On sufficient conditions for degrees of freedom counting of multi-field generalised Proca theories
arXiv:2303.15261 · doi:10.1007/s10714-023-03191-8
Abstract
We derive sufficient conditions for theories consisting of multiple vector fields, which could also couple to external fields, to be multi-field generalised Proca theories. The conditions are derived by demanding that the theories have the required structure of constraints, giving the correct number of degrees of freedom. The Faddeev-Jackiw constraint analysis is used and is cross-checked by Lagrangian constraint analysis. To ensure the theory is constraint, we impose a standard special form of Hessian matrix. The derivation benefits from the realisation that the theories are diffeomorphism invariance (or, in the case of flat spacetime, invariant under Lorentz isometry). The sufficient conditions obtained include a refinement of secondary-constraint enforcing relations derived previously in literature, as well as a condition which ensures that the iteration process of constraint analysis terminates. Some examples of theories are analysed to show whether they satisfy the sufficient conditions. Most notably, due to the obtained refinement on some of the conditions, some theories which are previously interpreted as being undesirable are in fact legitimate, and vice versa. This in turn affects the previous interpretations of cosmological implications which should later be reinvestigated.
arXiv comment32 pages, no figure. Version submitted to General Relativity and Gravitation. Only title is changed to match published version. Please see published version for substantial improvements in discussion and presentation with respect to this preprint version
References in corpus (26)
- Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
- Measurements of Omega and Lambda from 42 High-Redshift Supernovae
- Generalization of the Proca Action
- A systematic approach to generalisations of General Relativity and their cosmological implications
- Cosmic Acceleration from Abelian Symmetry Breaking
- Derivative self-interactions for a massive vector field
- Generalized Proca action for an Abelian vector field
- Beyond generalized Proca theories
- On the 4D generalized Proca action for an Abelian vector field
- Generalized SU(2) Proca Theory
- Covariantised Vector Galileons
- The complete theory of Maxwell and Proca fields
- A Lagrangian constraint analysis of first order classical field theories with an application to gravity
- The Maxwell-Proca theory: definition and construction
- Non-Abelian -term dark energy and inflation
- Scalar and vector Galileons
- Generalized SU(2) Proca theory reconstructed and beyond
- Faddeev-Jackiw quantization and the path integral
- A systematic procedure to build the beyond generalized Proca field theory
- Constant-roll inflation in the generalized SU(2) Proca theory
- Generalized Proca and its Constraint Algebra
- Stability Conditions in the Generalized SU(2) Proca Theory
- Hamiltonian analysis of General Relativity and extended gravity from the iterative Faddeev-Jackiw symplectic approach
- Quantum stability of Proca-Nuevo
- To Half--Be or Not To Be?
- On constrained analysis and diffeomorphism invariance of generalised Proca theories