Classical relativistic systems of charged particles in the front form of dynamics and the Liouville equation
نویسندگان
چکیده
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description is reduced by use of the geometrical concept of the forms of rel-ativistic dynamics. The remainder gauge degrees of freedom of the electromagnetic potential are analysed within the framework of Dirac's constrained Hamiltonian mechanics in the front form of dynamics. The results are implemented to the problems of relativistic statistical mechanics. Based on the corresponding Liouville equation the classical partition function of the system is written down in a gauge-invariant manner and an integration over field variables is performed.
منابع مشابه
An approximate analytical solution of the Bethe equation for charged particles in the range of radiotherapy energy
Charged particles such as protons and carbon ions are an increasing tool in radiation therapy. However, unresolved physical problems prevent optimal performance, including estimating the deposited dose in non-homogeneous tissue, is an essential aspect of optimizing treatment. The Monte Carlo (MC) method can be used to estimate the amount of radiation, but, this powerful computing operation is v...
متن کاملThe Asymptotic Form of Eigenvalues for a Class of Sturm-Liouville Problem with One Simple Turning Point
The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...
متن کاملClassical versus quantum dynamics for a driven relativistic oscillator
We compare the time evolution of the quantum-mechanical spatial probability density obtained by solving the time-dependent Dirac equation with its classical counterpart obtained from the relativistic Liouville equation for the phase-space density in a regime in which the dynamics is essentially relativistic. For a resonantly driven one-dimensional harmonic oscillator, the simplest nontrivial mo...
متن کاملThe Effects of Different SDE Calculus on Dynamics of Nano-Aerosols Motion in Two Phase Flow Systems
Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...
متن کاملNon-Relativistic Limit of Neutron Beta-Decay Cross-Section in the Presence of Strong Magnetic Field
One of the most important reactions of the URCA that lead to the cooling of a neutron star, is neutron beta-decay ( ). In this research, the energy spectra and wave functions of massive fermions taking into account the Anomalous Magnetic Moment (AMM) in the presence of a strong changed magnetic field are calculated. For this purpose, the Dirac-Pauli equation for charged and neutral fermions is ...
متن کامل