The method of covariant symbols in curved space-time

@article{Salcedo2006TheMO,
  title={The method of covariant symbols in curved space-time},
  author={L. L. Salcedo},
  journal={The European Physical Journal C},
  year={2006},
  volume={49},
  pages={831-850}
}
  • L. L. Salcedo
  • Published 8 June 2006
  • Mathematics
  • The European Physical Journal C
Diagonal matrix elements of pseudodifferential operators are needed in order to compute effective Lagrangians and currents. For this purpose the method of symbols is often used, which however lacks manifest covariance. In this work the method of covariant symbols, introduced by Pletnev and Banin, is extended to curved space-time with arbitrary gauge and coordinate connections. For the Riemannian connection we compute the covariant symbols corresponding to external fields, the covariant… 

Renormalization of vector fields with mass-like coupling in curved spacetime

Using the method of covariant symbols we compute the divergent part of the effective action of the Proca field with non-minimal mass term. Specifically a quantum abelian vector field with a

Renormalization of vector fields with mass-like coupling in curved spacetime

Using the method of covariant symbols we compute the divergent part of the effective action of the Proca field with non-minimal mass term. Specifically a quantum abelian vector field with a

Nonminimal non-Abelian quantum vector fields in curved spacetime

The quantum effective action of non-minimal vector fields with Abelian or non-Abelian gauge degrees of freedom in curved spacetime is studied. The Proca or Yang-Mills fields are coupled to a local

Gradient expansion of the non-Abelian gauge-covariant Moyal star-product

Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge

Direct construction of the effective action of chiral gauge fermions in the anomalous sector

The anomaly implies an obstruction to a fully chiral covariant calculation of the effective action in the abnormal-parity sector of chiral theories. The standard approach then is to reconstruct the

The invariant factor of the chiral determinant

The coupling of spin 0 and spin 1 external fields to Dirac fermions defines a theory which displays gauge chiral symmetry. Quantum-mechanically, functional integration of the fermions yields the

On the non-local heat kernel expansion

We propose a novel derivation of the non-local heat kernel expansion, first studied by Barvinsky, Vilkovisky, and Avramidi, based on simple diagrammatic equations satisfied by the heat kernel. For

Gravitational mass-shift effect in the standard model

The gravitational mass-shift effect is investigated in the framework of the standard model with the energy cutoff regularization both for stationary and non-stationary backgrounds at the one-loop

Leptonic CP violating effective action for Dirac and Majorana neutrinos

A bstractIn the Standard Model minimally extended to include massive neutrinos, we compute the leading CP-violating zero temperature contributions to the one-loop effective action induced by

Derivative expansion of the heat kernel at finite temperature

The method of covariant symbols of Pletnev and Banin is extended to space-times with topology $\R^n\times S^1\times ... \times S^1$. By means of this tool, we obtain explicit formulas for the

References

SHOWING 1-10 OF 102 REFERENCES

Index-free heat kernel coefficients

Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary.

Gauge invariant derivative expansion of the effective action at finite temperature and density and the scalar field in (2+1)-dimensions

A method is presented for the computation of the one-loop effective action at finite temperature and density. The method is based on an expansion in the number of spatial covariant derivatives. It

Curved-space trace, chiral, and Einstein anomalies from path integrals, using flat-space plane waves.

It is claimed that it is not necessary to insert factors of g/sup 1/4/ which are often added on grounds of covariance, since one-loop anomalies are local objects, while the trace of the Jacobian of the measure is a purely mathematical object which can be evaluated whether or not one has even heard about general relativity.

Wigner Transformation for the Determinant of Dirac Operators

We use theζ-function regularization and an integral representation of the complex power of a pseudo differential operator to give an unambiguous definition of the determinant of the Dirac operator.

A new algebraic approach for calculating the heat kernel in quantum gravity

It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e., in symmetric spaces, may be presented in the form of an averaging over the Lie

Evaluation of the heat kernel in Riemann-Cartan space

A method for calculating the asymptotic expansion coefficients of the heat kernel associated with a fermion of spin in an arbitrary-dimensional Riemann - Cartan spacetime is presented. It is shown

On gauge invariance and vacuum polarization

This paper is based on the elementary remark that the extraction of gauge invariant results from a formally gauge invariant theory is ensured if one employs methods of solution that involve only
...