相关论文: Model Dirac and Dirac-Hestenes equations as covari…

This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…

We suggest a so-called Dirac type tensor equation with nonabelian gauge symmetry on pseudo-Riemannian space. This equation reproduce some of the properties of spinor Dirac equation. A geometrical interpretation of results in terms of…

We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…

We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some…

In this paper, we consider a Class of Hessian quotient equations in Euclidean space. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the…

Almost all presentations of Dirac theory in first or second quantization in Physics (and Mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered…

Electromagnetic superradiant field coherence exists in a condensed matter system if the electromagnetic field oscillators undergo a mean displacement. Transitions into thermal states with ordered superradiant phases have been shown to…

Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…

We express discrete Painlev\'e equations as discrete Hamiltonian systems. The discrete Hamiltonian systems here mean the canonical transformations defined by generating functions. Our construction relies on the classification of the…

We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of…

In this paper we utilize the covariance of Ricatti equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of…

Use of certain non-commuting variables is considered in first-order differential equations. Superspace variables are discussed within the setting of first-order ordinary differential equations and n-ary algebras. Results on quadratic…

In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…

We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…

We describe a way of solving a partial differential equation using the differential invariants of its point symmetries. By first solving its quotient PDE, which is given by the differential syzygies in the algebra of differential…

The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…

In this paper, we study systems of nonlinear partial differential equations which describe surfaces of constant curvature. From the flatness condition of connection 1-forms, we present a classification of systems of Camassa-Holm-type…

In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished embedded Hecke…

Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…