3 research outputs found
Supersymmetric Field-Theoretic Models on a Supermanifold
We propose the extension of some structural aspects that have successfully
been applied in the development of the theory of quantum fields propagating on
a general spacetime manifold so as to include superfield models on a
supermanifold. We only deal with the limited class of supermanifolds which
admit the existence of a smooth body manifold structure. Our considerations are
based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In
particular, we show that the class of supermanifolds constructed by
Bonora-Pasti-Tonin satisfies the criterions which guarantee that a
supermanifold admits a Hausdorff body manifold. This construction is the
closest to the physicist's intuitive view of superspace as a manifold with some
anticommuting coordinates, where the odd sector is topologically trivial. The
paper also contains a new construction of superdistributions and useful results
on the wavefront set of such objects. Moreover, a generalization of the
spectral condition is formulated using the notion of the wavefront set of
superdistributions, which is equivalent to the requirement that all of the
component fields satisfy, on the body manifold, a microlocal spectral condition
proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy
Quantum field theory in static external potentials and Hadamard states
We prove that the ground state for the Dirac equation on Minkowski space in
static, smooth external potentials satisfies the Hadamard condition. We show
that it follows from a condition on the support of the Fourier transform of the
corresponding positive frequency solution. Using a Krein space formalism, we
establish an analogous result in the Klein-Gordon case for a wide class of
smooth potentials. Finally, we investigate overcritical potentials, i.e. which
admit no ground states. It turns out, that numerous Hadamard states can be
constructed by mimicking the construction of ground states, but this leads to a
naturally distinguished one only under more restrictive assumptions on the
potentials.Comment: 30 pages; v2 revised, accepted for publication in Annales Henri
Poincar