A note on unfree gauge symmetry

Abstract

We study the general structure of field theories with the unfree gauge symmetry where the gauge parameters are restricted by differential equations. The examples of unfree gauge symmetries include volume preserving diffeomorphisms in the unimodular gravity and various higher spin field theories with transverse gauge symmetries. All the known examples of the models with unfree gauge symmetry share one common feature. They admit local quantities which vanish on shell, though they are not linear combinations of Lagrangian equations and their derivatives. We term these quantities as mass shell completion functions. In the case of usual gauge symmetry with unconstrained gauge parameters, the irreducible gauge algebra involves the two basic constituents: the action functional and gauge symmetry generators. For the case of unfree gauge symmetry, we identify two more basic constituents: operators of gauge parameter constraints and completion functions. These two extra constituents are involved in the algebra of unfree gauge symmetry on equal footing with action and gauge symmetry generators. Proceeding from the algebra, we adjust the Faddeev-Popov (FP) path integral quantization scheme to the case of unfree gauge symmetry. The modified FP action involves the operators of the constraints imposed on the gauge parameters, while the corresponding BRST transformation involves the completion functions. The BRST symmetry ensures gauge independence of the path integral. We provide two examples which admit the alternative unconstrained parametrization of gauge symmetry and demonstrate that they lead to the equivalent FP path integral.

arXiv commentMinor corrections, references added

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Cited by in corpus (12)

• Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space
• Unfree gauge symmetry in the Hamiltonian formalism
• Hamiltonian constraints and unfree gauge symmetry
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity
• Generalized unimodular gravity as a form of k-essence
• Gauge symmetry of unimodular gravity in Hamiltonian formalism
• Restricted Gauge Theory Formalism and Unimodular Gravity
• Hamiltonian BFV-BRST Quantization for the Systems with Unfree Gauge Symmetry
• The Involutive System of Higher-Spin Equations
• Generalized unimodular gravity in Friedmann and Kantowski-Sachs universes
• Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
• Global conserved quantities and unfree gauge symmetry