No abstract

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 various nonrelativistic contractions of two classes of twisted Poincare algebra: canonical one (θ µν -deformation) and the one leading to Lie-algebraic models of noncommutative space-times. The cases of contraction-independent and contraction-dependent twist parameters are considered. We obtain five models of noncommutative nonrelativistic space-times, in particular, two new Lie-algebraic nonrelativistic deformations of space-time, respectively, with quantum time/classical space and with quantum space/classical time.

Doubly Special Relativity (DSR) is a class of theories of relativistic motion with two observer-independent scales. We investigate the velocity of particles in DSR, defining velocity as the Poisson bracket of position with the appropriate hamiltonian, taking care of the nontrivial structure of the DSR phase space. We find the general expression for four-velocity, and we show further that the three-velocity of massless particles equals 1 for all DSR theories. The relation between the boost parameter and velocity is also clarified.

The aim of this paper is to study in D = 4 the general framework providing various κ-deformations of field oscillators and consider the commutator function of the corresponding κ-deformed free fields. In order to obtain free κ-deformed quantum fields (with c-number commutators) we proposed earlier a particular model of a κ-deformed oscillator algebra (Daszkiewicz M, Lukierski J and Woronowicz M 2008 Mod. Phys. Lett. A 23 9 (arXiv:hep-th/0703200)) and the modification of κ-star product (Daszkiewicz M, Lukierski J, Woronowicz M 2008 Phys. Rev. D 77 105007 (arXiv:0708.1561 [hep-th])), implementing in the product of two quantum fields the change of standard κ-deformed mass-shell conditions. We recall here that other different models of κ-deformed oscillators recently introduced in Arzano M and Marciano A (2007 Phys. Rev. D 76 125005 (arXiv:0707.1329 [hep-th])), Young C A S and Zegers R (2008 Nucl. Phys. B 797 537 (arXiv: 0711.2206 [hep-th])), Young C A S and Zegers R (2008 arXiv: 0803.2659 [hep-th]) are defined on a standard κ-deformed mass shell. In this paper, we consider the most general κ-deformed field oscillators, parametrized by a set of arbitrary functions in 3-momentum space. First, we study the fields with the κ-deformed oscillators defined on the standard κ-deformed mass shell, and argue that for any such choice of a κ-deformed field oscillators algebra we do not obtain the free quantum κ-deformed fields with the c-number commutators. Further, we study κ-deformed quantum fields with the modified κ-star product and derive a large class of κ-oscillators defined on a suitably modified κ-deformed mass shell. We obtain a large class of κ-deformed statistics depending on six arbitrary functions which all provide the c-number field commutator functions. This general class of κ-oscillators can be described by the composition of suitably defined κ-multiplications and the κ-deformation of the flip operator.