相关论文: Consistent Quantization of Nearly Singular Superco…

We consider some perturbations of a family of pairwise commuting linear quantum Hamiltonians on the torus with possibly dense pure point spectra. We prove that the Rayleigh-Schr{\"o}dinger perturbation series converge near each unperturbed…

The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data…

A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect…

We discuss a new approach to describe mesoscopic systems, based on the ideas of quantum electrical circuits with charge discreteness. This approach has allowed us to propose a simple alternative descriptions of some mesoscopic systems, with…

We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb field of a point charge $Ze$. In the literature, it is often declared that a quantum-mechanical description of such a system does not exist…

I discuss theories that describe fully nonlinear physics, while being practically linear (PL), in that they require solving only linear differential equations. These theories may be interesting in themselves as manageable nonlinear…

The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the…

The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…

In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…

Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…

Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular. That is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption insures that (i)…

Spontaneous Lorentz violation models of antisymmetric tensor field are known to possess singular Hamiltonian on the vacuum manifold, leading to unresolvable pathologies that render such theories unfit for cosmological studies. In this work,…

We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…

We generalise the notion of the Pseudo-Laplacian on a hyperbolic Riemann surface with one cusp, that was studied by Lax and Phillips and Colin de Verdi\`ere, by considering a boundary condition of Robin type for the constant term instead of…

Non-commutative electrodynamics obtained through the Seiberg-Witten map ceases to have equivalent action-level and equation-level realizations once fixed external currents are introduced, and in the action-level construction associated with…

In Dirac materials, the low energy excitations obey the relativistic Dirac equation. This dependence implies that the electrons are exposed to strong spin-orbit coupling. Hence, real spin conservation is believed to be violated in Dirac…

Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path…

Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study…

The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $\alpha$ and…

All solutions of the no-birefringence conditions for nonlinear electrodynamics are found. In addition to the known Born-Infeld and Plebanski cases, we find a ``reverse Born-Infeld'' case, which has a limit to Plebanski, and an…