arXiv subjects

M. Daszkiewicz

Publications and source records attributed to M. Daszkiewicz.

9 recordsLinked to original sources

arXiv2008

Towards Quantum Noncommutative $κ$-deformed Field Theory

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.

hep-th↗

arXiv2008

$κ$-Deformed Statistics and Classical Fourmomentum Addition Law

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.

hep-th↗

arXiv2007

Magneto and ferroelectric phase transitions in HoMn2O5 monocrystals

From the physical point of view multiferroics present an extremely interesting class of systems and problems. These are essentially of two kinds. One is what are the microscopic conditions, and sometimes constrains, which determine the possibility to combine in one system both magnetic and ferroelectric properties. This turned out to be a quite nontrivial question, and usually, in conventional systems, these two phenomena tend to exclude one another. Why it is the case is an important and still not completely resolved issue. In the present article we report our results from magnetic properties measurements on HoMn2O5 with short discussion about it possible origin.

cond-mat.other↗

arXiv2005

Scalar field theory on $κ$-Minkowski space-time and Doubly Special Relativity

In this paper we recall the construction of scalar field action on $κ$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $κ$-Poincaré algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $Φ^4$ term we investigate the modified conservation laws. We show that the local interactions on $κ$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.

hep-th↗

arXiv2003

Phase spaces of Doubly Special Relativity

We show that depending on the direction of deformation of $κ$-Poincaré algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum spaces of the form of de Sitter, anti-de Sitter, and flat space, respectively.

hep-th↗

arXiv2003

Velocity of particles in Doubly Special Relativity

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 non-trivial 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.

hep-th↗

arXiv2003

Doubly Special Relativity with light-cone deformation

We propose a new Doubly Special Relativity theory based on the generalization of the $κ$-deformation of the Poincaré algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincaré algebra and use it to derive the phase space commutation relations. As in the DSR based on the standard quantum $κ$-Poincaré algebra we find that the space time is non-commutative. We investigate the fate of the properties of Special Relativity in the null basis: the split of the algebra of Lorentz and momentum generators into kinematical and dynamical parts, the action of the kinematical boost $M^{+-}$, and the emergence of the two dimensional Galilean symmetry.

hep-th↗

arXiv1997

Free strings in non-critical dimensions

The paper containes a classification of consistent free string models in physical dimensions and a brief discussion of recent results concerning relations between various models.

hep-th↗

arXiv1997

Non-Critical Light-Cone String

The free non-critical string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<D<25$. The longitudinal degrees of freedom are described by an abstract Verma module. The central charge of this module is restricted by the requirement of the closure of the nonlinear realization of the Poincare algebra. The spin content of the model is analysed. In particular for D=4 the explicit formulae for the character generating functions of the open and closed massive strings are given and the spin spectrum of first 12 excited levels is calculated. It is shown that for the space-time dimension in the range $1<D<25$ the non-critical light-cone string is equivalent to the critical massive string and to the non-critical Nambu-Goto string.

hep-th↗