arXiv subjects

Markus Lazar

Publications and source records attributed to Markus Lazar.

67 records · Page 4Linked to original sources

arXiv2003

Wedge disclination in the field theory of elastoplasticity

In this paper we study the wedge disclination within the elastoplastic defect theory. Using the stress function method we found exact analytical solutions for all characteristic fields of a straight wedge disclination in a cylinder. The elastic stress, elastic strain, elastic bend-twist, displacement and rotation have no singularities at the disclination line. We found a modified stress function for the wedge disclination.

cond-mat.mtrl-sci↗

arXiv2003

A nonsingular solution of the edge dislocation in the gauge theory of dislocations

A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and the solution agrees with the classical solution for the edge dislocation in the far field. The components of the stress, strain, distortion and displacement field are also defined in the dislocation core region and they have no singularity there. The dislocation density, moment and couple stress for an edge dislocation are calculated. The solution for the stress and strain field obtained here is in agreement with those obtained by Gutkin and Aifantis through an analysis of the edge dislocation in the strain gradient elasticity. Additionally, the relation between the gauge theory and Eringen's so-called nonlocal theory of dislocations is given.

cond-mat.mtrl-sci↗

arXiv2002

Screw dislocations in the field theory of elastoplasticity

A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so-called Eshelby twist which depends on a specific intrinsic material length.

cond-mat.mtrl-sci↗

arXiv2002

An elastoplastic theory of dislocations as a physical field theory with torsion

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.

cond-mat↗

arXiv2001

Nonlocal operators and distribution amplitudes of definite twist, WW-like relations, BC-like sum rules and power corrections for hard QCD processes

The decomposition of nonlocal operators (and of their matrix elements) into an (infinite) series w.r.t. geometric twist is used to introduce (new) parton distributions, generalized parton distributions and hadron wave functions of definite twist. Their comparision with the conventional distributions (of definite dynamical twist) leads to Wandzura-Wilczek like relations, Burkhardt-Cottingham like sum rules and allows for power corrections of the various distribution amplitudes. Some general aspects are reviewed.

hep-ph↗

arXiv2001

Power corrections of off-forward quark distributions and harmonic operators with definite twist

A group theoretical procedure for parametrizing non-forward matrix elements of non-local QCD operators is introduced. The related (two-variable) distribution amplitudes are given as sum over power corrections of the double distributions. For totally symmetric (local) operators the infinite twist decomposition is given completely and for operators with non-trivial symmetry type up to twist 3. The power corrections for most of the phenomenological relevant double distributions and the vector meson wave functions are determined. They may be obtained, by harmonic extension, from the corresponding operators or distribution amplitudes on the light-cone.

hep-ph↗

arXiv2001

Wandzura-Wilczek-type relations of $ρ$-meson wave functions

We give the geometric Wandzura-Wilczek-type relations between the meson wave functions of dynamical twist by means of the meson wave functions of geometric twist. We discuss the difference between geometric and dynamical Wandzura-Wilczek-type relations. Additionally, the interrelations between the different twist notations of meson wave functions are discussed.

hep-ph↗

arXiv2001

A Note on Wandzura-Wilczek Relations

Wandzura-Wilczek (WW) relations between matrix-elements of bilocal light-ray operators have recently regained interest in connection with off-forward scattering processes. Originally derived for matrix elements over leading-twist operators, their generalization to off-forward and exclusive processes gets complicated by the presence of higher-twist operators that are total derivatives of leading-twist ones and do not contribute to forward-scattering. We demonstrate that, for exclusive matrix-elements, the inclusion of these operators into WW-relations is essential for fulfilling constraints imposed by the conformal symmetry of massless QCD.

hep-ph↗

arXiv2001

$ρ$-Meson wave functions from nonlocal light-cone operators with definite twist

We introduce chiral-even and chiral-odd meson wave functions as vacuum-to-meson matrix elements of bilocal quark operators with well-defined (geometric) twist. Thereby, we achieve a Lorentz invariant classification of these distributions which differ from the conventional ones by explicitly taking into account the trace terms. The relations between conventional and new wave functions are given.

hep-ph↗

arXiv2000

Parton distribution functions from nonlocal light-cone operators with definite twist

We introduce the chiral-even and chiral-odd quark distributions as forward matrix elements of related bilocal quark operators with well-defined (geometric) twist. Thereby, we achieve a Lorentz invariant classification of these distributions which differ from the conventional ones by explicitly taking into account the necessary trace terms. The relations between both kinds of distribution functions are given and the mismatch between their different definition of twist is discussed. Wandzura-Wilczek--like relations between the conventional distributions (based on dynamical twist) are derived by means of geometric twist distribution functions.

hep-ph↗

arXiv2000

Quantum Fiel Theoretic Treatment of the Non-Forward Compton Amplitude in the Generalized Bjorken Region

A quantum field theoretic treatment of the leading light-cone part of the virtual Compton amplitude is presented. The twist-decomposition of the operators is performed by a group-theoretic procedure respecting the Lorentz group O(3,1). The twist-2 contributions to the Compton amplitude are calculated and it is shown that the electromagnetic current is conserved for these terms. Relations between the amplitude functions associated to the symmetric and asymmetric part of the Compton amplitude are derived. These relations generalize the Callan-Gross and Wandzura-Wilczek relations of forward scattering for the non-forward Compton amplitude.

hep-ph↗

arXiv2000

Dislocation theory as a 3-dimensional translation gauge theory

We consider the static elastoplastic theory of dislocations in an elastoplastic material. We use a Yang-Mills type Lagrangian (the teleparallel equivalent of Hilbert-Einstein Lagrangian) and some Lagrangians with anisotropic constitutive laws. The translational part of the generalized affine connection is utilized to describe the theory of elastoplasticity in the framework of a translation gauge theory. We obtain a system of Yang-Mills field equations which express the balance of force and moment.

cond-mat↗

arXiv2000

Twist decomposition of nonlocal light-cone operators II: General tensors of 2nd rank

A group theoretical procedure, introduced earlier (hep-th/9901090), to decompose bilocal light-ray operators into (harmonic) operators of definite twist is applied to the case of arbitrary 2nd rank tensors. As a generic example the bilocal gluon operator is considered which gets contributions of twist-2 up to twist-6 from four different symmetry classes characterized by conrresponding Young tableaus; also the twist decomposition of the related vector and scalar operators is considered. In addition, we extend these reselts to various trilocal light-ray operators, like the Shuryak-Vainshtein, the three-gluon and the four-quark operators, which are required for the consideration of higher twist distribution amplitudes. The present results rely on the knowledge of harmonic tensor polynomials of any order n which habe been determined up to the case of 2nd rank symmetric tensors for arbitrary space-time dimension.

hep-th↗