Canonical formalism for a2n-dimensional model with topological mass generation

Abstract

The four-dimensional model with topological mass generation that was found by Dvali, Jackiw, and Pi has recently been generalized to any even number of dimensions ($2n$ dimensions) in a nontrivial manner in which a St\"uckelberg-type mass term is introduced [S. Deguchi and S. Hayakawa, Phys. Rev. D 77, 045003 (2008)]. The present paper deals with a self-contained model, called here a modified hybrid model, proposed in this $2n$-dimensional generalization and considers the canonical formalism for this model. For the sake of convenience, the canonical formalism itself is studied for a model equivalent to the modified hybrid model by following the recipe for treating constrained Hamiltonian systems. This formalism is applied to the canonical quantization of the equivalent model in order to clarify observable and unobservable particles in the model. The equivalent model (with a gauge-fixing term) is converted to the modified hybrid model (with a corresponding gauge-fixing term) in a Becchi-Rouet-Stora-Tyutin-invariant manner. Thereby it is shown that the Chern-Pontryagin density behaves as an observable massive particle (or field). The topological mass generation is thus verified at the quantum-theoretical level.