Casimir energies for spheres in n-dimensional minkowski space and generalized bernoulli polynomials

Research output: Contribution to journalConference article

Abstract

We consider a mathematical version of conformal quantum field theory in n-dimensions which give a unified approach to quantum field theory on Minkowski space and the Einstein universe. This unifying treatment enables us to relate massless fields in Minkowski space with massless fields in the Einstein universe into which such fields uniquely and conformally extend. Apart from certain global differences, fields in the Einstein universe approximate fields in Minkowski space as the radius of the Einstein universe tends to infinity and we utilize this fact to describe what seems to be a precise method for determining Casimir energies on spheres of arbitrary radii in n-dimensional Minkowski space. Specifically, our exact results for Casimir energies of massless scalar fields in the n dimensional Einstein universe involving generalized Bernoulli polynomials together with results on conformal covariance properties of massless fields and a scaling property of the Casimir energy for n even should enable us to obtain exact results for Casimir energies for massless scalar fields with Dirichlet boundary conditions on spheres in n dimensional Minkowski space, at least for n even. We illustrate our calculational method in detail for the n 2 case, which is completely representative of the arbitrary n case (n even).

Original languageEnglish (US)
Article number012022
JournalJournal of Physics: Conference Series
Volume411
Issue number1
DOIs
StatePublished - Jan 1 2013
Event20th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2012 - Prague, Czech Republic
Duration: Jun 17 2012Jun 23 2012

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Minkowski space
polynomials
universe
energy
scalars
radii
infinity
boundary conditions
scaling

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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abstract = "We consider a mathematical version of conformal quantum field theory in n-dimensions which give a unified approach to quantum field theory on Minkowski space and the Einstein universe. This unifying treatment enables us to relate massless fields in Minkowski space with massless fields in the Einstein universe into which such fields uniquely and conformally extend. Apart from certain global differences, fields in the Einstein universe approximate fields in Minkowski space as the radius of the Einstein universe tends to infinity and we utilize this fact to describe what seems to be a precise method for determining Casimir energies on spheres of arbitrary radii in n-dimensional Minkowski space. Specifically, our exact results for Casimir energies of massless scalar fields in the n dimensional Einstein universe involving generalized Bernoulli polynomials together with results on conformal covariance properties of massless fields and a scaling property of the Casimir energy for n even should enable us to obtain exact results for Casimir energies for massless scalar fields with Dirichlet boundary conditions on spheres in n dimensional Minkowski space, at least for n even. We illustrate our calculational method in detail for the n 2 case, which is completely representative of the arbitrary n case (n even).",
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Casimir energies for spheres in n-dimensional minkowski space and generalized bernoulli polynomials. / Moylan, Patrick J.

In: Journal of Physics: Conference Series, Vol. 411, No. 1, 012022, 01.01.2013.

Research output: Contribution to journalConference article

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