Physical aspects of the space-time torsion

It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for important cosmological applications like the graceful exit from the inflation and low-energy quantum dynamics of the cosmological constant. We investigate, using both covariant and non-covariant methods of calculations and mass-dependent renormalization scheme, the vacuum quantum effects of a massive scalar field in curved space-time. In the higher derivative sector we arrive at the explicit form of decoupling and obtain the β-functions in both UV and IR regimes as the limits of general expressions. For the cosmological and Newton constants the corresponding β-functions are not accessible in the perturbative regime and in particular the form of decoupling remains unclear.

https://iopscience.iop.org/article/10.1088/1126-6708/2003/02/021/pdf

Renormalization group and decoupling in curved space

Neutron multiplicities in heavy-ion-induced fission: Timescale of fusion-fission

We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows full control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.

A Simple Method for One-Loop Renormalization in Curved Space-Time

We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.

A simple method for one-loop renormalization in curved space-time

A method is proposed for finding the effective potential in an external gravitational field on the basis of the equation of a renormalized group. The effective potential is found in the single-loop approximation for the scalar field theory and for the asymptotically free theory containing non-Abelian calibration fields, scalars, and spinors with an arbitrary value of the parameter of nonminimal coupling between the scalar and gravitational fields. The effect of quantum corrections on spontaneous symmetry violation is discussed.

Effective potential in a curved space-time

One-loop renormalization of the Yang-Mills field theory in a curved space-time

The renormalization group equation is formulated for the vacuum energy of a scalar field. We calculate the two-loop functions and study the asymptotic behavior of the vacuum energy.

Renormalization group equation for the vacuum energy of a scalar field in curved space-time

Vilkovisky-DeWitt effective action in multidimensional quantum gravity and antiperiodic boundary conditions

A calculation of the number of scalar and spinor particles created in the quasi-Euclidean cosmological model with an electric field is carried out. The inverse effect of the created particles on the electric field is investigated. It is shown that for large times the creation of particles leads to a decrease of the electric field. The imaginary part of the effective action in quasi-Euclidean space with constant electric and magnetic fields is found.

I. L. Bukhbinder

Papers

Effective potential in a curved space-time

One-loop renormalization of the Yang-Mills field theory in a curved space-time

Renormalization group equation for the vacuum energy of a scalar field in curved space-time

Vilkovisky-DeWitt effective action in multidimensional quantum gravity and antiperiodic boundary conditions

Creation of particles and the effective Lagrangian in the quasi-Euclidean model of the universe with an electro-magnetic field