Canonical Formalism for a 2n-Dimensional Model with Topological Mass Generation

TL;DR

This paper develops a canonical formalism for a 2n-dimensional topological mass generation model, clarifying the quantum behavior of the Chern-Pontryagin density as an observable massive particle.

Contribution

It introduces a self-contained modified hybrid model in 2n-dimensions and applies canonical quantization to demonstrate topological mass generation at the quantum level.

Findings

Chern-Pontryagin density acts as an observable massive particle

Canonical formalism for the 2n-dimensional model is established

Topological mass generation is confirmed quantum mechanically

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 Stueckelberg-type mass term is introduced [S. Deguchi and S. Hayakawa, Phys. Rev. D 77, 045003 (2008), arXiv:0711.1446]. 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 (BRST)-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.