Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-04-11
Theor.Math.Phys. 128 (2001) 1213-1224; Teor.Mat.Fiz. 128 (2001) 446-460
Physics
High Energy Physics
High Energy Physics - Theory
Contribution to a special issue of Theoretical and Mathematical Physics in honour of 75th birthday of Vladimir Ya. Fainberg; 9
Scientific paper
We discuss the path integral representation for the fermionic particles and strings and concentrate at the problems arising when some target-space dimensions are compact. An example of partition function for fermionic particle at finite temperature or with one compact target-space dimension is considered in detail. It is demonstrated that the first-quantized path integral requires, in general, presence of nonvanishing "Wilson loops" and modulo some common problems for real fermions in Grassmannian formulation one can try to reinterpret them in terms of condensates of the world-line fermions. The properties of corresponding path integrals in string theory are also discussed.
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