1,229 research outputs found
Tetrahedron Reflection Equation
Reflection equation for the scattering of lines moving in half-plane is
obtained. The corresponding geometric picture is related with configurations of
half-planes touching the boundary plane in 2+1 dimensions. This equation can be
obtained as an additional to the tetrahedron equation consistency condition for
a modified Zamolodchikov algebra.Comment: 10 pages, LaTe
Two-spinor description of massive particles and relativistic spin projection operators
On the basis of the Wigner unitary representations of the covering group
ISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions of
free massive particles with arbitrary spin. The wave functions automatically
satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor
formalism we construct spin-vectors of polarizations and obtain conditions that
fix the corresponding relativistic spin projection operators (Behrends-Fronsdal
projection operators). With the help of these conditions we find explicit
expressions for relativistic spin projection operators for integer spins
(Behrends-Fronsdal projection operators) and then find relativistic spin
projection operators for half integer spins. These projection operators
determine the nominators in the propagators of fields of relativistic
particles. We deduce generalizations of the Behrends-Fronsdal projection
operators for arbitrary space-time dimensions D>2.Comment: 34 page
Yang-Mills and Born-Infeld actions on finite group spaces
Discretized nonabelian gauge theories living on finite group spaces G are
defined by means of a geometric action \int Tr F\wedge *F . This technique is
extended to obtain a discrete version of the Born-Infeld action.Comment: Talk presented at GROUP24, Paris, July 2002. LaTeX, 4 pages, IOP
style
Baxterized Solutions of Reflection Equation and Integrable Chain Models
Non-polynomial Baxterized solutions of reflection equations associated with
affine Hecke and affine Birman-Murakami-Wenzl algebras are found. Relations to
integrable spin chain models with nontrivial boundary conditions are discussed.Comment: LaTeX, 18 pages, typos fixed, journal-ref adde
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