Related papers: Classical solutions in lattice gauge theories
We consider a class of electromagnetic fields that contains crossed fields combined with longitudinal electric and magnetic fields. We study the motion of a classical particle (solutions of the Lorentz equations) in such fields. Then, we…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type…
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows…
For a large class of Abelian lattice models with sign problems, including the case of non-zero chemical potential, duality maps models with complex actions into dual models with real actions. For extended regions of parameter space,…
Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas of mathematics and physics and have attracted much attention over the last thirty years. In this paper we investigate whether…
After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we discuss the analytic and numerical evidence that abelian lattice chiral gauge theories can be non-perturbatively…
Some elements of classical mechanics and classical statistical mechanics are formulated in terms of fibre bundles. In the bundle approach the dynamical and distribution functions are replaced by liftings of paths in a suitably chosen…
We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations.…
We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…
We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged)…
We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for…
We study lattice gauge theory with discrete, non-Abelian gauge groups. We extend the formalism of previous studies on D-Wave's quantum annealer as a computing platform to finite, simply reducible gauge groups. As an example, we use the…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system,…