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Computing in Science & Engineering

Computational complexity for physicists

Stephan Mertens

Published Jan 1, 2002• 60 citations
Publisher

Abstract

The theory of computational complexity has some interesting links to physics, in particular to quantum computing and statistical mechanics. The article contains an informal introduction to this theory and its links to physics.
DOI
10.1109/5992.998639

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One of the most successful physicists of the generation immediately before Hugh Everett III, E. T. Jaynes shared both Everett's interest in applications of information theory to physics and his foundational orientation. But whereas Everett focused on quantum mechanics, much of Jaynes' work concerned how to use information theory in thermodynamics. Here Everett sketches an initial reaction to a published paper of Jaynes', "Information Theory and Statistical Mechanics," Physical Review, 106, 620-630 (1957). The date on the document corresponds to the date that Jaynes' article appeared in print, and not necessarily to the date on which the notes were written.
This translation of the survey article by I. M. Gel'fand and A. M. Yaglom on the theory and applications of integration in functional spaces in problems of quantum physics was prepared because it was felt that such a review would be of interest and of use to mathematical physicists working in several different fields. The article begins with a discussion of Wiener measure, after which the extension is made to the complex measure introduced by Feynman in his formulation of quantum mechanics, and examples are given of the use of these methods in quantum mechanics, quantum field theory, and quantum statistical physics. A comprehensive bibliography of works devoted to the theory and applications of functional integration methods is included.