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⊗U(1)YSU(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