182 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
Fermionic determinant as an overlap between bosonic vacua
We find a representation for the determinant of a Dirac operator in an even
number of Euclidean dimensions as an overlap between two different
vacua, each one corresponding to a bosonic theory with a quadratic action in dimensions, with identical kinetic terms, but differing in their mass
terms. This resembles the overlap representation of a fermionic determinant
(although bosonic fields are used here). This representation may find
applications to lattice field theory, as an alternative to other bosonized
representations for Dirac determinants already proposed.Comment: 9 pages, Latex; added reference, minor comments adde
Non local parity transformations and anomalies
We present an alternative derivation of the parity anomaly for a massless
Dirac field in 2+1 dimensions coupled to a gauge field. The anomaly functional,
a Chern-Simons action for the gauge field, is obtained from the non-trivial
Jacobian corresponding to a non local symmetry of the Pauli-Villars regularized
action. That Jacobian is well-defined, finite, and yields the standard
Chern-Simons term when the cutoff tends to infinity.Comment: 10 pages, Latex fil
New tests and applications of the worldline path integral in the first order formalism
We present different non-perturbative calculations within the context of
Migdal's representation for the propagator and effective action of quantum
particles. We first calculate the exact propagators and effective actions for
Dirac, scalar and Proca fields in the presence of constant electromagnetic
fields, for an even-dimensional spacetime. Then we derive the propagator for a
charged scalar field in a spacelike vortex (i.e., instanton) background, in a
long-distance expansion, and the exact propagator for a massless Dirac field in
1+1 dimensions in an arbitrary background. Finally, we present an
interpretation of the chiral anomaly in the present context, finding a
condition that the paths must fulfil in order to have a non-vanishing anomaly.Comment: 26 page
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