Local invariance and covariant conservation laws are independent in field theories; the paper gives requirements for Noether's second theorem to produce the latter and shows the two are not equivalent.
Invariant Variation Problems
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of Lie's group theory. For special groups and problems in variation, this combination of methods is not new; I may cite Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker), Weyl and Klein for special infinite groups. Especially Klein's second Note and the present developments have been mutually influenced by each other, in which regard I may refer to the concluding remarks of Klein's Note.
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Extends gauge invariance via operator shifting in quantum statistical mechanics, deriving sum rules and hyperdensity functionals for equilibrium and nonequilibrium cases.
Derives a generic chiral anomaly formula incorporating multiple Feynman diagrams, from which abelian, singlet, consistent, and covariant forms follow, with topological discussion and FeynCalc code.
TEGR is argued to admit a gauge theory formulation on principal bundles with Poincaré or Lorentz structure groups, where the gauge group is the diffeomorphism group if the teleparallel connection is not treated as an absolute element.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
An introductory review of renormalisation procedures, the renormalisation group, and scale-setting optimisation in gauge theories such as QCD.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.