Abstract
We investigate the vacuum energy in $\kappa$-Poincar\'e invariant field theories. It is shown that for the equivariant Dirac operator one obtains an improvement in UV behavior of the vacuum energy and therefore the cosmological constant problem has to be revised.
Highlights
The history of the cosmological constant starts with Albert Einstein, where in his first paper on the application of general relativity (GR) to cosmology [1], he aimed to construct a static universe with a finite average density of matter
It is shown that for the equivariant Dirac operator one obtains an improvement in UV behavior of the vacuum energy and the cosmological constant problem has to be revised
We require the action functional Sκ to be κ-Poincareinvariant which is a reasonable assumption regarding the important role played by the Poincaresymmetries in standard quantum field theory (QFT) together with the fact that κ-Poincarealgebra can be viewed as describing the quantum symmetries of the κ-Minkowski space-time [29,30,31]
Summary
The history of the cosmological constant starts with Albert Einstein, where in his first paper on the application of general relativity (GR) to cosmology [1], he aimed to construct a static universe with a finite average density of matter. The one-loop contribution to the 4-point function is even found UV finite [47] for some models whose kinetic operators are related to the square of the Dirac operator involved in the construction of an equivariant spectral triple [48] aiming to encode the geometry of κ-Minkowski space. This is partly due to the large spatial momentum damping in the propagator which decays as 1=p4. Technical details on construction of the ⋆-product and appropriate Hilbert product are given in the Appendixes
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