13,367 research outputs found
A Conducting surface in Lee-Wick electrodynamics
The Lee-Wick electrodynamics in the vicinity of a conducting plate is
investigated. The propagator for the gauge field is calculated and the
interaction between the plate and a point-like electric charge is computed. The
boundary condition imposed on the vector field is taken to be the one that
vanishes, on the plate, the normal component of the dual field strength to the
plate. It is shown that the image method is not valid in Lee-Wick
electrodynamics.Comment: 11 pages, 1 figur
Transition amplitude, partition function and the role of physical degrees of freedom in gauge theories
This work explores the quantum dynamics of the interaction between scalar
(matter) and vectorial (intermediate) particles and studies their thermodynamic
equilibrium in the grand-canonical ensemble. The aim of the article is to
clarify the connection between the physical degrees of freedom of a theory in
both the quantization process and the description of the thermodynamic
equilibrium, in which we see an intimate connection between physical degrees of
freedom, Gibbs free energy and the equipartition theorem. We have split the
work into two sections. First, we analyze the quantum interaction in the
context of the generalized scalar Duffin-Kemmer-Petiau quantum electrodynamics
(GSDKP) by using the functional formalism. We build the Hamiltonian structure
following the Dirac methodology, apply the Faddeev-Senjanovic procedure to
obtain the transition amplitude in the generalized Coulomb gauge and, finally,
use the Faddeev-Popov-DeWitt method to write the amplitude in covariant form in
the no-mixing gauge. Subsequently, we exclusively use the Matsubara-Fradkin
(MF) formalism in order to describe fields in thermodynamical equilibrium. The
corresponding equations in thermodynamic equilibrium for the scalar, vectorial
and ghost sectors are explicitly constructed from which the extraction of the
partition function is straightforward. It is in the construction of the
vectorial sector that the emergence and importance of the ghost fields are
revealed: they eliminate the extra non-physical degrees of freedom of the
vectorial sector thus maintaining the physical degrees of freedom
Piecewise contractions defined by iterated function systems
Let be Lipschitz contractions. Let
, and . We prove that for Lebesgue almost every
satisfying , the piecewise
contraction defined by is
asymptotically periodic. More precisely, has at least one and at most
periodic orbits and the -limit set is a periodic orbit of
for every .Comment: 16 pages, two figure
Asymptotically periodic piecewise contractions of the interval
We consider the iterates of a generic injective piecewise contraction of the
interval defined by a finite family of contractions. Let , , be -diffeomorphisms with whose images are
pairwise disjoint. Let and let be a
partition of the interval into subintervals having interior
, where and . Let be the
map given by if , for . Among other
results we prove that for Lebesgue almost every , the
piecewise contraction is asymptotically periodic.Comment: 8 page
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