A Lagrangian constraint analysis of first order classical field theories with an application to gravity

Abstract

We present a method that is optimized to explicitly obtain all the constraints and thereby count the propagating degrees of freedom in (almost all) manifestly first order classical field theories. Our proposal uses as its only inputs a Lagrangian density and the identification of the a priori independent field variables it depends on. This coordinate-dependent, purely Lagrangian approach is complementary to and in perfect agreement with the related vast literature. Besides, generally overlooked technical challenges and problems derived from an incomplete analysis are addressed in detail. The theoretical framework is minutely illustrated in the Maxwell, Proca and Palatini theories for all finite $d\ge 2$ spacetime dimensions. Our novel analysis of Palatini gravity constitutes a noteworthy set of results on its own. In particular, its computational simplicity is visible, as compared to previous Hamiltonian studies. We argue for the potential value of both the method and the given examples in the context of generalized Proca and their coupling to gravity. The possibilities of the method are not exhausted by this concrete proposal.

arXiv comment44 pages, 1 figure. v2: references added; journal version

References in corpus (55)

• Covariant Galileon
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Dilaton Gravity in Two Dimensions
• Ghost-free Massive Gravity with a General Reference Metric
• Cosmic Acceleration from Abelian Symmetry Breaking
• Derivative self-interactions for a massive vector field
• Arbitrary p-form Galileons
• Asymptotic Reissner-Nordstrom black holes
• Generalized Proca action for an Abelian vector field
• Positivity Bounds for Massive Spin-1 and Spin-2 Fields
• On the 4D generalized Proca action for an Abelian vector field
• Classical and quantum ghosts
• Higher Derivative Field Theories: Degeneracy Conditions and Classes
• Generalized SU(2) Proca Theory
• Scalar-Vector-Tensor Gravity Theories
• Generalized multi-Proca fields
• BF gravity and the Immirzi parameter
• Finite Field-Energy and Interparticle Potential in Logarithmic Electrodynamics
• $BF$ gravity
• Lagrangian approach to the physical degree of freedom count
• The complete theory of Maxwell and Proca fields
• BRST Quantization of the Proca Model based on the BFT and the BFV Formalism
• The Maxwell-Proca theory: definition and construction
• Geometric Lagrangian approach to the physical degree of freedom count in field theory
• Scalar and vector Galileons
• Léon Rosenfeld's general theory of constrained Hamiltonian dynamics
• Ghost and singularity free theories of gravity
• Renormalization of generalized vector field models in curved spacetime
• A Canonical Approach to the Einstein-Hilbert Action in Two Spacetime Dimensions
• A Canonical Analysis of the Einstein-Hilbert Action in First Order Form
• Generalized Proca and its Constraint Algebra
• New solutions in pure gravity with degenerate tetrads
• Recursive Construction of Generator for Lagrangian Gauge Symmetries
• Nonlocal quantum field theory without acausality and nonunitarity at quantum level: is SUSY the key?
• Modified Hamiltonian formalism for higher-derivative theories
• One-loop renormalization in Galileon effective field theory
• Quantum Stability of Generalized Proca Theories
• The Canonical Structure of the First Order Einstein-Hilbert Action
• Quantum corrections to the generalized Proca theory via a matter field
• Geometrized quantum Galileons
• Diffeomorphism Symmetry in the Lagrangian Formulation of Gravity
• Canonical analysis of $n$-dimensional Palatini action without second-class constraints
• Generalised Proca Theories
• Inequivalence of First and Second Order Formulations in D=2 Gravity Models
• Is the principle of least action a must?
• Irregular Hamiltonian Systems
• 2-Form Gravity of the Lorentzian Signature
• An Analysis of the First Order Form of Gauge Theories
• A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
• Symplectic Analysis of the Two Dimensional Palatini Action
• Dirac quantization of noncommutative Abelian Proca field
• On constrained analysis and diffeomorphism invariance of generalised Proca theories
• Structure of Constrained Systems in Lagrangian Formalism and Degree of Freedom Count
• Quantization of Massive Non-Abelian Gauge Fields in The Hamiltonian Path Integral Formalism
• A Reexamination of the Canonical Structure of the Einstein-Hilbert Action in First-Order Form

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• On sufficient conditions for degrees of freedom counting of multi-field generalised Proca theories
• Symplectic quantization of multi-field Generalized Proca electrodynamics
• Non-minimal non-Abelian quantum vector fields in curved spacetime