We classify all massive irreducible representations of super Poincaré in D = 10. New Casimir operators of super Poincaré are presented whose eigenvalues completely specify the representation. It is shown that a scalar superfield contains three irreducible representations of massive supersymmetry and we find the corresponding superprojectors. We apply these new tools to the quantization of the m...

The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as the arising of gauge theory. Furthermore, a manifestly causal and covariant formulation of quantum field theory is presented which surpasses the usual Hamilton...

A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify the Glashow-Weinberg-Salam model. Since SU (3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U (3) to obtain all the correct quantum numbers. A surplus gauge scalar...

We show that, up to terms of order κ−5, the κ-deformed Poincaré algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders. In the context of κ-deformed quantum field theory, we argue that this structure, assuming it exists to all orders, ensures that states of any number of identical particles, in any ...

We reformulate free equations of motion for massive spin 0 and spin 1/2 matter fields in 2+1 dimensional anti-de Sitter space in the form of some covariant constantness conditions. The infinite-dimensional representation of the anti-de Sitter algebra underlying this formulation is shown to admit a natural realization in terms of the algebra of deformed oscillators with a deformation parameter r...

We address the deformation quantization of generally parametrized systems displaying a natural time variable. The purpose of this exercise is twofold: first, to illustrate through a pedagogical example the potential of quantum phase space methods in the context of constrained systems and particularly of generally covariant systems. Second, to show that a causal representation for quantum phase ...

We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time dependent coordinate transformations. This result considerably enlarges the set of possible phase space representations of quantum mechanics and makes it po...

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on Rn if the ...

We define the Zappa-Szép product of a Fell bundle by groupoid, which turns out to be over underlying groupoids. Under certain assumptions, every groupoids arises in this manner. then study representation associated with and show its relation covariant representations. Finally, we universal C⁎-algebra, C⁎-blend, generalizing an earlier result about groupoid C⁎-algebras. In case discrete groups, ...

The generalized covariant derivative, that uses both scalar and vector bosons, is defined. It is shown how a grand unified theory of the Standard Model can be constructed using a generalized Yang-Mills theory. 1 The generalized covariant derivative Last year the authors developed a generalized Yang-Mills theory (GYMT) that used a covariant derivative that included not only vector bosons but sca...