Dimensional renormalization of scalar field theory in curved space-time
The regularization and renormalization of an interacting scalar field f in a curved space-time background is performed by the method of continuation to n dimensions. In addition to the familiar counter terms of the flat-space theory, c-number, ''vacuum'' counter terms must also be introduced. These involve zero, first, and second powers of the Riemann curvature tensor R/sub abgd/. Moreover, the renormalizability of the theory requires that the Lagrange function couple f/sup 2/ to the curvature scalar R with a coupling constant h. The coupling h must obey an inhomogeneous renormalization group equation, but otherwise it is an arbitrary, free parameter. All the counter terms obey renormalization group equations which determine the complete structure of these quantities in terms of the residues of their simple poles in n-4. The coefficient functions of the counter terms determine the construction of f/sup 2/ and f/sup 4/ in terms of renormalized composite operators 1, (f/sup 2/), and (f/sup 4/). Two of the counter terms vanish in conformally flat space-time. The others may be computed from the theory in purely flat space-time. They are determined, in a rather intricate fashion, by the additive renormalization for two-point functions of (f/sup 2/) and (f/sup 4/) in Minkowski space--time. In particular, using this method, we compute the leading divergence of the R/sup 2/ interaction which is of fifth order in the coupling constant l.
- Research Organization:
- Institute for Advanced Study, Princeton, New Jersey 08540
- OSTI ID:
- 6391423
- Journal Information:
- Ann. Phys. (N.Y.); (United States), Vol. 130:1
- Country of Publication:
- United States
- Language:
- English
Similar Records
Spontaneous symmetry breaking and pseudo-Goldstone bosons in curved space-time
Effective Lagrangian for lambdaphi/sup 4/ theory in curved spacetime with varying background fields: Quasilocal approximation