Generalized two-dimensional QED and functional determinants

M. Hortaçsu; K. D. Rothe; B. Schroer

doi:10.1103/PhysRevD.20.3203

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Generalized two-dimensional QED and functional determinants

M. Hortaçsu^*, K. D. Rothe, and B. Schroer

Institut für Theoretische Physik, Freie Universität Berlin, D-1000 Berlin 33, Arnimallee 3, Germany

^*On leave of absence from Bo $\tilde{g}$ azici University, Istanbul, Turkey.

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Phys. Rev. D 20, 3203 – Published 15 December, 1979

DOI: https://doi.org/10.1103/PhysRevD.20.3203

Abstract

We obtain a closed expression for the functional determinant of the Dirac operator in two-dimensional QED by confronting results on cluster decomposition with direct fermion integration in the presence of Atiyah-Singer zero modes. The result is shown to be identical with the one obtained from the $ζ$ -function definition and the use of the modified anomaly equation.

Comments & Replies

More about the fermion determinant in two-dimensional QED

Adrian Patrascioiu

Phys. Rev. D 22, 3142 (1980)

Still more about the fermion determinant in two-dimensional QED

M. Hortaçsu, K. D. Rothe, and B. Schroer

Phys. Rev. D 22, 3145 (1980)

References (21)

H. J. Rothe, K. D. Rothe, and J. A. Swieca, Phys. Rev. D 19, 3020 (1979)
L. V. Belvedere, K. D. Rothe, B. Schroer, and J. A. Swieca, Nucl. Phys. B153, 112 (1979)
A. M. Polyakov, private communication through P. Weisz
B. Berg and M. Lüscher, Commun. Math. Phys. 69, 57 (1979)
K. D. Rothe and J. A. Swieca, Ann. Phys. (N.Y.) 117, 382 (1979)
B. Schroer, Acta Phys. Austriaca, Suppl. 19, 155 (1978)
R. T. Seeley, Proc. Symp. Pure and Appl. Math. 10, 288 (1967)
P. B. Gilkey, J. Diff. Geom. 10, 601 (1975)
S. Hawking, Commun. Math. Phys. 55, 133 (1977)
N. K. Nielsen and B. Schroer, Nucl. Phys. B127, 493 (1977)
A. S. Schwarz, Commun. Math. Phys. 64, 233 (1979) V. A. Fateev, I. V. Frolov, and A. S. Schwarz, Nucl. Phys. B154, 1 (1979) J. S. Dowker and Raymond Critchley, Phys. Rev. D 13, 3224 (1976) ibid. 16, 3390 (1977)
Seeley's [8] De Witt's N. K. Nielsen (unpublished) [6]
N. K. Nielsen, H. Römer, and B. Schroer, Nucl. Phys. B136, 475 (1978)
M. F. Atiyah, N. Hitchin, and I. M. Singer, Proc. R. Soc. London (to be published)
J. Schwinger, Phys. Rev. 128, 2425 (1962)
N. K. Nielsen and B. Schroer, Nucl. Phys. B120, 62 (1977)
J. H. Lowenstein and J. A. Swieca, Ann. Phys. (N.Y.) 68, 172 (1971)
Sec. III of [5]
A. D'Adda, M. Lüscher, and P. Di Vecchia, Nucl. Phys. B146, 63 (1978) H. Eichenherr, ibid. B146, 215 (1978)
A. Patrascioiu, Phys. Rev. D 20, 491 (1979)
M. A. Atiyah, V. K. Patodi, and I. M. Singer, Math. Proc. Camb. Phil. Soc. 77, 43 (1975)

[c1] H. J. Rothe, K. D. Rothe, and J. A. Swieca, Phys. Rev. D 19, 3020 (1979)

[c2] L. V. Belvedere, K. D. Rothe, B. Schroer, and J. A. Swieca, Nucl. Phys. B153, 112 (1979)

[c3] A. M. Polyakov, private communication through P. Weisz

[c4] B. Berg and M. Lüscher, Commun. Math. Phys. 69, 57 (1979)

[c5] K. D. Rothe and J. A. Swieca, Ann. Phys. (N.Y.) 117, 382 (1979)

[c6] B. Schroer, Acta Phys. Austriaca, Suppl. 19, 155 (1978)

[c7] R. T. Seeley, Proc. Symp. Pure and Appl. Math. 10, 288 (1967)

[c8] P. B. Gilkey, J. Diff. Geom. 10, 601 (1975)

[c9] S. Hawking, Commun. Math. Phys. 55, 133 (1977)

[c10] N. K. Nielsen and B. Schroer, Nucl. Phys. B127, 493 (1977)

[c11] A. S. Schwarz, Commun. Math. Phys. 64, 233 (1979) V. A. Fateev, I. V. Frolov, and A. S. Schwarz, Nucl. Phys. B154, 1 (1979) J. S. Dowker and Raymond Critchley, Phys. Rev. D 13, 3224 (1976) ibid. 16, 3390 (1977)

[c12] Seeley's [8] De Witt's N. K. Nielsen (unpublished) [6]

[c13] N. K. Nielsen, H. Römer, and B. Schroer, Nucl. Phys. B136, 475 (1978)

[c14] M. F. Atiyah, N. Hitchin, and I. M. Singer, Proc. R. Soc. London (to be published)

[c15] J. Schwinger, Phys. Rev. 128, 2425 (1962)

[c16] N. K. Nielsen and B. Schroer, Nucl. Phys. B120, 62 (1977)

[c17] J. H. Lowenstein and J. A. Swieca, Ann. Phys. (N.Y.) 68, 172 (1971)

[c18] Sec. III of [5]

[c19] A. D'Adda, M. Lüscher, and P. Di Vecchia, Nucl. Phys. B146, 63 (1978) H. Eichenherr, ibid. B146, 215 (1978)

[c20] A. Patrascioiu, Phys. Rev. D 20, 491 (1979)

[c21] M. A. Atiyah, V. K. Patodi, and I. M. Singer, Math. Proc. Camb. Phil. Soc. 77, 43 (1975)

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Generalized two-dimensional QED and functional determinants

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More about the fermion determinant in two-dimensional QED

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References (21)

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