Geodesic
First-Quantized Fermions in Compact Dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 446-460 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{TMF_2001_128_3_a9,
     author = {A. V. Marshakov},
     title = {First-Quantized {Fermions} in {Compact} {Dimensions}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {446--460},
     year = {2001},
     volume = {128},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a9/}
}
TY  - JOUR
AU  - A. V. Marshakov
TI  - First-Quantized Fermions in Compact Dimensions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 446
EP  - 460
VL  - 128
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a9/
LA  - ru
ID  - TMF_2001_128_3_a9
ER  - 
%0 Journal Article
%A A. V. Marshakov
%T First-Quantized Fermions in Compact Dimensions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 446-460
%V 128
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a9/
%G ru
%F TMF_2001_128_3_a9
A. V. Marshakov. First-Quantized Fermions in Compact Dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 446-460. http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a9/

[1] A. Polyakov, Phys. Lett. B, 103 (1981), 207–210 ; 211–214 | DOI | MR | MR

[2] V. Fainberg, A. Marshakov, Nucl. Phys. B, 306 (1988), 659–676 | DOI | MR

[3] E. S. Fradkin, A. A. Tseytlin, Nucl. Phys. B, 261 (1985), 1–27 ; А. А. Цейтлин, ТМФ, 128:3 (2001), 540 | DOI | MR | DOI | MR | Zbl

[4] L. Brink, P. Di Vecchia, P. Howe, S. Deser, B. Zumino, Phys. Lett. B, 64 (1976), 435–438 | DOI

[5] A. M. Polyakov, Kalibrovochnye polya i struny, Izd. ITF im. L. D. Landau, Chernogolovka, 1995

[6] Vl. Dotsenko, Nucl. Phys. B, 285 (1987), 45–69 | DOI | MR

[7] A. Cohen, G. Moore, P. Nelson, J. Polchinski, Nucl. Phys. B, 267 (1986), 143–157 | DOI | MR

[8] A. V. Marshakov, V. Ya. Fainberg, Tr. FIAN, 201, 1990, 139–179 | MR

[9] V. Fainberg, A. Marshakov, Phys. Lett. B, 211 (1988), 81–85 | DOI | MR

[10] S. Deser, B. Zumino, Phys. Lett. B, 65 (1976), 369–373 | DOI | MR

[11] J. Atick, E. Witten, Nucl. Phys. B, 310 (1988), 291–334 | DOI | MR

[12] J. Ambjorn, Yu. Makeenko, G. Semenoff, R. Szabo, Screening and D-brane dynamics in finite temperature superstring theory, E-print hep-th/9906134 | MR