Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1993-05-11
Physics
High Energy Physics
High Energy Physics - Phenomenology
52 pages, OKHEP-93-07
Scientific paper
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy based on the method of finite elements. We are able to formulate fully consistent quantum-mechanical systems directly on a lattice in terms of operator difference equations. One advantage of this discretized formulation of quantum mechanics is that the ambiguities associated with operator ordering are eliminated. Furthermore, the scheme provides an easy way in which to obtain the energy levels of the theory numerically. A generalized version of this discretization scheme can be applied to quantum field theory problems. The difficulties normally associated with fermion doubling are eliminated. Also, one can incorporate local gauge invariance in the finite-element formulation. Results for some field theory models are summarized. In particular, we review the calculation of the anomaly in two-dimensional quantum electrodynamics (the Schwinger model). Finally, we discuss nonabelian gauge theories.
Bender Carl M.
Mead Lawrence R.
Milton Kimball A.
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