Lattice fractional quantum field theory: Exact differences approach

An approach, which is based on exact fractional differences, is used to formulate a lattice fractional field theories on unbounded lattice spacetime. An exact discretization of differential and integral operators of integer and non-integer orders is suggested. New type of fractional differences of integer and non-integer orders, which are represented by infinite series, are used in quantum field theory with non-locality. These exact differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. In addition, characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Lattice analogs of the fractional-order N-dimensional differential operators are proposed. The continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum four-dimensional spacetime. The fractional field equations, which are derived from equations for lattice spacetime with long-range properties of power-law type, contain the Riesz type derivatives on non-integer orders with respect to spacetime coordinates.

Single crystal plasticity theories predicting bounded lattice rotation under simple shear deformation

Up to now, models for single crystal plasticity predict unbounded lattice rotations under simple shear. Asaro et al. proposed a model that predicts bounded rotations as long as the viscosity parameters are appropriately chosen. In every case, ideal plasticity models imply unbounded lattice rotations. Hence, it leads to the question whether one can develop a single crystal plasticity theory exhibiting hardening effects, which can predict bounded lattice rotations dependent on the choice of the hardening parameters. It is shown that this is possible by assuming latent hardening to apply.