Background Field Method Versus Normal Field Theory in Explicit Examples: One Loop Divergences in S Matrix and Green's Functions for Yang-Mills and Gravitational Fields

Grisaru, Marcus T.; van Nieuwenhuizen, P.; Wu, C.C.

doi:10.1103/PhysRevD.12.3203

Background Field Method Versus Normal Field Theory in Explicit Examples: One Loop Divergences in S Matrix and Green's Functions for Yang-Mills and Gravitational Fields

Marcus T. Grisaru
(
- Brandeis U.
)
,
P. van Nieuwenhuizen
(
- Brandeis U.
)
,
C.C. Wu
(
- Brandeis U.
)

Jun, 1975

31 pages

Published in:

Phys.Rev.D 12 (1975) 3203

DOI:

10.1103/PhysRevD.12.3203

Report number:

Print-75-0480 (BRANDEIS)

View in:

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Abstract: (APS)

The gauge dependence in the background-field method of counterterms on and off the mass shell is investigated in several gauges for Yang-Mills and gravitational fields, including the axial gauge. The results agree with theorems of DeWitt and Kallosh. The relation between the quantum and classical gauge-fixing terms is discussed. It is shown how to determine specific S-matrix elements in the background-field method. A complete calculation using normal field theory of the one-loop divergences of scalar-scalar scattering through graviton exchange is presented. The results agree with those obtained in the background-field method by 't Hooft and Veltman.

MODEL: FIELD THEORY
FIELD THEORY: YANG-MILLS
FIELD THEORY: GRAVITATION
FIELD THEORY: BACKGROUND
FIELD THEORY: GAUGE
DEPENDENCE: GAUGE
MODEL: ON-SHELL
MODEL: OFF-SHELL
SCATTERING: SCALAR SCALAR
POSTULATED PARTICLE: GRAVITON

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