Abstract
The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.
Highlights
Noncommutative models [1,2] may improve the behavior of field theories in the ultraviolet region by smoothing or removing some of the singularities of commutative quantum field theory
The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry
This argument is almost certainly wrong, since it is not based on a well-defined theory and predicts a value that can be 120 orders of magnitudes greater than the observed one, it can still be interesting to check if the noncommutativity parameter can act as a natural cutoff and improve the ultraviolet behavior of the theory
Summary
Noncommutative models [1,2] may improve the behavior of field theories in the ultraviolet region by smoothing or removing some of the singularities of commutative quantum field theory. The scale κ is usually assumed to of the order of the Planck mass MP ∼ 1019 GeV (but lower values are not excluded), and may act as a natural cutoff on the divergences of quantum field theory, in contrast with the commutative case where the cutoff must be imposed by hand. This possibility may be tested in the calculation of the vacuum energy of quantum fields. The best improvement occurs in the anti-Snyder model, where the trace of the heat kernel is finite, and the divergence of the vacuum energy is only logarithmic
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