Complex fermion mass term, regularization and CP violation

It is well known that the CP violating theta term of QCD can be converted to a phase in the quark mass term. However, a theory with a complex mass term for quarks can be regularized so as not to violate CP, for example through a zeta function. The contradiction is resolved through the recognition of a dependence on the regularization or measure. The appropriate choice of regularization is discussed and implications for the strong CP problem are pointed out.Comment: REVTeX, 4 page

Multiplicative anomaly and zeta factorization

Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the multiplicative anomaly issue is discussed. We look primordially into the zeta functions instead of the determinants themselves, as was done in previous work. That provides a supplementary view, regarding the appearance of the multiplicative anomaly. Finally, we briefly discuss determinants of zeta functions that are not in the pseudodifferential operator framework.Comment: 20 pages, AIP styl

On the issue of imposing boundary conditions on quantum fields

An interesting example of the deep interrelation between Physics and Mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields. This procedure has recently been re-examined with care. Comments on that and previous analysis are here provided, together with considerations on the results of the purely mathematical zeta-function method, in an attempt at clarifying the issue. Hadamard regularization is invoked in order to fill the gap between the infinities appearing in the QFT renormalized results and the finite values obtained in the literature with other procedures.Comment: 13 pages, no figure

The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell

We calculate the zero point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta function type. We use zeta functional regularization and express the regularized ground state energy in terms of the Jost function of the related scattering problem. Then we find the corresponding heat kernel coefficients and perform the renormalization, imposing the normalization condition that the ground state energy vanishes when the mass of the quantum field becomes large. Finally the ground state energy is calculated numerically. Corresponding plots are given for different values of the strength of the background potential, for both attractive and repulsive potentials.Comment: 15 pages, 5 figure

Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect

Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two-- and higher--dimensional surfaces (being able to mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero depths). What we have considered is the {\it additional} contribution to the cc coming from the non-trivial topology of space or from specific boundary conditions imposed on braneworld models (kind of cosmological Casimir effects). Assuming someone will be able to prove (some day) that the ground value of the cc is zero, as many had suspected until very recently, we will then be left with this incremental value coming from the topology or BCs. We show that this value can have the correct order of magnitude in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.Comment: 9 pages, 1 figure, Talk given at the Seventh International Workshop Quantum Field Theory under the Influence of External Conditions, QFEXT'05, Barcelona, September 5-9, 200

Topology, Mass and Casimir energy

The vacuum expectation value of the stress energy tensor for a massive scalar field with arbitrary coupling in flat spaces with non-trivial topology is discussed. We calculate the Casimir energy in these spaces employing the recently proposed {\it optical approach} based on closed classical paths. The evaluation of the Casimir energy consists in an expansion in terms of the lengths of these paths. We will show how different paths with corresponding weight factors contribute in the calculation. The optical approach is also used to find the mass and temperature dependence of the Casimir energy in a cavity and it is shown that the massive fields cannot be neglected in high and low temperature regimes. The same approach is applied to twisted as well as spinor fields and the results are compared with those in the literature.Comment: 18 pages, 1 figure, RevTex format, Typos corrected and references adde

Antisymmetric tensor fields on spheres: functional determinants and non--local counterterms

The Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields is considered. Explicit expressions for the spectrum are derived in a quite direct way, confirming previous results. Associated functional determinants and the heat kernel expansion are evaluated. Using this method, new non--local counterterms in the quantum effective action are obtained, which can be expressed in terms of Betti numbers.Comment: LaTeX, 22 pages, no figure

Zeta-Function Regularization is Uniquely Defined and Well

Hawking's zeta function regularization procedure is shown to be rigorously and uniquely defined, thus putting and end to the spreading lore about different difficulties associated with it. Basic misconceptions, misunderstandings and errors which keep appearing in important scientific journals when dealing with this beautiful regularization method ---and other analytical procedures--- are clarified and corrected.Comment: 7 pages, LaTeX fil