The Maxwell-Proca theory: definition and construction

Abstract

We present a systematic construction of the most general first order Lagrangian describing an arbitrary number of interacting Maxwell and Proca fields on Minkowski spacetime. To this aim, we first formalize the notion of a Proca field, in analogy to the well known Maxwell field. Our definition allows for a non-linear realization of the Proca mass, in the form of derivative self-interactions. Consequently, we consider so-called generalized Proca/vector Galileons. We explicitly demonstrate the ghost-freedom of this complete Maxwell-Proca theory by obtaining its constraint algebra. We find that, when multiple Proca fields are present, their interactions must fulfill non-trivial differential relations in order to ensure the propagation of the correct number of degrees of freedom. These relations had so far been overlooked, which means previous multi-Proca proposals generically contain ghosts. This is a companion paper to arXiv:1905.06968 [hep-th]. It puts on a solid footing the theory there introduced.

9 pages + 8 pages appendix. v2: References added. v3: Footnote 3 deleted. v4: Journal version. This work is dedicated to María José Díez Segoviano

References in corpus (36)

• The Dynamics of General Relativity
• The galileon as a local modification of gravity
• Resummation of Massive Gravity
• Generalization of the Fierz-Pauli Action
• Ghost-free Massive Gravity with a General Reference Metric
• On Non-Linear Actions for Massive Gravity
• 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
• Arbitrary p-form Galileons
• Cosmology in generalized Proca theories
• Generalized Proca action for an Abelian vector field
• Beyond generalized Proca theories
• Galileons in the Sky
• Generalizing Galileons
• Black Holes and Abelian Symmetry Breaking
• Observational constraints on generalized Proca theories
• On the 4D generalized Proca action for an Abelian vector field
• A no-go theorem for generalized vector Galileons on flat spacetime
• A small cosmological constant from Abelian symmetry breaking
• Black holes and solitons in an extended Proca theory
• Generalized SU(2) Proca Theory
• Generalized multi-Proca fields
• Covariantised Vector Galileons
• A First Class Constraint Generates Not a Gauge Transformation, But a Bad Physical Change: The Case of Electromagnetism
• The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories
• Black Holes and Neutron Stars in Vector Galileons
• Lagrangian approach to the physical degree of freedom count
• The complete theory of Maxwell and Proca fields
• Geometric Lagrangian approach to the physical degree of freedom count in field theory
• Hairy black hole solutions in $U(1)$ gauge-invariant scalar-vector-tensor theories
• Scalar and vector Galileons
• On the (A)dS Decoupling Limits of Massive Gravity
• A new multisymplectic unified formalism for second-order classical field theories
• Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations

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