Advances in Theoretical and Mathematical Physics

Volume 8 (2004)

Number 1

Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory

Pages: 1 – 82

DOI: http://dx.doi.org/10.4310/ATMP.2004.v8.n1.a1

Authors

Giovanni Landi

Fedele Lizzi

Richard J. Szabo

Abstract

We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the perturbative dynamics of scalar field theory, to tachyon dynamics in string field theory, and to the Hamiltonian dynamics of noncommutative gauge theory in two dimensions. We also describe the adiabatic dynamics of solitons on the noncommutative torus and compare various classes of noncommutative solitons on the torus and the plane.

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