Introduction to Relativistic Quantum Chemistry (original) (raw)
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Quantum Phase Space in Relativistic Theory: the Case of Charge-Invariant Observables
2004
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of problems is band structure of energy spectrum for a relativistic particle. This corresponds to an internal degree of freedom, so-called charge variable. In physical problems we often deal with such of dynamical variables that do not depend on this degree of freedom. These are position, momentum, and any combination of them. Restricting our consideration to this kind of observables we propose the relativistic Weyl--Wigner--Moyal formalism that contains some surprising differences from its non-relativistic counterpart.
The New Relativistic Quantum Theory of the Electron
In this paper we introduce a framework to unify quantum and special relativity theories conforming the principle of causality through a new concept of fundamental particle mass based on new models of both stochastic process and elementary particles as concentrated energy localized on the surface of 3-dimensional sphere-form (2-manifold without boundary). The natural picture of fundamental connection between quantum and special relativistic aspects of particles is described by the existence of the intrinsic random vibrating motion of an elementary particle in a quantum-sized volume (Planck scale) directly connected with a spin phenomenon, which is playing fundamental role as internal time. The results show that fir st, relativistic effects fundamentally relate to dynamic aspects of a particle. Second, new equations indicate antiparticle (antimatter) must have positive energy. Third, these are different from the Dirac's equation exhibiting an electric moment in a pure imaginary. Our equation presents a real electric moment. We also show that the antiparticles only present in strong potential causing the non-symmetry reality between matter and antimatter in the universe.
Relativistic quantum mechanics of many-electron systems
Journal of Molecular Structure: THEOCHEM, 2001
The present review surveys the single-and multicon®guration matrix Dirac±Fock self-consistent ®eld methods and their many-body theoretical re®nements developed in our group over the last decade. Implementation with analytic basis sets of Gaussian spinors is discussed in detail. q (Y. Ishikawa). Y. Ishikawa, M.J. Vilkas / Journal of Molecular Structure (Theochem) 573 (2001) 139±169 Fig. 1. 1s 1=2 relativistic wave functions, 1=2P 1s 1=2 r; of gold representing the nucleus as a point and a ®nite sphere of uniform proton charge. Nonrelativistic 1s orbital of Au is also displayed for comparison.
Theoretical and Mathematical Physics, 1981
For the case of a charged scalar field described by a quadratic Hamiltonian, an equivalent relativistic quantum mechanics in the single-particle sector is constructed. The motion of a charged relativistic particle in a Coulomb field is completely investigated. This paper is a continuation of [1] and describes the motion of a charged scalar particle in a Coulomb field from the point of view of relativistic quantum mechanics. In [1], we proposed a method for associating a quantum field theory with quadratic Hamiltonian with a quantum-mechanical problem that leads in the sector with fixed number of physical particles to the same scattering matrix as in the original field theory. The obtained quantum-mechanical formulation is determined by a Hamiltonian acting on a space with indefinite metric. The physical subspace is formed by the eigenvectors of the Hamiltonian with positive norm and
Foundations of the relativistic theory of many-electron bound states
International Journal of Quantum Chemistry, 1984
Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac-Coulomb Hamiltonian HDc. However, because the electron-electron interaction mixes positive-and negative-energy states, the operator HDc has no normalizable eigenfunctions.
2008
A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory describing the system in arbitrary admissible non-inertial frames in Minkowski space-time, which allows one to define the energy-momentum tensor of the system and to show the independence of the description from the clock synchronization convention and from the choice of the 3-coordinates. In the inertial rest frame the isolated system is seen as a decoupled non-covariant canonical external center of mass carrying a pole-dipole structure (the invariant mass MMM and the rest spin vecbarS{\vec {\bar S}}vecbarS of the system) and an external realization of the Poincare' group. Then an isolated system of positive-energy charged scalar articles plus an arbitrary electro-magnetic field in the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric charges of the particles are Grassmann-valued to regularize the self-energies. The rest-frame conditions and their gauge-fixings (needed for the elimination of the internal 3-center of mass) are explicitly given. It is shown that there is a canonical transformation which allows one to describe the isolated system as a set of Coulomb-dressed charged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these two subsystems are not mutually interacting and are interconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore in this framework with a fixed number of particles there is a way out from the Haag theorem,at least at the classical level.
This textbook deals with advanced topics in the field of quantum mechanics, material which is usually encountered in a second university course on quantum mechanics. The book, which comprises a total of 15 chapters, is divided into three parts: I. Many-Body Systems, II. Relativistic Wave Equations, and III. Relativistic Fields. The text is written in such a way as to attach importance to a rigorous presentation while, at the same time, requiring no prior knowledge, except in the field of basic quantum mechanics. The inclusion of all mathematical steps and full presentation of intermediate calculations ensures ease of understanding. A number of problems are included at the end of each chapter. Sections or parts thereof that can be omitted in a first reading are marked with a star, and subsidiary calculations and remarks not essential for comprehension are given in small print. It is not necessary to have read Part I in order to understand Parts II and III. References to other works in the literature are given whenever it is felt they serve a useful purpose. These are by no means complete and are simply intended to encourage further reading. A list of other textbooks is included at the end of each of the three parts.