Do you want to publish a course? Click here

A Master Equation Approach to the `3 + 1 Dirac Equation

152   0   0.0 ( 0 )
 Added by Keith Earle
 Publication date 2011
  fields Physics
and research's language is English




Ask ChatGPT about the research

A derivation of the Dirac equation in `3+1 dimensions is presented based on a master equation approach originally developed for the `1+1 problem by McKeon and Ord. The method of derivation presented here suggests a mechanism by which the work of Knuth and Bahrenyi on causal sets may be extended to a derivation of the Dirac equation in the context of an inference problem.



rate research

Read More

Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows to write down the master equation based on the type of of the kinetic equations and assumptions about the nature of the process. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. Leaving in the expansion terms up to the second order we can get the Fokker-Planck equation, and thus the Langevin equation. It should be clearly understood that these equations are approximate recording of the master equation. However, this does not eliminate the need for the study of the master equation. Moreover, the power series produced during the master equation decomposition may be divergent (for example, in spatial models). This makes it impossible to apply the classical perturbation theory. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. As an example the Verhulst model is used because of its simplicity and clarity (the first order equation is independent of the spatial variables, however, contains non-linearity). We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation.
This article reviews recent work on the Kac master equation and its low dimensional counterpart, the Kac equation.
We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved quantities that diffuse to zero, and fast variables that are slaved to the slow ones. This slaving implies the Fourier law, which relates the induced currents to the gradients of the conserved quantities.
A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, that is, for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has been done successfully already in 1 space dimension, and more generally for codimension-1 boundaries, the situation of point sources in 3 dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3d, which also correspond to a boundary condition. And indeed, we confirm this expectation here by proving that there is no self-adjoint operator on (a truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with IBC (on the boundary consisting of configurations with a particle at the origin) that are, away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential.
228 - Andrzej Okninski 2011
Recently, we have demonstrated that some subsolutions of the free Duffin-Kemmer-Petiau and the Dirac equations obey the same Dirac equation with some built-in projection operators. In the present paper we study the Dirac equation in the interacting case. It is demonstrated that the Dirac equation in longitudinal external fields can be also splitted into two covariant subequations.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا