Linear independence of renormalization counterterms in curved space-times of arbitrary dimensionality

Journal Article · Fri May 01 04:00:00 EDT 1987 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527559· OSTI ID:6919583

Jack, I; Parker, L

The counterterms in the Lagrangian of a renormalizable quantum field theory that involve the Riemann curvature tensor are considered. It is proved that for six or fewer dimensions the counterterms not containing derivatives of the Riemann tensor are linearly independent. It is shown that there appears to be a maximum space-time dimension for which identities can exist among invariants involving the product of n Riemann tensors (without derivatives acting on them.) Space-times that would require these products as counterterms for a renormalizable theory have a dimensionality which is one higher than this maximum dimension. This makes it plausible that the required set of counterterms not involving derivatives of the Riemann tensor is linearly independent in arbitrary dimensions. In the Appendix, a relation cubic in the Weyl tensor, which relates invariants cubic in the Riemann tensor in five dimensions, is proved.

• Research Organization: Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
• OSTI ID: 6919583
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 28:5; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIMENSIONS
FIELD THEORIES
FUNCTIONS
LAGRANGIAN FUNCTION
MATHEMATICAL SPACE
QUANTUM FIELD THEORY
QUANTUM GRAVITY
RENORMALIZATION
RIEMANN SPACE
SPACE
SPACE-TIME
TENSORS