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Phys. Rev. D 35, 3081–3091 (1987)

Discrete-time quantum mechanics. III. Spin systems

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Carl M. Bender
Department of Physics, Washington University, St. Louis, Missouri 63130

Fred Cooper
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Kimball A. Milton
Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019

Stephen S. Pinsky
Department of Physics, Ohio State University, Columbus, Ohio 43210

L. M. Simmons, Jr.
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Received 10 November 1986; published in the issue dated 15 May 1987

A program is underway to obtain numerical solutions to quantum field theories by formulating them in terms of operator difference equations on a Minkowski space-time lattice. The most crucial unsolved problem is implementing non-Abelian gauge invariance. This paper initiates the study of this difficult problem by treating spin systems. The central problem here is to preserve exactly the (q-number) non-Abelian commutation relations at each lattice site. The solution we propose requires that the spin variables be expressed in terms of more fundamental oscillator variables which satisfy the Heisenberg algebra.

© 1987 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.35.3081
DOI:
10.1103/PhysRevD.35.3081
PACS:
11.15.Ha
 
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