scholarly journals Current Developments in the Relativistic Quantum Mechanics of Atoms and Molecules

1986 ◽  
Vol 39 (5) ◽  
pp. 649 ◽  
Author(s):  
IP Grant
Keyword(s):  
Electronic Structure ◽  
Quantum Mechanics ◽  
Atomic Structure ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Finite Basis ◽  
Basis Set ◽  
Structure Theory ◽  
Relativistic Quantum Mechanics ◽  
Atoms And Molecules

Current work in relativistic quantum mechanics by the author and his associates focusses on four topics: atomic structure theory using the GRASP package (Dyall 1986); extension of GRASP to handle electron continuum processes; the relation of quantum electrodynamics and relativistic quantum mechanics of atoms and molecules; and development of methods using finite basis set expansions for studying electronic structure of atoms and molecules. This paper covers only the last three topics, giving emphasis to growing points and outstanding difficulties.

scholarly journals Derivation of the Local Lorentz Gauge Transformation of a Dirac Spinor Field in Quantum Einstein-Cartan Theory

2019 ◽  
Author(s):  
Rainer Kühne
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Relativistic Quantum Mechanics ◽  
Dirac Spinor ◽  
Dirac Algebra ◽  
Gauge Transformations ◽  
Cartan Theory

I examine the groups which underly classical mechanics, non-relativistic quantum mechanics, special relativity, relativistic quantum mechanics, quantum electrodynamics, quantum flavourdynamics, quantum chromodynamics, and general relativity. This examination includes the rotations SO(2) and SO(3), the Pauli algebra, the Lorentz transformations, the Dirac algebra, and the U(1), SU(2), and SU(3) gauge transformations. I argue that general relativity must be generalized to Einstein-Cartan theory, so that Dirac spinors can be described within the framework of gravitation theory.

scholarly journals ON NON-SELF-ADJOINT OPERATORS FOR OBSERVABLES IN QUANTUM MECHANICS AND QUANTUM FIELD THEORY

2010 ◽  
Vol 25 (09) ◽  
pp. 1785-1818 ◽  
Author(s):  
ERASMO RECAMI ◽  
VLADISLAV S. OLKHOVSKY ◽  
SERGEI P. MAYDANYUK
Keyword(s):  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Nuclear Physics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Dissipation ◽  
Interesting Possibility ◽  
Nonrelativistic Quantum Mechanics ◽  
Adjoint Operators ◽  
Unstable States

The aim of this paper is to show the possible significance, and usefulness, of various non-self-adjoint operators for suitable Observables in nonrelativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically, this work deals with: (i) the maximal Hermitian (but not self-adjoint) time operator in nonrelativistic quantum mechanics and in quantum electrodynamics; (ii) the problem of the four-position and four-momentum operators, each one with its Hermitian and anti-Hermitian parts, for relativistic spin-zero particles. Afterwards, other physically important applications of non-self-adjoint (and even non-Hermitian) operators are discussed: in particular, (iii) we reanalyze in detail the interesting possibility of associating quasi-Hermitian Hamiltonians with (decaying) unstable states in nuclear physics. Finally, we briefly mention the cases of quantum dissipation, as well as of the nuclear optical potential.

NEW DEVELOPMENTS IN THE STUDY OFTIMEAS A QUANTUM OBSERVABLE

2008 ◽  
Vol 22 (12) ◽  
pp. 1877-1897 ◽  
Author(s):  
V. S. OLKHOVSKY ◽  
E. RECAMI
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Selfadjoint Operator ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
New Developments ◽  
Quantum Observable ◽  
Time In Quantum Mechanics

Some results are briefly reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the hermitian (more precisely, maximal hermitian, but non-selfadjoint) operator for Time which appears: (i) for particles, in ordinary non-relativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics).

scholarly journals Derivation of the Local Lorentz Gauge Transformation of a Dirac Spinor Field in Quantum Einstein-Cartan Theory

2018 ◽  
Author(s):  
Rainer Kühne
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Relativistic Quantum Mechanics ◽  
Dirac Spinor ◽  
Dirac Algebra ◽  
Gauge Transformations ◽  
Cartan Theory

I examine the groups which underly classical mechanics, non-relativistic quantum mechanics, special relativity, relativistic quantum mechanics, quantum electrodynamics, quantum flavourdynamics, quantum chromodynamics, and general relativity. This examination includes the rotations SO(2) and SO(3), the Pauli algebra, the Lorentz transformations, the Dirac algebra, and the U(1), SU(2), and SU(3) gauge transformations. I argue that general relativity must be generalized to Einstein-Cartan theory, so that Dirac spinors can be described within the framework of gravitation theory.

scholarly journals Application of relativistic quantum mechanics in radial problems and E/M equations

2021 ◽  
Vol 1869 (1) ◽  
pp. 012187
Author(s):  
G Y Arygunartha ◽  
N M D Janurianti ◽  
Y P Situmeang
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics

Stochastic microcausality in relativistic quantum mechanics

1984 ◽  
Vol 14 (9) ◽  
pp. 883-906 ◽  
Author(s):  
D. P. Greenwood ◽  
E. Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals Relativistic quantum mechanics, relativistic quantum fields

1978 ◽  
Vol 28 (1) ◽  
pp. 87
Author(s):  
Gian-Carlo Rota
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Fields
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