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TMF, 2001, Volume 128, Number 3, Pages 446–460 (Mi tmf508)  

First-Quantized Fermions in Compact Dimensions

A. V. Marshakovab

a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: We discuss a path integral representation for fermionic particles and strings in the spirit of V. Ya. Fainberg and the author [1], [2]. We concentrate on the problems arising when some target-space dimensions are compact. We consider the partition function for a fermionic particle at a finite temperature or in compact time in detail as an example. We demonstrate that a self-consistent definition of the path integral generally requires introducing nonvanishing background Wilson loops and that modulo some common problems for real fermions in the Grassmannian formulation, these loops can be interpreted as condensates of world-line fermions. Properties of the corresponding string-theory path integrals are also discussed.

DOI: https://doi.org/10.4213/tmf508

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English version:
Theoretical and Mathematical Physics, 2001, 128:3, 1213–1224

Bibliographic databases:

Received: 20.04.2001

Citation: A. V. Marshakov, “First-Quantized Fermions in Compact Dimensions”, TMF, 128:3 (2001), 446–460; Theoret. and Math. Phys., 128:3 (2001), 1213–1224

Citation in format AMSBIB
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\by A.~V.~Marshakov
\paper First-Quantized Fermions in Compact Dimensions
\jour TMF
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\vol 128
\issue 3
\pages 446--460
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\crossref{https://doi.org/10.4213/tmf508}
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\zmath{https://zbmath.org/?q=an:1040.81076}
\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 128
\issue 3
\pages 1213--1224
\crossref{https://doi.org/10.1023/A:1012311919795}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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