By L D Landau (Eds.)
Translated from the sixth Russian version, this most up-to-date variation includes seven new sections with chapters on basic Relativity, Gravitational Waves and Relativistic Cosmology, the place Professor Lifshitz's pursuits lay. The textual content of the third English version has been completely revised and extra difficulties inserted
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Extra resources for The Classical Theory of Fields. The Classical Theory of Fields
9) Let us now turn once again to the general case of collision of particles of arbitrary mass. The collision is most simply treated in the C-system. Designating quantities in this system by the additional subscript 0, we have p 10 = - ρ 2 0 Ξ Ρο· From the conservation of momen tum, during the collision the momenta of the two particles merely rotate, remaining equal in magnitude and opposite in direction. From the conservation of energy, the value of each of the momenta remains unchanged. 38 RELATIVISTIC MECHANICS § 13 Let χ be the angle of scattering in the C-system—the angle through wiiich the momenta p 1 0 and p 2 0 are rotated by the collision.
But, as we have seen, the theory of relativity shows that it is impossible for absolutely rigid bodies to exist. Thus we come to the conclusion that in classical (non-quantum) relativistic mechanics, we cannot ascribe finite dimensions to particles which we regard as elementary. t § 16. 1) for the free particle, and a term describing the interaction of-the particle with the field. The latter term must contain quantities characterizing the particle and quantities characterizing the field. It turns outj that the properties of a particle with respect to interaction with the electro magnetic field are determined by a single parameter—the charge e of the particle, which can be either positive or negative (or equal to zero).
O As /—>oo, it increases much more slowly than /, according to the law c/w In (Iwtjc). CHAPTER 2 RELATIVISTIC MECHANICS § 8. The principle of least action In studying the motion of material particles, we shall start from the Principle of Least Action. f To determine the action integral for a free material particle (a particle not under the influence of any external force), we note that this integral must not depend on our choice of reference system, that is, it must be invariant under Lorentz transformations.
The Classical Theory of Fields. The Classical Theory of Fields by L D Landau (Eds.)