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We investigate the Hamiltonian analysis of Nappi-Witten model (WZW actionbased on non semi simple gauge group) and find a time dependentnon-commutativity by canonical quantization. Our procedure is based onconstraint analysis of the model in two parts. A first class analysis is usedfor gauge fixing the original model following by a second class analysis inwhich the boundary condition are treated as Dirac constraints. We find thereduced phase space by imposing our second class constraints on the variablesin an extended Fourier space.

Constraint structure and Hamiltonian treatment of Nappi-Witten model