Simplified vacuum energy expressions for radial backgrounds and domain walls

@article{Dunne2008SimplifiedVE,
  title={Simplified vacuum energy expressions for radial backgrounds and domain walls},
  author={Gerald V. Dunne and Klaus Kirsten},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2008},
  volume={42},
  pages={075402}
}
  • G. DunneK. Kirsten
  • Published 2 December 2008
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
We extend our previous results of simplified expressions for functional determinants for radial Schrödinger operators to the computation of vacuum energy, or mass corrections, for static but spatially radial backgrounds, and for domain wall configurations. Our method is based on the zeta function approach to the Gel'fand–Yaglom theorem, suitably extended to higher-dimensional systems on separable manifolds. We find new expressions that are easy to implement numerically, for both zero and non… 

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References

SHOWING 1-10 OF 70 REFERENCES

Functional determinants for radial operators

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of

Vacuum energy in smooth background fields

We consider the ground-state energy of a scalar field in the background of a general potential which depends on one coordinate. We consider a general expression following from the analytical

One loop corrections to the metastable vacuum decay

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self-interacting scalar field in $3+1$ dimensions. We use a numerical method, established some time ago, which is

Beyond the thin-wall approximation : Precise numerical computation of prefactors in false vacuum decay

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a

Renormalized effective actions in radially symmetric backgrounds: Exact calculations versus approximation methods

Our previously developed calculational method (the partial-wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge

Negative energy densities in quantum field theory with a background potential

We present a general procedure for calculating one-loop ``Casimir'' energy densities for a scalar field coupled to a fixed potential in renormalized quantum field theory. We implement direct

One-loop quantum energy densities of domain wall field configurations

We discuss a simple procedure for computing one-loop quantum energies of any static field configuration that depends nontrivially on only a single spatial coordinate. We specifically focus on

Dependence of the vacuum energy on spherically symmetric background fields

The vacuum energy of a scalar field in a spherically symmetric background field is considered. Based on previous work [hep-th/9608070], the numerical procedure is refined further and applied to

Fast way to compute functional determinants of radially symmetric partial differential operators in general dimensions

Recently the partial-wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an
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