5,114 research outputs found
Effective action for the Yukawa model in curved spacetime
We consider the one-loop renormalization of a real scalar field interacting
with a Dirac spinor field in curved spacetime. A general Yukawa interaction is
considered which includes both a scalar and a pseudoscalar coupling. The scalar
field is assumed to be non-minimally coupled to the gravitational field and to
have a general quartic self-interaction potential. All of the one-loop
renormalization group functions are evaluated and in the special case where
there is no mass scale present in the classical theory (apart from the fields)
we evaluate the one-loop effective action up to and including order in
the curvature. In the case where the fermion is massive we include a chiral
term in and we show that although the term can be removed
by a redefinition of the spinor field an anomaly in the effective action arises
that is related to the familiar axial current anomaly.Comment: 28 page
Renormalization and vacuum energy for an interacting scalar field in a \delta-function potential
We study a self-interacting scalar field theory in the presence of a
\delta-function background potential. The role of surface interactions in
obtaining a renormalizable theory is stressed and demonstrated by a two-loop
calculation. The necessary counterterms are evaluated by adopting dimensional
regularization and the background field method. We also calculate the effective
potential for a complex scalar field in a non-simply connected spacetime in the
presence of a \delta-function potential. The effective potential is evaluated
as a function of an arbitrary phase factor associated with the choice of
boundary conditions in the non-simply connected spacetime. We obtain asymptotic
expansions of the results for both large and small \delta-function strengths,
and stress how the non-analytic nature of the small strength result vitiates
any analysis based on standard weak field perturbation theory.Comment: To appear in the special issue of J. Phys. A to honour J. S. Dowke
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