852 research outputs found
Generalized solutions and distributional shadows for Dirac equations
We discuss the application of recent results on generalized solutions to the
Cauchy problem for hyperbolic systems to Dirac equations with external fields.
In further analysis we focus on the question of existence of associated
distributional limits and derive their explicit form in case of free Dirac
fields with regularizations of initial values corresponding to point-like
probability densities
Temperature in Fermion Systems and the Chiral Fermion Determinant
We give an interpretation to the issue of the chiral determinant in the
heat-kernel approach. The extra dimension (5-th dimension) is interpreted as
(inverse) temperature. The 1+4 dim Dirac equation is naturally derived by the
Wick rotation for the temperature. In order to define a ``good'' temperature,
we choose those solutions of the Dirac equation which propagate in a fixed
direction in the extra coordinate. This choice fixes the regularization of the
fermion determinant. The 1+4 dimensional Dirac mass () is naturally
introduced and the relation: 4 dim electron momentum
ultraviolet cut-off, naturally appears. The chiral anomaly is explicitly
derived for the 2 dim Abelian model. Typically two different regularizations
appear depending on the choice of propagators. One corresponds to the chiral
theory, the other to the non-chiral (hermitian) theory.Comment: 24 pages, some figures, to be published in Phys.Rev.
Local spinfoam expansion in loop quantum cosmology
The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and
Bianchi I models defined by loop quantum cosmology have recently been
translated into a spinfoam-like formalism. The construction is facilitated by
the presence of a massless scalar field which is used as an internal clock. The
implicit integration over the matter variable leads to a nonlocal spinfoam
amplitude. In this paper we consider a vacuum Bianchi I universe and show that
by choosing an appropriate regulator a spinfoam expansion can be obtained
without selecting a clock variable and that the resulting spinfoam amplitude is
local.Comment: 12 page
Distributional approach to point interactions in one-dimensional quantum mechanics
We consider the one-dimensional quantum mechanical problem of defining
interactions concentrated at a single point in the framework of the theory of
distributions. The often ill-defined product which describes the interaction
term in the Schr\"odinger and Dirac equations is replaced by a well-defined
distribution satisfying some simple mathematical conditions and, in addition,
the physical requirement of probability current conservation is imposed. A
four-parameter family of interactions thus emerges as the most general point
interaction both in the non-relativistic and in the relativistic theories (in
agreement with results obtained by self-adjoint extensions). Since the
interaction is given explicitly, the distributional method allows one to carry
out symmetry investigations in a simple way, and it proves to be useful to
clarify some ambiguities related to the so-called interaction.Comment: Open Access link:
http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/abstrac
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