arXiv subjects
Publications and source records attributed to M. Woronowicz.
The Lie algebras expansion method is used to show that the Maxwell (super)algebras and some of their generalizations can be derived in a simple way as particular expansions of o(3,2) and osp(N|4).
We introduce new $κ$-star product describing the multiplication of quantized $κ$-deformed free fields. The $κ$-deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the $κ$-deformation of field oscillators algebra - we relate these two deformations. We demonstrate that for suitable choice of $κ$-deformed field oscillators algebra the $κ$-deformed version of microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the $κ$-deformed mass shell. We show by constructing the $κ$-deformed Fock space that the use of $κ$-deformed oscillator algebra permits to preserve the bosonic statistics of n-particle states. The proposed star product is extended to the product of $n$ fields, which for $n=4$ defines the interaction vertex in perturbative description of noncommutative quantum $λϕ^4$ field theory. It appears that the classical fourmomentum conservation law is satisfied at the interaction vertices.
We consider $κ$-deformed relativistic symmetries described algebraically by modified Majid-Ruegg bicrossproduct basis and investigate the quantization of field oscillators for the $κ$-deformed free scalar fields on $κ$-Minkowski space. By modification of standard multiplication rule, we postulate the $κ$-deformed algebra of bosonic creation and annihilation operators. Our algebra permits to define the n-particle states with classical addition law for the fourmomenta in a way which is not in contradiction with the nonsymmetric quantum fourmomentum coproduct. We introduce $κ$-deformed Fock space generated by our $κ$-deformed oscillators which satisfy the standard algebraic relations with modified $κ$-multiplication rule. We show that such a $κ$-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of $κ$-deformed algebra of oscillators in field-theoretic noncommutative framework.
We describe the twisted space-time symmetries which imply the quantum Poincaré covariance of noncommutative Minkowski spaces, with constant, Lie algebraic and quadratic commutators. Further we present the relativistic and nonrelativistic particle models invariant respectively under twisted relativistic and twisted Galilean symmetries.
We consider two new classes of twisted D=4 quantum Poincaré symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincaré algebras which provide the examples of Lie-algebraic noncommutativity of the translations. The corresponding associative star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the twist deformations of Poincaré symmetries generated by the twist with its carrier in Lorentz algebra. We describe corresponding deformed Poincaré group which provides the quadratic deformations of translation sector and define the quadratically deformed Minkowski space-time algebra.