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We first consider an interacting two-dimensional electron gas in a ballistic quantum wire in an external magnetic field. Self-consistent calculations are made of the electrostatic Hall potential (EHP), the local chemical potential (LCP), and current density in a uniform ballistic quantum wire containing two-dimensional electrons in a perpendicular magnetic field B when either one or two subbands are occupied. The corresponding Hall resistances, REHP and RLCP, are also calculated. The former is nearly linear in B in spite of subband depopulation. The latter is quantised but the quantisation steps are rounded because of overlap of the forward and backward going wave functions. Secondly, self-consistent calculations are also made of wave functions and the two kinds of Hall resistances for the same system in a weak perpendicular magnetic field when several subbands are occupied. We find intermittent quenching of the Hall resistance associated with the local chemical potential as the electron density varies. The quenching is due to the overlap of opposite-going wave functions in the same subband, which is enhanced significantly by the singularity of the density of states at the subband minima aa well as by Coulomb interactions between the electrons. Finally, with a, model calculation, we demonstrate that a non-invasive measurement of intrinsic quantum Hall effect defined by the local chemical potential in a ballistic quantum wire can be achieved with the aid of a pair of voltage leads which are separated 9Y potential barriers from the wire. Biittiker's formula is used to determine the chemical potential being measured and is shown to reduce exactly to the local chemical potential in the limit of strong potential confinement in the voltage leads. Conditions for quantisation of Hall resistance and measuring local chemical potential are given.

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The thesis is primarily concerned with these objectives: to say what is a quantum field theory, and to explain why and how relativistic quantum field theory differs from non-relativistic quantum field theory, even in the free or weakly interacting (quasi-free) case. Following the ideas of Irving Segal, I shall establish that in this case there is an essential identity in structure of the non-relativistic and relativistic field theories. Novel but straightforward applications of this theory are made to the complex scalar field,and in relation to t.he Dirac hole theory. Although the structure of the relativistic and non-relativistic quasi-free theories is essentially identical, the concept of localization finds different expressions. This plays a fundamental role when interactions are introduced, and leads to two quite distinct notions of causality. I shall confine the detailed study to the massive scalar and spin 1/2 linear field theories, for the most part in the quasi-free case. Not even the latter are trivial, for they descri,be the observed phenomenology and are therefore of central empistemological importance to relativistic quantum theory. I al so advance a general interpretat i ve framework for the philosophical analysis of quantum theory. This is essent ially a real ist interpretation founded on abstract • C -algebras, and it is applied to the measurement problem. The physical and mathematical theories that I draw upon are developed in a historical context. The mathematical theory is presented in a largely heuristic way.

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No description available.

No description available.