DOI: https://doi.org/10.30970/jps.03.284
STATISTICAL DENSITY MATRIX AND HAMILTONIAN OF A SYSTEM OF RELATIVISTIC CHARGED PARTICLES
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Journal of Physical Studies 3(3), 284–290 (1999)
DOI: https://doi.org/10.30970/jps.03.284 STATISTICAL DENSITY MATRIX AND HAMILTONIAN OF A SYSTEM OF RELATIVISTIC CHARGED PARTICLES |
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L. F. Blazhyjevskii
Ivan Franko National University of Lviv, Chair of Theoretical Physics
12 Drahomanov Str., UA-79005, Lviv, Ukraine
A system of relativistic charged particles in statistical equilibrium is considered. $N$–particle density matrix is found on the base of field theory. Within the first order approximation it is represented as a phase–space path integral of the functional $\exp(W)$, where $W$ as a non–additive action. We show that in the classical case this representation leads to Gibbs distribution for a system of relativistic particles with the direct interaction. The approximate Hamiltonian of a system of relativistic particles is found. The screening of the effective relativistic two–particle interaction as well as the renormalization of the one–particle Hamiltonian appear as a peculiarity of obtained formulae. This can be interpreted as an environment influence, which is relativistic generalization of the post–Newtonian Hamiltonian of spinless charged particles such that the relativistic interaction is described by Breit's formula, where particles impulses ${\bf p}$ are substituted by ${mc^2\over ε}{\bf p}$, ($ε=√{m^2c^2+c^2p^2}$).