Constraint structure and Hamiltonian treatment of Nappi-Witten model

TL;DR

This paper performs a Hamiltonian analysis of the Nappi-Witten model, revealing time-dependent non-commutativity through canonical quantization and detailed constraint analysis.

Contribution

It introduces a novel Hamiltonian approach to the Nappi-Witten model, incorporating boundary conditions as Dirac constraints and deriving the reduced phase space.

Findings

Discovery of time-dependent non-commutativity

Implementation of boundary conditions as Dirac constraints

Explicit construction of the reduced phase space

Abstract

We investigate the Hamiltonian analysis of Nappi-Witten model (WZW action based on non semi simple gauge group) and find a time dependent non-commutativity by canonical quantization. Our procedure is based on constraint analysis of the model in two parts. A first class analysis is used for gauge fixing the original model following by a second class analysis in which the boundary condition are treated as Dirac constraints. We find the reduced phase space by imposing our second class constraints on the variables in an extended Fourier space.