RELATIVISTIC CORRECTIONS IN THE STATISTICAL MECHANICS OF INTERACTING PARTICLES

Journal Article · Sat Dec 15 04:00:00 EST 1962 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.128.2916· OSTI ID:4751768

Krizan, J E; Havas, P

In previous work on statistical mechanics, the consequences of the theory of relativity have only been investigated for the ideal gas. This study is concerned with relativistic effects for systems of interacting particles. The noninstantaneous nature of the forces leads to dynamical equations which cannot be treated by known mathematical methods; however, the interaction terms can be expanded to obtain a description of the system in terms of the positions and their derivatives of all orders at a single time. If one stops at the (v/c)/sup 2/ approximation, a specification in terms of positions and velocities is obtained; in electrodynamics this corresponds to the Darwin Hamiltonian. A system described by this Hamiltonian is investigated with the methods of equilibrium statistical mechanics. The cluster expansion with subsequent summation of diagrams as employed by Mayer for the Coulomb case is used; the modifications necessary due to the presence of momentumdependent terms in the interaction are developed. In evaluating the lowest order nonvanishing (ring approximation, mathematical difficulties peculiar to the relativistic interactions force restriction to calculation of the relativistic short-range correlation effects in the charged system. A modified Debye-Huckel law is obtained, including a relativistic correction term which is small compared to the static one. At the high temperatures required for appearance of relativistic effects, the static term is itself negligible except at very high densities. Thus the relativistic contribution can in effect be neglected in this- approximation. The difficulty of extending the method to mesonic or gravitational interactions is discussed. (auth)

• Research Organization: Lehigh Univ., Bethlehem, Penn.
• NSA Number: NSA-17-005564
• OSTI ID: 4751768
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 128; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CLUSTER EXPANSION
CONFIGURATION
CORRELATION FUNCTION
DENSITY
DIAGRAMS
DIFFERENTIAL EQUATIONS
ELECTRIC CHARGES
ELECTRIC POTENTIAL
ELECTRODYNAMICS
EQUATIONS
ERRORS
FIELD THEORY
GASES
GRAVITATION
HAMILTONIAN
HAMILTONIAN FUNCTION
INTERACTIONS
MATHEMATICS
MECHANICS
MESONS
MOMENTUM
MOTION
NUMERICALS
PARTICLES
PERTURBATION THEORY
PHYSICS
RELATIVITY THEORY
STATISTICS
TEMPERATURE
VELOCITY