Quantum Poincare Algebra Research Articles

An Axiomatic System Suggested by Quantum Computation

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincare algebra. Such a system allows to establish a completeness theorem.

Quantum Poincare Algebra and Ultra High Energy Cosmic Rays(Quantum Field Theories: Fundamental Problems and Applications)

Quantum Poincare Algebra and Ultra High Energy Cosmic Rays(Quantum Field Theories: Fundamental Problems and Applications)

Representations of quantum bicrossproduct algebras

We present a method to construct induced representations of quantum algebras having the structure of bicrossproduct. We apply this procedure to some quantum kinematical algebras in (1+1)--dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum kappa Galilei algebra.

Non-standard quantumso(3, 2) and its contractions

A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the (2 + 1)-dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf structures for the conformal algebras of the 2 + 1 Galilean and Carroll spacetimes. Relations between the latter and the null-plane quantum Poincare algebra are studied.

New quantum deformations ofD=4 conformal algebra

We consider new class of classicalr-matrices forD=4 conformal Lie algebra. These r-matrices do satisfy the classical Yang-Baxter equation and as two-tensors belong to the tensor product of Borel subalgebras. In such a way we generalize the lowest order of known nonstandard quantum deformation ofsl(2) to the Lie algebrasl(4)≅so(6). As an exercise we interpret nonstandard deformation ofsl(2) as describing quantumD=1 conformal algebra with fundamental mass parameter. Further we describeD=4 conformal bialgebras with deformation parameters equal to the inverse of fundamental masses. It appears that forD=4 the deformation of the Poincare algebra sector coincides with “null plane” quantum Poincare algebra.

Quantum poincaré algebra with standard real structure

A new real quantum Poincare algebra which is a standard ∗-Hopf algebra is obtained by the construction of Uq (O(3,2)) (q real). The deformation parameter K is mass-like, and the classical Poincare algebra is obtained in the limit K → ∞. For our K-Poincare algebra both Casimirs are given.