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SUMMARY:Partha Mukhopadhyay (IMSc (Chennai))
DTSTART:20231213T183000Z
DTEND:20231213T193000Z
DTSTAMP:20260423T041820Z
UID:UKYhepth/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UKYhepth/68/
 ">Construction of Poincaré invariant theories on a lattice</a>\nby Partha
  Mukhopadhyay (IMSc (Chennai)) as part of Theoretical Physics Seminars (Ke
 ntucky)\n\nLecture held in CP 303.\n\nAbstract\nIn constructing lattice ve
 rsions of physical theories\, usually the spacetime symmetries are given u
 p. This is because of the use of difference approximation of the derivativ
 e operator which does not satisfy Leibniz rule. The same is responsible fo
 r the fermion doubling problem and the associated loss of chirality. We in
 troduce a non-local lattice derivative\, hereafter to be called logarithmi
 c discrete derivative (LDD)\, as it admits a logarithmic expansion in powe
 rs of the difference operator and a formal lattice integral (LI) which is 
 inverse of LDD. The pair (LDD\, LI) can be shown to satisfy the same diffe
 rential and integral calculi of the continuum. We demonstrate how the pair
  can be used to construct lattice theories with Poincaré invariance. A st
 riking property of the resulting model is a local correspondence which say
 s that local equations of the continuum theory still hold true on the latt
 ice\, site-wise. Although such a construction looks very formal in positio
 n space\, in momentum space the action takes a simple form which may allow
  for numerical simulations. We show that the same momentum space results c
 an also be obtained by using summation\, instead of LI\, by using a techni
 que involving finer lattices. Similar concept was earlier arrived at by G.
  Bergner while studying SLAC-type non-local derivatives. We explain how LD
 D is related to SLAC derivative and indicate how the new understanding of 
 locality in position space could potentially allow for more effective use 
 of non-local derivatives in lattice studies. Time permitting\, we shall al
 so discus a generalisation of the construction to a class of curved backgr
 ounds and another form of the lattice derivative that achieves the same th
 ing but takes the form of an inverse sine hyperbolic function.\n
LOCATION:https://researchseminars.org/talk/UKYhepth/68/
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