865 research outputs found

### The exponential map for the unitary group SU(2,2)

In this article we extend our previous results for the orthogonal group,
$SO(2,4)$, to its homomorphic group $SU(2,2)$. Here we present a closed, finite
formula for the exponential of a $4\times 4$ traceless matrix, which can be
viewed as the generator (Lie algebra elements) of the $SL(4,C)$ group. We apply
this result to the $SU(2,2)$ group, which Lie algebra can be represented by the
Dirac matrices, and discuss how the exponential map for $SU(2,2)$ can be
written by means of the Dirac matrices.Comment: 10 page

### 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 Exponential Map for the Conformal Group 0(2,4)

We present a general method to obtain a closed, finite formula for the
exponential map from the Lie algebra to the Lie group, for the defining
representation of the orthogonal groups. Our method is based on the
Hamilton-Cayley theorem and some special properties of the generators of the
orthogonal group, and is also independent of the metric. We present an explicit
formula for the exponential of generators of the $SO_+(p,q)$ groups, with $p+q
= 6$, in particular we are dealing with the conformal group $SO_+(2,4)$, which
is homomorphic to the $SU(2,2)$ group. This result is needed in the
generalization of U(1) gauge transformations to spin gauge transformations,
where the exponential plays an essential role. We also present some new
expressions for the coefficients of the secular equation of a matrix.Comment: 16pages,plain-TeX,(corrected TeX

### 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

### Variational problem for the Frenkel and the Bargmann-Michel-Telegdi (BMT) equations

We propose Lagrangian formulation for the particle with value of spin fixed
within the classical theory. The Lagrangian turns out to be invariant under
non-abelian group of local symmetries. As the gauge-invariant variables for
description of spin we can take either the Frenkel tensor or the BMT vector.
Fixation of spin within the classical theory implies $O(\hbar)$-corrections to
the corresponding equations of motion.Comment: 04 pages, notations changed, misprints correcte

### Boson mass spectrum in $SU(4)_L\otimes U(1)_Y$ model with exotic electric charges

The boson mass spectrum of the electro-weak \textbf{$SU(4)_{L}\otimes
U(1)_{Y}$} model with exotic electric charges is investigated by using the
algebraical approach supplied by the method of exactly solving gauge models
with high symmetries. Our approach predicts for the boson sector a
one-parameter mass scale to be tuned in order to match the data obtained at
LHC, LEP, CDF.Comment: 12 pages, 1 Table with numerical estimates and 1 Figure added,
mistaken results correcte

### Variational principle for the Wheeler-Feynman electrodynamics

We adapt the formally-defined Fokker action into a variational principle for
the electromagnetic two-body problem. We introduce properly defined boundary
conditions to construct a Poincare-invariant-action-functional of a finite
orbital segment into the reals. The boundary conditions for the variational
principle are an endpoint along each trajectory plus the respective segment of
trajectory for the other particle inside the lightcone of each endpoint. We
show that the conditions for an extremum of our functional are the
mixed-type-neutral-equations with implicit state-dependent-delay of the
electromagnetic-two-body problem. We put the functional on a natural Banach
space and show that the functional is Frechet-differentiable. We develop a
method to calculate the second variation for C2 orbital perturbations in
general and in particular about circular orbits of large enough radii. We prove
that our functional has a local minimum at circular orbits of large enough
radii, at variance with the limiting Kepler action that has a minimum at
circular orbits of arbitrary radii. Our results suggest a bifurcation at some
radius below which the circular orbits become saddle-point extrema. We give a
precise definition for the distributional-like integrals of the Fokker action
and discuss a generalization to a Sobolev space of trajectories where the
equations of motion are satisfied almost everywhere. Last, we discuss the
existence of solutions for the state-dependent delay equations with slightly
perturbated arcs of circle as the boundary conditions and the possibility of
nontrivial solenoidal orbits

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