Relativistic quantum mechanics and mass-quantization

J. S. Faulkner

Xue You Lee

Abstract：Geometrical optics has high similarity with classical particle mechanics. After first quantization program classical particle mechanics can obtain non-relativistic quantum mechanics that suitable for micro, but quantum mechanics does not describe the photon that its static mass is zero. So whether there is a kind of "quantization " approach for geometrical optics, by which non-relativistic quantum mechanics that can be used to describe the photon can be obtained. It’s quantum mechanics of photon similar to the Schrödinger wave mechanics under the neglection of the formation and annihilation of photon. In this paper, several methods that can be used to find

Zoltán Papp

David Alba, Horace W. Crater, Luca Lusanna

A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics, where the world-lines of the particles are parametrized in terms of the Fokker-Pryce center of inertia and of Wigner-covariant relative 3-coordinates inside the instantaneous Wigner 3-spaces, and where there is a decoupled (non-covariant and non-local) canonical relativistic center of mass. This approach: (a) allows us to make a consistent quantization in every inertial frame; (b) leads to a description of both bound and scattering states; (c) offers new insights on the relativistic localization problem; (d) leads to a non-relativistic limit with a Hamilton-Jacobi treatment of the Newton center of mass; (e) clarifies non-local aspects (spatial non-separability) of relativistic entanglement connected with Lorentz signature and not present in its non-relativistic treatment.

K. J. Le Couteur

Abstract There are many problems of relativistic quantum mechanics which cannot be treated by working with a positive definite metric in the vector space of the fully quantized system. In this paper it is shown that, independently of the signs of energy and charge in the c number theory, any relativistic wave equation can be quantized and interpreted in terms of positive energies by use of an indefinite metric of suitable signature. A powerful method of obtaining positive definite transition probabilities from an indefinite metric is introduced and the concept of ‘negative probability’ is entirely avoided.The transition probabilities are defined as the squared matrix elements of a unitary matrix T, which is obtained from the solution of the Schrodinger equation by means of a special transformation.These techniques make it possible to treat relativistic wave equations which describe particles with several mass and spin states and to give a satisfactory account of the transition between two such mass states, a problem which is otherwise quite intractable. The relationship of spin and statistics is discussed and it is concluded that, apart from the special cases of spin 0, ½, 1, there is no necessary connexion between spin and statistics.