Effective Lagrangian for λ φ 4 theory in curved spacetime with varying background fields: Quasilocal approximation

摘要: By means of a Riemann normal coordinate expansion for the metric and momentum-space representation Green's function, we derive in analytic form one-loop effective Lagrangian $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ theory curved spacetime which is exact to all orders $\ensuremath{\lambda}$ includes variation background field up second order. Ultraviolet divergences are removed by small-proper-time dimensional regularization. We obtain generalized expression ${a}_{2}$ Minakshisundaram-DeWitt coefficient scalar wave operator with spacetime-dependent field. A set renormalization-group equations coupling constants obtained, can be used analyzing their curvature energy dependence. An alternative derivation presented via heat-kernel technique anisotropic harmonic oscillators. Our result useful study quantum processes early universe or black holes under conditions where dynamical effects important. When suitably generalized, obtained here quasipotential should provide an improvement over flat-space Coleman-Weinberg potential assumed most discussions new inflationary universe. Possible directions developing our method more general problems also discussed.