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 Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

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.

scholarly journals What is time in quantum mechanics?

2014 ◽  
Vol 11 (07) ◽  
pp. 1460019
Author(s):  
Arkadiusz Jadczyk
Keyword(s):  
Quantum Mechanics ◽  
Quantum Dynamics ◽  
Relativistic Quantum ◽  
The Other ◽  
Relativistic Quantum Mechanics ◽  
Time Of Arrival ◽  
Free Particles ◽  
General Relativistic ◽  
Irreversible Quantum Dynamics ◽  
Time In Quantum Mechanics

Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by Kijowski and the event enhanced quantum theory (EEQT) method. It is suggested that for free particles the two methods may lead to the same result. On the other hand, the EEQT method can be easily geometrized within the framework of Galilei–Newton general relativistic quantum mechanics developed by M. Modugno and collaborators, and it can be applied to non-free evolutions. The way of geometrization of irreversible quantum dynamics based on dissipative Liouville equation is suggested.

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.

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].

Sign in / Sign up

Export Citation Format

Share Document