Effective Action For Scalar Fields Research Articles

Covariant effective action for scalar-tensor theories of gravity

We develop the calculation of the divergent part of one-loop covariant effective action for scalar fields minimally and non-minimally coupled to gravity using the generalized Schwinger-DeWitt technique. We derive the field-space metric using Vilkovisky's prescription and obtain new terms in the one-loop corrections which are absent in past literature with trivial choices of field-space metric. We further calculate the covariant versions of past results, obtained using the standard approach, by applying Barvinsky and Vilkovisky's extension to the ordinary Schwinger-DeWitt approach. For completeness, we study the one-loop gravitational corrections for a dilaton-extended two-field Starobinsky model and compare with known results.

A NATURAL RENORMALIZATION OF THE ONE-LOOP EFFECTIVE ACTION FOR SCALAR FIELD IN CURVED SPACETIME

It has been shown that the negative norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter space.1,2 In this process, ultraviolet and infrared divergences have been automatically eliminated.3 A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λϕ4 theory) has been achieved through the consideration of the negative norm states.4 The one-loop effective action for scalar field in a general curved space-time has been calculated by this method, and a natural renormalization procedure in the one-loop approximation has been established.

Effective action for scalar fields and generalized zeta-function regularization

Motivated by the study of quantum fields in a Friedmann-Robertson-Walker space-time, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\ifmmode\times\else\texttimes\fi{}{H}^{3}/\ensuremath{\Gamma},$ ${H}^{3}/\ensuremath{\Gamma}$ being the finite volume, noncompact, hyperbolic spatial section, is investigated by a generalization of zeta-function regularization. It is shown that additional divergences may appear at the one-loop level. The one-loop renormalizability of the model is discussed and, making use of a generalization of zeta-function regularization, the one-loop renormalization group equations are derived.

Effective Action for Scalar Fields in Two-Dimensional Gravity

We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.

Two-dimensional effective action for matter fields coupled to the dilaton

We revise the calculation of the one-loop effective action for scalar and spinor fields coupled to the dilaton in two dimensions. Applying the method of covariant perturbation theory for the heat kernel we derive the effective action in an explicitly covariant form that produces both the conformally invariant and the conformally anomalous terms. For scalar fields the conformally invariant part of the action is nonlocal. The obtained effective action is proved to be infrared finite. We also compute the one-loop effective action for scalar fields at finite temperature.

Conformal properties of the heat-kernel expansion. Application to the effective Lagrangian.

Conformal properties of the Minakshisundaram coefficients are developed. As an example of their use we discuss the equivalence of the dimensional and \ensuremath{\zeta}-function regularization treatments of the conformal anomaly and the one-loop effective action for scalar fields.

Quantum effects in the early universe. II. Effective action for scalar fields in homogeneous cosmologies with small anisotropy

The one-loop contributions of conformally invariant scalar fields to the effective action are calculated for homogeneous cosmological models with small anisotropy. The dynamical equations which determine the classical geometry are displayed and the matrix elements of the stress-energy tensor between the initial and final vacuums are determined.