Here I give a very non-technical introduction to the idea of edge modes, that are needed in order to maintain gauge invariance in the presence of a boundary. The edge modes are gauge transformations on the boundary, that ensure the bulk gauge fields when restricted to the boundary are gauge equivalent to the boundary gauge fields (fixed on the boundary). In future videos I will fully construct edge modes using the homotopy pullback, but for now this is simply a schematic argument.
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Edge Modes #4 - Edge Modes (Briefly)
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MathsMathPhysicsTensorVectorAlgebraAbstract AlgebraAlgebraic StructureGroupDifferential GeometryLinear AlgebraMultilinear AlgebraUndergraduateEducationTopologyTopological SpacesManifoldsContinuityMapsSetsCircleTorusS^1AbstractSetEquivalence RelationGaugeGauge theoryEinstein Cartan theoryEdge modesEinsteinCartanBoundaryBoundary conditionHomotopyPullbackCategoryGroupoid