Over the past one hundred years Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Initially proposed as a phenomenological paradigm for atomistic matter interactions, the original theory has ever since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics....

This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time theory. For completeness, we give a brie...

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which suppress quantum tun...

Relativistic particle physics is described by relativistic quantum field theory; the theories explaining the fundamental interactions are gauge theories. QFT as it is formulated in terms of Lagrangians and functional integration has to be regularized. The only known regularization scheme that retains the gauge symmetry is replacement of the space-time continuum by a space-time lattice. For conv...

We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the co...

We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the co...

Bibliography 43 3 Contents 4 Preface The present manuscript are lecture notes on an introduction to relativistic transport theory, held at the SERC School on Modern Theories of Nuclear Reactions in Roorkee, India. The aim of these lectures is to provide a self-contained presentation of the general foundations of rela-tivistic transport theory with the aim to provide the theoretical tools for th...

By the Bogoliubov prescription and the method of Gross and Pitaevskii in quantum field theory, the relativistic almost ideal Bose-Eintein gas at zero temperature is discussed. Special attention is given to the study of a vortex in the gas. The field description and fluid approximation are compared. PACS: 11.10.-z, 05.30.Jp, 47.75.+f, 47.37.+q

The theory of the Relativistic Schrödinger Equations is further developped and extended to non-linear field equations. The technical advantage of the Relativistic Schrödinger approach is demonstrated explicitly by solving the coupled Einstein-Klein-Gordon equations including a non-linear Higgs potential in case of a Robertson-Walker universe. The numerical results yield the effect of dynamical ...

This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book “Quantum electrodynamics” we present traditional views on theoretical foundations of particle physics. Our discussion proceeds systematically from the principle of relativity and postulates of measurements to the renormalization in quantum electrodynamics. In the sec...