We associate a boundary $\mathcal B_{\pi ,u}$ to each covariant representation $(\pi ,u,H)$ of $C^*$-dynamical system $(G,A,\alpha )$ and study the action $G$ on its amenability properties. relate rigidity properties traces associated crossed product $C^*$-algebra faithfulness group this boundary.

Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce automatically the transformation rules of composite mesons for general symmetry operations from those of constituent (exciton) quarks. Applying this we investigate...

The covariant level-classification scheme of hadrons with Ũ(12)SF ⊗ O(3, 1)L symmetry has been proposed, 1) which gives a covariant quark representation for composite hadrons with definite Lorentz and chiral transformation properties. This covariant classification scheme unifies two seemingly contradictory viewpoints, nonrelativistic and extremely relativistic ones, of quark-model classificatio...

Abstract: We use an algebraic approach based on representations of de Sitter group to construct covariant quantum fields in arbitrary dimensions. We study the complementary and the discrete series which correspond to light and massless fields and which lead new feature with respect to the massive principal series we previously studied (hep-th/0606119). When considering the complementary series,...

In this brief article we discuss spin polarization operators and spin polarization states of 2 + 1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2 + 1 field theory. Another advantage of this representation...

A covariant scalar representation of iosp(d, 2/2) is constructed and analysed in comparison with existing methods for the quantization of the scalar relativistic particle. It is found that, with appropriately defined wavefunctions, this iosp(d, 2/2) produced representation can be identified with the state space arising from the canonical BFV-BRST quantization of the modular invariant, unoriente...

It is often inevitable to introduce an indefinite-metric space in quantum field theory, for example, which is explained for the sake of the manifestly covariant quantization of the electromagnetic field. We show two more evident mathematical reasons why such indefinite metric appears. The first idea is the replacement of involution on an algebra. For an algebra A with an involution † such that ...

We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is furnished and the commutative localizations are singled out. As a consequence, we also get a vector sequence characterization of the covariant phase observables.

A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in [2]. In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial differential operators as well as its natural (Fock type) representation. We shall also define co-universal vector fields and covariant derivatives.