Related papers: Consistency of multi-time Dirac equations with gen…
In this paper, the Dirac's quantum mechanical interaction picture is applied to option pricing to obtain a solution of the Black-Scholes equation in the presence of a time-dependent arbitrage bubble. In particular, for the case of a call…
For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition…
We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…
We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von-Neumann-Wigner…
This paper is an investigation of the class of real classical Markov processes without a birth process that will generate the Dirac equation in 1+1 dimensions. The Markov process is assumed to evolve in an extra (ordinal) time dimension.…
We generalize previous results and demonstrate that the Dirac representation theory can be effectively adjusted and applied to continuous or discrete signals of infinite time duration. The role of the identity and projection operators is…
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…
Nonperturbative methods have been well-developed for QED with the so-called t-electric potential steps. In this case a calculation technique is based on the existence of specific exact solutions (in and out solutions) of the Dirac equation.…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that…
The Dicke model -- a paradigmatic example of superradiance in quantum optics -- describes an ensemble of atoms which are collectively coupled to a leaky cavity mode. As a result of the cooperative nature of these interactions, the system's…
In 1905, Einstein's theory of Brownian motion supported the molecular basis of the diffusion equation and introduced two complementary viewpoints: a deterministic field description and a probabilistic formulation based on stochastic…
Propagation of the heavy quark in the field of a static antiquark source is studied in the framework of effective Dirac equation. The model of QCD vacuum is described by bilocal gluonic correlators. In the heavy quark limit the effective…
This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through…
From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the…
Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 in his famous quantum mechanics text has been well studied, a not famous formula related to the delta function using the Heaviside step function in a single-variable…
We study the classical dynamics of a particle in Snyder spacetime, adopting the formalism of constrained Hamiltonian systems introduced by Dirac. We show that the motion of a particle in a scalar potential is deformed with respect to…