IJUP08 - Universidade do Porto

Quantum Vacuum Energy in General Relativity (The Casimir
Effect)
M. Barbosa 1
1 Department of Physics, Faculty of Science, University of Porto, Portugal.
My work is about the calculation of the zero-point energy (or vacuum energy) of a scalar
field in a curved space, which exists by a phenomena known as Casimir effect.
In 1948, Casimir showed that the fluctuations of the electromagnetic field in vacuum,
between to parallel conductive plates, is not zero and gives rise to an attractive force
between them. It’s a very weak force but perfectly measurable.
Applying Casimir’s calculation method to general relativity, we can verify that when we
have a scalar field (that can represent a particle, for example) in a curved space, if we
consider its small fluctuations, we will obtain a non-zero vacuum energy. A lot of research
work is being done to understand this non-zero vacuum energy and its relationship with the
deformation of the space-time.
This is a theoretical work, involving hard mathematical concepts. As we will have a very
general audience, I will not focus my presentation in the expressions and results I found.
Instead, I will try to give a basic point of view about what is a curved space, vacuum
energy, etc., and what kind of phenomena we can get with its connections. This will put the
audience closer to a big Physics’ topic - The General Relativity.
Resuming, I will try not to show just complicated equations that the most part of the
audience wouldn’t understand, but I will try to make them have a simple and intuitive idea
about the physical concepts used in my work.
References:
[1] L. H. Ford, Phys, Rev. D 11, 3370 (1975)
[2] L. H. Ford, Phys. Rev. D 14, 3305
[3] N. D. Birrell, P. C. W. Davies, Quantum fields in curved space, Cambridge University Press
(1999)
[4] K. A. Milton, The Casimir Effect, World Scientific (2001)
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