible\nconsistent ways in which
preparations and measurements can interact\nstatistically in a laboratory.
I give an explicit example of a set of\nprinciples that implies quantum t
heory\, describe how the hunt for\n“higher-order interference” led to
a scientific detective story\, and\nshow how these insights and techniques
can shed surprising light on the\nrelation between quantum theory and spa
cetime.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tevian Dray and Corinne Manogue (Oregon State University)
DTSTART;VALUE=DATE-TIME:20220411T150000Z
DTEND;VALUE=DATE-TIME:20220411T163000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/11
DESCRIPTION:Title: A Division Algebra Description of the Magic Square\,
including E_8\nby Tevian Dray and Corinne Manogue (Oregon State Univer
sity) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nT
he Freudenthal-Tits magic square of Lie algebras provides an abstract para
meterization of a family of Lie algebras in terms of two division algebras
\, with the exceptional cases all involving the octonions. In the non-oct
onionic cases\, it is straightforward to provide a matrix interpretation o
f the magic square\, which can be exponentiated to yield a parametrization
of the corresponding Lie groups. We describe here joint work with Rob Wi
lson that extends these constructions to E_8\, thus providing an explicit
representation in terms of (two copies of) the octonions.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corinne Manogue and Tevian Dray (Oregon State University)
DTSTART;VALUE=DATE-TIME:20220425T150000Z
DTEND;VALUE=DATE-TIME:20220425T163000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/12
DESCRIPTION:Title: E8 and the Standard Model\nby Corinne Manogue and
Tevian Dray (Oregon State University) as part of Algebra\, Particles\, an
d Quantum theory\n\n\nAbstract\nUsing an explicit parameterization in term
s of octonions\, we interpret\nthe elements of the Lie algebra $\\frak{e}_
8$ as objects in the Standard\nModel. We obtain lepton and quark spinors
with the usual properties\,\nthe Standard Model Lie algebra $\\frak{su}(3)
+\\frak{su}(2)+\\frak{u}(1)$\,\nand the Lorentz Lie algebra $\\frak{so}(3\
,1)$.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Carroll (Caltech)
DTSTART;VALUE=DATE-TIME:20220613T160000Z
DTEND;VALUE=DATE-TIME:20220613T173000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/13
DESCRIPTION:Title: Extracting the Universe from the Wave Function\nb
y Sean Carroll (Caltech) as part of Algebra\, Particles\, and Quantum theo
ry\n\n\nAbstract\nQuantum mechanics is a theory of wave functions in Hilbe
rt space. Many features that we generally take for granted when we use qua
ntum mechanics -- classical spacetime\, locality\, the system/environment
split\, collapse/branching\, preferred observables\, the Born rule for pro
babilities -- should in principle be derivable from the basic ingredients
of the quantum state and the Hamiltonian. I will discuss recent progress o
n these problems\, including consequences for emergent spacetime and quant
um gravity.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denjoe O'Connor (DIAS)
DTSTART;VALUE=DATE-TIME:20221205T170000Z
DTEND;VALUE=DATE-TIME:20221205T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/14
DESCRIPTION:Title: Fuzzy Spaces: An exceptional example.\nby Denjoe
O'Connor (DIAS) as part of Algebra\, Particles\, and Quantum theory\n\n\nA
bstract\nI will review the ideas behind fuzzy spaces such as the fuzzy\nsp
here\, discuss some of the physics one can encounter and where they\narise
. I will then describe the fuzzy spaces associated with the\nexceptional g
roup G_2 and their relation to the octonions.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shogo Tanimura (Nagoya University)
DTSTART;VALUE=DATE-TIME:20230116T100000Z
DTEND;VALUE=DATE-TIME:20230116T113000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/15
DESCRIPTION:Title: Superselection rule from measurement theory\nby S
hogo Tanimura (Nagoya University) as part of Algebra\, Particles\, and Qua
ntum theory\n\n\nAbstract\nIn quantum theory\, physically measurable quant
ities of a microscopic system are represented by self-adjoint operators. H
owever\, not all of the self-adjoint operators correspond to measurable qu
antities. The superselection rule is a criterion for distinguishing measur
able quantities from non-measurable quantities. Any measurable quantity mu
st satisfy the superselection rules. By contraposition\, any quantity whic
h does not satisfy the superselection rules are not be measurable.\nIn thi
s talk\, I will show deduction of superselection rules from an assumption
on symmetry property of measurement process. I introduce the notion of cov
ariant indicator\, which is a macroscopic observable covariant with a micr
oscopic observable under some group actions. If the object system has a qu
antity that is conserved during the measurement process\, another quantity
that do not commute with the conserved quantity are non-measurable by a n
on-trivial covariant indicator. Our derivation of superselection rules can
be considered as an extreme case of the Wigner-Araki-Yanase uncertainty r
elation.\n\nReference: \nhttps://arxiv.org/abs/1112.5701\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baez (U. C. Riverside)
DTSTART;VALUE=DATE-TIME:20230206T180000Z
DTEND;VALUE=DATE-TIME:20230206T193000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/16
DESCRIPTION:Title: The Tenfold Way\nby John Baez (U. C. Riverside) a
s part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nThe impo
rtance of the tenfold way in physics was only recognized in this century.
Simply put\, it implies that there are ten fundamentally different kinds
of matter. But it goes back to 1964\, when the topologist C. T. C. Wall
classified the associative real super division algebras and found ten of t
hem. The three "purely even" examples were already familiar: the real nu
mbers\, complex numbers and quaternions. The rest become important when
we classify representations of groups or supergroups on Z/2-graded vector
spaces. We explain this classification\, its connection to Clifford alge
bras\, and some of its implications.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L Glaser (University of Vienna)
DTSTART;VALUE=DATE-TIME:20230320T170000Z
DTEND;VALUE=DATE-TIME:20230320T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/18
DESCRIPTION:Title: Imaging finite spectral triples\nby L Glaser (Uni
versity of Vienna) as part of Algebra\, Particles\, and Quantum theory\n\n
\nAbstract\nSpectral triples are a way to rewrite a manifold in algebraic
language\, through the triple of Algebra\, Hilbert space and Dirac operato
r. But they can not only describe continuum manifolds\, they also lend the
mselves to discretizing space\, by using finite algebras and Hilbert space
s.\n\nFuzzy spaces are closely related to some especially symmetric finite
spectral triples. But what about more general spectral triples? If finite
spectral triples are to be useful in regularizing a path integral over ge
ometries then at least some of them should also correspond to less regular
geometries.\n\nIn this talk I will present work in which I reconstruct ge
ometry from a spectral triple\, using numerical methods. In particular I w
ill also show that a deformation of the fuzzy sphere leads to a fuzzy elli
psoid.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Huerta (University of Lisbon)
DTSTART;VALUE=DATE-TIME:20230403T160000Z
DTEND;VALUE=DATE-TIME:20230403T173000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/19
DESCRIPTION:Title: The algebra of grand unified theories\nby John Hu
erta (University of Lisbon) as part of Algebra\, Particles\, and Quantum t
heory\n\n\nAbstract\nGrand unification was a program from the 1970s to uni
fy the strong\, weak and electromagnetic interactions. It is a junction wh
ere the theory of Lie groups and their finite-dimensional representations
meets particle physics\, providing a wonderful example of Lie theory and s
hedding light on the physics. We will take this point of view to introduce
three grand unified theories: the Georgi–Glashow SU(5) theory\, the Pat
i–Salam model based on SU(2) x SU(2) x SU(4)\, and Georgi's Spin(10) the
ory. We describe how all three extend the standard model\, and how these e
xtensions are compatible\, fitting together into a "cube" of grand unified
theories.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasia Rejzner (University of York)
DTSTART;VALUE=DATE-TIME:20230501T160000Z
DTEND;VALUE=DATE-TIME:20230501T173000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/20
DESCRIPTION:Title: Quantization\, Dequantization\, and Distinguished Sta
tes on causal sets and beyond\nby Kasia Rejzner (University of York) a
s part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nIn this
talk I will discuss the results of the paper "Quantization\, Dequantizatio
n\, and Distinguished States" written in callaboration with Eli Hawkins an
d Christoph Minz. In this work we consider free quantum fields on a causal
set and demonstrate how methods of geometric quantization can be applied
in that case. We compare the result with the Sorkin-Johnson construction a
nd demonstrate that both approaches single out the same quantum state.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Vaidman (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20230522T160000Z
DTEND;VALUE=DATE-TIME:20230522T173000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/21
DESCRIPTION:Title: The many-worlds interpretation of quantum mechanics a
nd the Born rule\nby Lev Vaidman (Tel Aviv University) as part of Alge
bra\, Particles\, and Quantum theory\n\n\nAbstract\nI will argue that the
many-worlds interpretation is the best interpretation of quantum mechanics
and discuss the status of the probability assignments in this determinist
ic theory.\n\nThe background can be found in\n\nThe Many-Worlds Interpreta
tion of Quantum Mechanics\, L. Vaidman\,\nThe Stanford Encyclopedia of Phi
losophy (Summer 2021 Edition)\, E. N. Zalta (ed.)\nhttps://plato.stanford.
edu/entries/qm-manyworlds/\n\nDerivations of the Born Rule\, L. Vaidman\,\
nQuantum\, Probability\, Logic\, Jerusalem Studies in Philosophy and Histo
ry of Science\, M. Hemmo\, O. Shenker (eds.)\, Chapter 26 (Springer Nature
Switzerland AG 2020)\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Penrose (University of Oxford)
DTSTART;VALUE=DATE-TIME:20230302T170000Z
DTEND;VALUE=DATE-TIME:20230302T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/22
DESCRIPTION:Title: From basic Twistor Theory to Split-Octonions. Does Tw
istor Theory also Address the SU(3) of Strong Interactions?\nby Roger
Penrose (University of Oxford) as part of Algebra\, Particles\, and Quantu
m theory\n\n\nAbstract\nTwistor theory was introduced in the mid-1960s as
an approach to combining quantum theory with space-time structure. Its ini
tial role was to relate the quantum-field-theoretic requirement of positiv
e frequency to the structure of space-time. Twistor space was introduced t
o codify space-time in an unusual way\, so that this twistor space would s
plit into two halves representing positive and negative frequency respecti
vely\, the points of their common boundary representing light rays in Mink
owski space.\n\nHowever\, this splitting turned out to have two quite diff
erent basic physical interpretations\, namely positive/negative helicity a
s well as positive/negative frequency\, which ought not to be confused in
the formalism\, and the notion of “bi-twistors” is introduced to resol
ve this issue. The algebra of bi-twistors turned out to provide a represen
tation of split-octonions. It also presents the possibility of generalizin
g a construction due to Ward for incorporating electromagnetism into twist
or theory\, which might now incorporates the SU(3) of strong interactions.
\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aiyalam Balachandran (Syracuse University)
DTSTART;VALUE=DATE-TIME:20230328T150000Z
DTEND;VALUE=DATE-TIME:20230328T163000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/24
DESCRIPTION:Title: Spin 1/2 from Gluons and a Little More\nby Aiyala
m Balachandran (Syracuse University) as part of Algebra\, Particles\, and
Quantum theory\n\n\nAbstract\nThe theta vacuum in QCD is the standard vacu
um\, twisted by the exponential of\nthe Chern-Simons term. But what is the
quantum operator U(g) for winding number 1?\n\nWe construct U(g) in this
talk. The Poincare’ generators commute with it only if\nthey are augment
ed by a spin 1/2 representation of the Lorentz group coming from\nlarge ga
uge transformations. This result is analogous to the ‘spin-isospin ‘ m
ixing result\ndue to Jackiw and Rebbi\, and Hasenfratz and ’t Hooft and
a similar result in fuzzy\nphysics. ( See ‘Lectures on Fuzzy and Fuzzy S
USY Physics \, Balachandran\, S.\nKurkcuoglu and S.Vaidya\, chapters 5.4.1
\, 8.4.1).\n\nHence states can drastically affect representations of obser
vables. This fact is\nfurther shown by charged states dressed by infrared
clouds. Following Mund\, Rehren\nand Schroer (arXiv:2109.10342 )\, we find
that Lorentz invariance is spontaneously\nbroken in these sectors. This r
esult is extended to QCD where even the global QCD\ngroup is shown to be b
roken.\n\nIt is argued that the escort fields of Mund et al. are the Higgs
fields for Lorentz and\ncolour breaking. They are string-localised fields
where the strings live in a union of de\nSitter spaces. Their oscillation
s and those of the infrared clouds generate the Goldstone\nmodes.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baez (U.C. Riverside)
DTSTART;VALUE=DATE-TIME:20230515T170000Z
DTEND;VALUE=DATE-TIME:20230515T183000Z
DTSTAMP;VALUE=DATE-TIME:20241016T083029Z
UID:AlgebraParticlesFoundations/25
DESCRIPTION:Title: Symmetric spaces and the tenfold way\nby John Bae
z (U.C. Riverside) as part of Algebra\, Particles\, and Quantum theory\n\n
\nAbstract\nThe tenfold way has many manifestations. It began as a tenfol
d classification of states of matter based on their behavior under time re
versal and charge conjugation. Mathematically\, it relies on the fact th
at there are ten super division algebra and ten kinds of Clifford algebras
\, where two Clifford algebras are of the same kind if they have equivalen
t categories of representations. But Cartan also showed that there are te
n infinite families of compact symmetric spaces! After explaining symmet
ric spaces\, we describe two ways to get compact symmetric spaces from Cli
fford algebras\, which give different correspondences between these two ma
nifestations of the tenfold way.\n
LOCATION:https://researchseminars.org/talk/AlgebraParticlesFoundations/25/
END:VEVENT
END:VCALENDAR