Avoiding Negative Probabilities in Relativistic Quantum Mechanics.

Taeseung Choi, Yeong Deok Han

P. T. Landsberg, K. A. Johns

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.

K. V. Roberts

Laurent Baulieu, J. Iliopoulos, Roland Sénéor

Abstract Towards a relativistic quantum mechanics. Klein–Gordon and the problems of the probability current and the negative energy solutions. The Dirac equation and negative energies. P, C, and T symmetries. Positrons. The Schrödinger equation as the non-relativistic limit of relativistic equations. Majorana and Weyl equations. Relativistic corrections in hydrogen-like atoms. The Dirac equation as a quantum system with an infinite number of degrees of freedom.

Hartland S. Snyder