arXiv subjects
Publications and source records attributed to P. Maślanka.
The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.
The application of the chiral decomposition procedure to hybrid graphene h-BN systems revealed rules for the partition of the system into effective subsystems being bilayers plus monolayer in case the number of layers is odd. Three types of subsystems have been detected namely purely graphene bilayers and monolayers, mixed bilayers and pure h-BN monolayers depending on the hybrid composition. The effective parameters characterizing these chiral subsystems consist of the interlayer couplings and on-site potentials which shows the mechanism of compensation of the asymmetry introduced into the system by h-BN layers. For illustration, we provide a pedagogical overview about chiral tunneling in graphene subsystems (MLG, BLG) present in hybrid with one h-BN layer. We have established the parameter ranges for which the characteristic features in the spectrum are observed, such as Fabry-Pérot resonances in the case of MLG and "magic angles" in the case of effective BLG. We also consider different hybrid stacking in order to indicate effective systems with the desired properties required in the electronic and spintronic applications.
The generalization of Bertrand's theorem to the case of the motion of point particle on the surface of a cone is presented. The superintegrability of such models is discussed. The additional integrals of motion are analyzed for the case of Kepler and harmonic oscillator potentials.
We consider the dynamics invariant under the action of l-conformal Galilei group using the method of nonlinear realizations. We find that by an appropriate choice of the coset space parametrization one can achieve the complete decoupling of the equations of motion. The Lagrangian and Hamiltonian are constructed. The results are compared with those obtained by Galajinsky and Masterov [Nucl. Phys. B860, (2013), 212].
This paper is presented on the occasion of 60-th birthday of Jose Adolfo de Azcarraga who in his very rich scientific curriculum vitae has also a chapter devoted to studies of quantum-deformed symmetries, in particular deformations of relativistic and Galilean space-time symmetries [1-4]. In this paper we provide new steps toward describing the $κ$-deformed D=4 conformal group transformations. We consider the quantization of D=4 conformal group with dimensionful deformation parameter $κ$. Firstly we discuss the noncommutativity following from the Lie-Poisson structure described by the light-cone $κ$-Poincaré $r$-matrix. We present complete set of D=4 conformal Lie-Poisson brackets and discuss their quantization. Further we define the light-cone $κ$-Poincaré quantum $R$-matrix in O(4,2) vector representation and discuss the inclusion of noncommutative conformal translations into the framework of $κ$-deformed conformal quantum group. The problem with real structure of $κ$-deformed conformal group is pointed out.
We describe the generalized kappa-deformations of D=4 relativistic symmetries with finite masslike deformation parameter kappa and an arbitrary direction in kappa-deformed Minkowski space being noncommutative. The corresponding bicovariant differential calculi on kappa-deformed Minkowski spaces are considered. Two distinguished cases are discussed: 5D noncommutative differential calculus (kappa-deformation in time-like or space-like direction), and 4D noncommutative differential calculus having the classical dimension (noncommutative kappa-deformation in light-like direction). We introduce also left and right vector fields acting on functions of noncommutative Minkowski coordinates, and describe the noncommutative differential realizations of kappa-deformed Poincare algebra. The kappa-deformed Klein-Gordon field on noncommutative Minkowski space with noncommutative time (standard kappa-deformation) as well as noncommutative null line (light-like kappa-deformation) are discussed. Following our earlier proposal (see {1,2]) we introduce an equivalent framework replacing the local noncommutative field theory by the nonlocal commutative description with suitable nonlocal star product multiplication rules. The modification of Pauli--Jordan commutator function is described and the kappa-dependence of its light-cone behaviour in coordinate space is explicitly given. The problem with the kappa-deformed energy- momentum conservation law is recalled.
We describe the extension of the Wigner`s infinite-dimensional unitary representations of Poincaré group to the case of $κ$-deformed Poincaré group. We show that the corresponding coordinate wave functions on noncommutative space-time are described by free field equations on $κ$-deformed Minkowski space. The cases of Klein--Gordon, Dirac, Proca and Maxwell fields are considered. Finally some aspects of second quantization are also discussed.
The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $κ$- deformed Minkowski space, transforming under $κ$-deformed Poincaré group with noncommutative parameters. By extending the star product to the tensor product of functions on $κ$-deformed Minkowski space and $κ$-deformed Poincaré group we represent the algebra of noncommutative parameters of deformed relativistic symmetries by functions on classical Poincaré group.
We describe the local D=4 field theory on $κ$--deformed Minkowski space as nonlocal relativistic field theory on standard Minkowski space--time. For simplicity the case of $κ$-deformed scalar field $ϕ$ with the interaction $λϕ^{4}$ is considered, and the $κ$--deformed interaction vertex is described. It appears that fundamental mass parameter $κ$ plays a role of regularizing imaginary Pauli--Villars mass in $κ$--deformed propagator.
Two properties of Calogero wave functions for rational Calogero models are studied: (i) the representation of the wave functions in terms of the exponential of Lassalle operators, (ii) the $sL(2,\rr)$ structure of the Calogero--Moser wave functions.
The Calogero model with negative harmonic term is shown to be equivalent to the set of negative harmonic oscillators. Two time-independent canonical transformations relating both models are constructed: one based on the recent results concerning quantum Calogero model and one obtained from dynamical $sL(2,\rr)$ algebra. The two-particle case is discussed in some detail.
A particular deformation of central extended Galilei group is considered. It is shown that the deformation influences the rules of constructing the composed systems while one particle states remain basically unaffected. In particular the mass appeared to be non additive.
The deformed double covering of E(2) group, denoted by $\tilde{E}_κ(2)$, is obtained by contraction from the $SU_μ(2)$. The contraction procedure is then used for producing a new examples of differential calculi: 3D-left covariant calculus on both $\tilde{E}_κ(2)$ and the deformed Euclidean group $E_κ(2)$ and two different 4D-bicovariant calculi on $\tilde{E}_κ(2)$ which correspond to the one 4D-bicovariant calculi on $E_κ(2)$ described in Ref.\cite{b14}.
The quantum Galilei group $G_{\varkappa}$ is defined. The bicrossproduct structure of $G_{\varkappa}$ and the corresponding Lie algebra is revealed. The projective representations for the two-dimensional quantum Galilei group are constructed.
We present here the general solution describing generators of \kdef \poin algebra as the functions of classical \poin algebra generators as well as the inverse formulae. Further we present analogous relations for the generators of N=1 D=4 \kdef \poin superalgebra expressed by the classical \poin superalgebra generators. In such a way we obtain the \kdef \poin (super)algebras with all the quantum deformation present only in the coalgebra sector. Using the classical basis of \kdef \poin superalgebra we obtain as a new result the $\k$-deformation of supersymmetric covariant spin square Casimir.