Related papers: Nambu-Type Generalization of the Dirac Equation
In the framework of nonlinear Hamiltonian lattices, we revisit the proof of Moser-Darboux's Theorem, in order to present a general scheme for its constructive applicability to Hamiltonian models with non-standard symplectic structures. We…
We develop estimates for the solutions and derive existence and uniqueness results of various local boundary value problems for Dirac equations that improve all relevant results known in the literature. With these estimates at hand, we…
We derive the Dirac brackets for the O(N) nonlinear sigma model in the lightfront description with and without the constraint. We bring out various subtleties that arise including the fact that anti-periodic boundary condition seems to be…
We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
This article studies the breaking of the Lorentz symmetry at the Planck length in quantum mechanics. We use three-dimensional p-adic vectors as position variables, while the time remains a real number. In this setting, the Planck length is…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a…
We derive an exact solitary wave solution for the $\PTb$-symmetric nonlinear Dirac equation with a scalar-scalar interaction. We consider a power-law nonlinearity of the form $|\bar{\Psi}\,\Psi|^{k}\,\Psi$ for positive values of $k$. The…
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of…
This paper studies a class of nonlinear massless Dirac equations in one dimension, which include the equations for massless Thirring model and massless Gross-Neveu model. Under the assumptions that the initial data has small charge and is…
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations…
This paper concerns the boundary behavior of solutions of certain fully nonlinear equations with a general drift term. We elaborate on the non-homogeneous generalized Harnack inequality proved by the second author in (Julin, ARMA -15), to…
We show that the covariant derivative of Dirac fermion fields in the presence of a general linear connection on a world manifold is universal for Einstein's, gauge and affine-metric gravitation theories.
At an elementary level, we present some non-perturbative aspects of non-abelian gauge theories in four dimensional space-time. Some rigorous results have been obtained in the framework of supersymmetric theories, and a very rich physics…
In this paper, we present extensively the observational consequences of massless dilaton theories at the post-Newtonian level. We extend previous work by considering a general model including a dilaton-Ricci coupling as well as a general…
A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…