We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies and field dependence in vector generators. construct a charge bracket that generalizes one introduced by Barnich Troessaert includes contributions from Lagrangian its anomaly. This is uniquely determined choice of representative theory. then extend notion corner symmetry algebra to include surface translat...

We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satis...

When utilizing a cluster decomposible relativistic scattering formalism, it is most convenient that the covariant field equations take on a linear form with respect to the energy and momentum dispersion on the fields in the manner given by the Dirac form for spin 1 2 systems. A general spinor formulation is given for arbitrary spins by minimally extending the Lorentz algebra to include operator...

In this work the electromagnetic radius and the polarizability of the mesons are obtained by use of the effective Lagrangians constructed on the one hand with taking into account of general principles of the relativistic quantum field theory and on the other hand with taking into account of the compound relativistic model meson representation. Also using a relativistic constituent quark model b...

We developed the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the N-particle system for two-particles plus N-2 intermediate bosons. We derived an infinite set of coupled hierarchy equations or iterated resolvent from which the Green...

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry tr...

For discrete Hecke pairs (G,H), we introduce a notion of covariant representation which reduces in the case where H is normal to the usual definition of covariance for the action of G/H on c0(G/H) by right translation; in many cases where G is a semidirect product, it can also be expressed in terms of covariance for a semigroup action. We use this covariance to characterise the representations ...

It is shown how to associate to a highest weight Λ of the Lie superalgebra gl(m|n) a composite partition ν; μ with composite Young diagram F (ν; μ). The corresponding supersymmetric Schur function sν;μ(x/y) is defined. However, it is known that this S-function does not always coincide with the character of the irreducible representation VΛ with highest weight Λ. Only for covariant, contravarian...

We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a noncocommutative Hopf algebra structure, simple realizations and quantum tensor operators. The deformation of the group is achieved by using the adjoint representation. The elements of quantum matrix form a Hopf algebra. Furthermore, we construct a differential calcu...

We develop the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the N-particle system for two-particles plus N-2 intermediate bosons. We derive an infinite set of coupled hierarchy equations or iterated resolvents from which the Green's...