3,642 research outputs found
First quantized electron and photon model of QED and radiative processes
In this study we combine the classical models of the massive and massless
spinning particles, derive the current-current interaction Lagrangian of the
particles from the gauge transformations of the classical spinors, and discuss
radiative processes in electrodynamics by using the solutions of the Dirac
equation and the quantum wave equations of the photon. The longitudinal
polarized photon states give a new idea about the vacuum concept in
electrodynamics.Comment: LaTeX file, 20 pages, 7 figures. to appear in Canadian Journal of
Physic
The exponential map for the unitary group SU(2,2)
In this article we extend our previous results for the orthogonal group,
, to its homomorphic group . Here we present a closed, finite
formula for the exponential of a traceless matrix, which can be
viewed as the generator (Lie algebra elements) of the group. We apply
this result to the group, which Lie algebra can be represented by the
Dirac matrices, and discuss how the exponential map for can be
written by means of the Dirac matrices.Comment: 10 page
Field theory of the spinning electron: Internal motions
We present here a field theory of the spinning electron, by writing down a
new equation for the 4-velocity field v^mu (different from that of Dirac
theory), which allows a classically intelligible description of the electron.
Moreover, we make explicit the noticeable kinematical properties of such
velocity field (which also result different from the ordinary ones). At last,
we analyze the internal zitterbewegung (zbw) motions, for both time-like and
light-like speeds. We adopt in this paper the ordinary tensorial language. Our
starting point is the Barut-Zanghi classical theory for the relativistic
electron, which related spin with zbw. This paper is dedicated to the memory of
Asim O. Barut, who so much contributed to clarifying very many fundamental
issues of physics, and whose work constitutes a starting point of these
articles.Comment: standard LaTeX fil
Adaptive robust variable selection
Heavy-tailed high-dimensional data are commonly encountered in various
scientific fields and pose great challenges to modern statistical analysis. A
natural procedure to address this problem is to use penalized quantile
regression with weighted -penalty, called weighted robust Lasso
(WR-Lasso), in which weights are introduced to ameliorate the bias problem
induced by the -penalty. In the ultra-high dimensional setting, where the
dimensionality can grow exponentially with the sample size, we investigate the
model selection oracle property and establish the asymptotic normality of the
WR-Lasso. We show that only mild conditions on the model error distribution are
needed. Our theoretical results also reveal that adaptive choice of the weight
vector is essential for the WR-Lasso to enjoy these nice asymptotic properties.
To make the WR-Lasso practically feasible, we propose a two-step procedure,
called adaptive robust Lasso (AR-Lasso), in which the weight vector in the
second step is constructed based on the -penalized quantile regression
estimate from the first step. This two-step procedure is justified
theoretically to possess the oracle property and the asymptotic normality.
Numerical studies demonstrate the favorable finite-sample performance of the
AR-Lasso.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1191 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Solution of Massless Spin One Wave Equation in Robertson-Walker Space-time
We generalize the quantum spinor wave equation for photon into the curved
space-time and discuss the solutions of this equation in Robertson-Walker
space-time and compare them with the solution of the Maxwell equations in the
same space-time.Comment: 16 Pages, Latex, no figures, An expanded version of paper published
in International Journal of Modern Physics A, 17 (2002) 113
Conformal covariance of massless free nets
In the present paper we review in a fibre bundle context the covariant and
massless canonical representations of the Poincare' group as well as certain
unitary representations of the conformal group (in 4 dimensions). We give a
simplified proof of the well-known fact that massless canonical representations
with discrete helicity extend to unitary and irreducible representations of the
conformal group mentioned before. Further we give a simple new proof that
massless free nets for any helicity value are covariant under the conformal
group. Free nets are the result of a direct (i.e. independent of any explicit
use of quantum fields) and natural way of constructing nets of abstract
C*-algebras indexed by open and bounded regions in Minkowski space that satisfy
standard axioms of local quantum physics. We also give a group theoretical
interpretation of the embedding {\got I} that completely characterizes the
free net: it reduces the (algebraically) reducible covariant representation in
terms of the unitary canonical ones. Finally, as a consequence of the conformal
covariance we also mention for these models some of the expected algebraic
properties that are a direct consequence of the conformal covariance (essential
duality, PCT--symmetry etc.).Comment: 31 pages, Latex2
Wess-Zumino-Witten Model for Galilean Conformal Algebra
In this note, we construct a Wess-Zumino-Witten model based on the Galilean
conformal algebra in 2-spacetime dimensions, which is a nonrelativistic
analogue of the relativistic conformal algebra. We obtain exact background
corresponding to \sigma-models in six dimensions (the dimension of the group
manifold) and a central charge c=6. We carry out a Sugawara type construction
to verify the conformal invariance of the model. Further, we discuss the
feasibility of the background obtained as a physical spacetime metric.Comment: Latex file, 11 pages, v2: minor changes, references adde
The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of modern renormalization theory
This paper uses elementary techniques drawn from renormalization theory to
derive the Lorentz-Dirac equation for the relativistic classical electron from
the Maxwell-Lorentz equations for a classical charged particle coupled to the
electromagnetic field. I show that the resulting effective theory, valid for
electron motions that change over distances large compared to the classical
electron radius, reduces naturally to the Landau-Lifshitz equation. No
familiarity with renormalization or quantum field theory is assumed
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