Functional versus canonical quantization of a nonlocal massive vector-gauge theory

Abstract

It has been shown in literature that a possible mechanism of mass generation for gauge fields is through a topological coupling of vector and tensor fields. After integrating over the tensor degrees of freedom, one arrives at an effective massive theory that, although gauge invariant, is nonlocal. Here we quantize this nonlocal resulting theory both by path integral and canonical procedures. This system can be considered as equivalent to one with an infinite number of time derivatives and consequently an infinite number of momenta. This means that the use of the canonical formalism deserves some care. We show the consistency of the formalism we use in the canonical procedure by showing that the obtained propagators are the same as those of the (Lagrangian) path integral approach. The problem of nonlocality appears in the obtainment of the spectrum of the theory. This fact becomes very transparent when we list the infinite number of commutators involving the fields and their velocities.

12 pages, Latex, to appear in J. Math. Phys

References in corpus (6)

• Antibracket, Antifields and Gauge-Theory Quantization
• Nonabelian Topological Mass Generation in 4 Dimensions
• Canonical quantization of non-local field equations
• Constrained Dynamics of the Coupled Abelian Two-Form
• BV QUANTIZATION OF A VECTOR-TENSOR GAUGE THEORY WITH TOPOLOGICAL COUPLING
• Symplectic Quantization for Reducible Systems

Cited by in corpus (6)

• Chiral-Symmetry Breaking in Pseudo Quantum Electrodynamics at Finite Temperature
• Remarks on the canonical quantization of noncommutative theories
• Hamiltonian embedding of the massive noncommutative U(1) theory
• Noncommutative QCD, first-order-in-theta-deformed instantons and 't Hooft vertices
• The U(1)A anomaly in noncommutative SU(N) theories
• Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch