Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory
- Departament ECM and ICC, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain)
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.
- OSTI ID:
- 21501245
- Journal Information:
- Journal of Mathematical Physics, Vol. 52, Issue 1; Other Information: DOI: 10.1063/1.3532941; (c) 2011 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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