2009/02/27 by Josep M. Pons · 49 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal symmetry #Cosmology and Gravitation Theories #Covariant transformation #Gauge theory #Invariant (physics) #Invariant theory #Noether's theorem #Noncommutative and Quantum Gravity Theories #Spacetime #Spacetime symmetries #Tensor (intrinsic definition) #Tensor field #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.3532941
published in Journal of Mathematical Physics 52(1) (American Institute of Physics) · 31 pag
arxiv created 2009/02/27 · openalex publication_date 2011/01/01 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 Poincaré 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 Poincaré 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 Poincaré. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincaré 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.