775 research outputs found
Interacting fermions and domain wall defects in 2+1 dimensions
We consider a Dirac field in 2+1 dimensions with a domain wall like defect in
its mass, minimally coupled to a dynamical Abelian vector field. The mass of
the fermionic field is assumed to have just one linear domain wall, which is
externally fixed and unaffected by the dynamics. We show that, under some
general conditions on the parameters, the localized zero modes predicted by the
Callan and Harvey mechanism are stable under the electromagnetic interaction of
the fermions
Making Sense of Singular Gauge Transformations in 1+1 and 2+1 Fermion Models
We study the problem of decoupling fermion fields in 1+1 and 2+1 dimensions,
in interaction with a gauge field, by performing local transformations of the
fermions in the functional integral. This could always be done if singular
(large) gauge transformations were allowed, since any gauge field configuration
may be represented as a singular pure gauge field. However, the effect of a
singular gauge transformation of the fermions is equivalent to the one of a
regular transformation with a non-trivial action on the spinorial indices. For
example, in the two dimensional case, singular gauge transformations lead
naturally to chiral transformations, and hence to the usual decoupling
mechanism based on Fujikawa Jacobians. In 2+1 dimensions, using the same
procedure, different transformations emerge, which also give rise to Fujikawa
Jacobians. We apply this idea to obtain the v.e.v of the fermionic current in a
background field, in terms of the Jacobian for an infinitesimal decoupling
transformation, finding the parity violating result.Comment: 14 pages, Late
Neumann Casimir effect: a singular boundary-interaction approach
Dirichlet boundary conditions on a surface can be imposed on a scalar field,
by coupling it quadratically to a -like potential, the strength of
which tends to infinity. Neumann conditions, on the other hand, require the
introduction of an even more singular term, which renders the reflection and
transmission coefficients ill-defined because of UV divergences. We present a
possible procedure to tame those divergences, by introducing a minimum length
scale, related to the non-zero `width' of a {\em nonlocal} term. We then use
this setup to reach (either exact or imperfect) Neumann conditions, by taking
the appropriate limits. After defining meaningful reflection coefficients, we
calculate the Casimir energies for flat parallel mirrors, presenting also the
extension of the procedure to the case of arbitrary surfaces. Finally, we
discuss briefly how to generalize the worldline approach to the nonlocal case,
what is potentially useful in order to compute Casimir energies in theories
containing nonlocal potentials; in particular, those which we use to reproduce
Neumann boundary conditions.Comment: New title and reference adde
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