Some contributions to the theory and application of the Bethe-Salpeter equation

Mandelstam, S. (1956). Some contributions to the theory and application of the Bethe-Salpeter equation. University of Birmingham. Ph.D.

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Abstract

This thesis consists of two parts. The first is concerned with the general quantum field theory of bound states. It is shown that a knowledge of the behaviour of the propagators around their singularities enables one to determine, not only the masses of bound states, but also the matrix element of any dynamical variable between two bound states. One is thus enabled to find such a matrix element, to any order in the coupling constant, by the integration of certain expressions over the relevant Bethe-Salpeter wave-functions. One of the consequences of this is that it is possible to find normalization and orthogonality properties of these wave-functions. The formalism is extended to scattering states in which some of the particles may be composite. In particular, an expression for the S-matrix is obtained.

Part II is concerned with the solubility of Bethe-Salpeter equations in their lowest approximation. As they are singular integral equations, it is not certain a priori that solutions exist. Certain results of Part I are used to determine what solutions are acceptable. It is then shown that the equation for nucleon-nucleon scattering is soluble for states of all angular momentum, parity and isotopic spin if and only if \(\frac{g^2}{4\pi}\) is less than \(\frac{\pi}{6}\). The range of values of g for which there exist solutions of a particular angular momentum and parity is given. The Bethe-Salpeter equation for meson nucleon scattering is also examined; the results are rather different from those obtained for the equation for nucleon-nucleon scattering.

Type of Work:	Thesis (Doctorates > Ph.D.)
Award Type:	Doctorates > Ph.D.
College/Faculty:	Faculties (to 1997) > Faculty of Science
School or Department:	Department of Mathematical Physics
Funders:	None/not applicable
Subjects:	Q Science > QC Physics
URI:	http://etheses.bham.ac.uk/id/eprint/17469

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