相关论文: Massless Dirac equation as a special case of Cosse…

The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of…

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…

We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a…

The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the…

We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by…

We present a geometric formulation of classical Cosserat elasticity in which the coframe and rotational connection are treated as independent variational fields. In contrast to conventional metric-based approaches, this formulation makes…

The problem of Dirac's equation in a rotating electromagnetic field can be reduced to the stationary by using a transformation for point rotating reference frames. The general form of the non-Galilean transformation is deduced in the paper.…

We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled…

Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and…

We propose nonlinear Dirac equations where the conformal degree of the self-interaction terms are equal to that of the Dirac operator and the coupling parameters are dimensionless. As such, the massless equation is conformally invariant and…

In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the exact nonlinear kinematic relationships in the sense of Cosserat…

A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret & Raoult. Specific characterizations of the 2D elastic…

In this paper we do a comparative presentation of the linear isotropic Cosserat elastic model from two perspectives: the classical Mindlin-Eringen-Nowacki description in terms of a microrotation vector and a new formulation in terms of a…

We study the evolution of neutrinos electroweakly interacting with a rotating matter. The description of neutrinos is based on the Dirac equation in the corotating noninertial frame where matter is at rest. We find solution of this Dirac…

We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material…

Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…

We develop a variationally consistent mesoscopic extension of Cosserat elasticity motivated by the breakdown of compatibility in classical formulations. By admitting compatibility-breaking perturbations, the classical theory ceases to…

Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a…

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to…

This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with…