BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Robert Leigh DTSTART:20220316T135000Z DTEND:20220316T143000Z DTSTAMP:20260423T004546Z UID:PhysBound/8 DESCRIPTION:Title: Symmetries of Diff-invariant theories\nby Robert Leigh as part of Ph ysics @ Boundaries Workshop\n\n\nAbstract\nIn this talk\, I will consider a universal group of symmetries that are associated to embedded surfaces i n a classical spacetime. In the codimension-2 case\, we refer to these sur faces as corners\, and the symmetry as the extended corner symmetry. In th e context of the Einstein-Hilbert theory\, we show that the Noether charge s supported by such a corner coincide precisely with the extended corner s ymmetry. The inclusion of the embedding map into the phase space of the th eory allows for a calculation of the algebra of charges. We then show that within the covariant phase space formalism\, there is a precise way of ex tending the phase space such that all charges are integrable and associate d with Hamiltonian vector fields on field space. The algebra of charges is then consistently represented in terms of the Poisson brackets of this ex tended phase space theory. This resolves an old conundrum in gravity\, sep arating the notion of non-integrability from non-conservation. Finally\, w e discuss some recent work employing the orbit method which relates corner s to certain symplectic reductions. This gives an entirely group theoretic al characterization of corners without reference to an underlying classica l spacetime\, and thus might be regarded as the building blocks of a quant um theory.\n LOCATION:https://researchseminars.org/talk/PhysBound/8/ END:VEVENT END:VCALENDAR