Loop diagrams in boxes

C. Peterson; T. H. Hansson; K. Johnson

doi:10.1103/PhysRevD.26.415

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Loop diagrams in boxes

C. Peterson^*

T. H. Hansson^†

K. Johnson^‡

Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

Institute for Theoretical Physics, University of California, Santa Barbara, California 93103 and NORDITA, Bledgamsvej 17, DK-2100 Copenhagen, Denmark

Institute for Theoretical Physics, University of California, Santa Barbara, California 93103

^*On leave from NORDITA, Copenhagen, Denmark.
^†Address after 1 September 1981.
^‡On leave from Center for Theoretical Physics, MIT, Cambridge, Massachusetts 02139.

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Phys. Rev. D 26, 415 – Published 15 July, 1982

DOI: https://doi.org/10.1103/PhysRevD.26.415

Abstract

Methods for computing loop diagrams in confined scalar and gauge theories are developed. We construct propagators with different types of boundary conditions in boxes (rectangular cavities) using the method of image charges, which allows for a separation of the short-distance singularities. The techniques are illustrated by a calculation of the Casimir effect in a box using a covariant gauge, and of the energy shift of a photon in confined scalar QED. The relevance of such a calculation for a proposed model for the QCD vacuum is discussed.

References (18)

H. B. G. Casimir, Proc. K. Ned. Akad. Wet. B51, 793 (1948) [8,9]
A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn, and V. F. Weisskopf, Phys. Rev. D 9, 3471 (1974) T. DeGrand, R. L. Jaffe, K. Johnson, and J. Kiskis, ibid. 12, 2060 (1975)
T. H. Hansson, K. Johnson, and C. Peterson, UCSB Report No. NSF-ITP-82-1 (unpublished)
C. E. Carlson, T. H. Hansson, and C. Peterson, Report No. SLAC-PUB-2873 (unpublished) C. B. Thorn and J. Kiskis (unpublished)
Omitted endnote
T. D. Lee, Phys. Rev. D 19, 1802 (1979) F. E. Close and R. R. Horgan, Nucl. Phys. B164, 413 (1980) R. Balian and C. Bloch, Ann. Phys. (N.Y.) 60, 41 (1970) ibid.64, 271 (1971)
K. A. Milton, Phys. Rev. D 22, 1441 (1980)
L. S. Brown and G. J. Maclay, Phys. Rev. 184, 1272 (1969) W. Lukosz, Z. Phys. 262, 327 (1973)
R. Balian and B. Duplantier, Ann. Phys. (N.Y.) 112, 165 (1978)
Omitted endnote
Omitted endnote
J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)
Omitted endnote
Omitted endnote
Omitted endnote
A. Chodos and C. B. Thorn, Phys. Lett. 53B, 359 (1974)
Omitted endnote
J. C. Taylor, Gauge Theories of Weak Interactions (Cambridge Univ. Press, New York, 1976)

[c1] H. B. G. Casimir, Proc. K. Ned. Akad. Wet. B51, 793 (1948) [8,9]

[c2] A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn, and V. F. Weisskopf, Phys. Rev. D 9, 3471 (1974) T. DeGrand, R. L. Jaffe, K. Johnson, and J. Kiskis, ibid. 12, 2060 (1975)

[c3] T. H. Hansson, K. Johnson, and C. Peterson, UCSB Report No. NSF-ITP-82-1 (unpublished)

[c4] C. E. Carlson, T. H. Hansson, and C. Peterson, Report No. SLAC-PUB-2873 (unpublished) C. B. Thorn and J. Kiskis (unpublished)

[c5] Omitted endnote

[c6] T. D. Lee, Phys. Rev. D 19, 1802 (1979) F. E. Close and R. R. Horgan, Nucl. Phys. B164, 413 (1980) R. Balian and C. Bloch, Ann. Phys. (N.Y.) 60, 41 (1970) ibid.64, 271 (1971)

[c7] K. A. Milton, Phys. Rev. D 22, 1441 (1980)

[c8] L. S. Brown and G. J. Maclay, Phys. Rev. 184, 1272 (1969) W. Lukosz, Z. Phys. 262, 327 (1973)

[c9] R. Balian and B. Duplantier, Ann. Phys. (N.Y.) 112, 165 (1978)

[c10] Omitted endnote

[c11] Omitted endnote

[c12] J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)

[c13] Omitted endnote

[c14] Omitted endnote

[c15] Omitted endnote

[c16] A. Chodos and C. B. Thorn, Phys. Lett. 53B, 359 (1974)

[c17] Omitted endnote

[c18] J. C. Taylor, Gauge Theories of Weak Interactions (Cambridge Univ. Press, New York, 1976)

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Loop diagrams in boxes

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