U(1)×SU(2)-gauge invariance of non-relativistic quantum mechanics, and generalized Hall effects

1992 ◽  
Vol 148 (3) ◽  
pp. 553-600 ◽  
Author(s):  
J. Fröhlich ◽  
U. M. Studer
Keyword(s):  
Quantum Mechanics ◽  
Gauge Invariance ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Hall Effects

GAUGE INVARIANCE IN NON-RELATIVISTIC MANY-BODY THEORY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2201-2208 ◽  
Author(s):  
J. FRÖHLICH ◽  
U.M. STUDER
Keyword(s):  
Quantum Mechanics ◽  
Gauge Invariance ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Spin Liquids ◽  
Many Body ◽  
Many Body Theory ◽  
Hall Effects ◽  
Body Theory

We review some recent results on the physics of two-dimensional, incompressible electron and spin liquids. These results follow from Ward identities reflecting the U(1) em × SU(2) spin -gauge invariance of non-relativistic quantum mechanics. They describe a variety of generalized quantized Hall effects.

Gauge Invariance in non-relativistic quantum mechanics

1994 ◽  
Vol 109 (10) ◽  
pp. 1115-1118 ◽  
Author(s):  
T. K. Rai Dastidar ◽  
K. Rai Dastidar
Keyword(s):  
Quantum Mechanics ◽  
Gauge Invariance ◽  
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 PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

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