On the many-body problem in relativistic quantum mechanics

1985 ◽  
Vol 433 (4) ◽  
pp. 605-618 ◽  
Author(s):  
F.M. Lev
Keyword(s):  
Quantum Mechanics ◽  
Body Problem ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Many Body ◽  
The Many

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.

The Many-Body Problem in Quantum Mechanics

1969 ◽  
Vol 37 (1) ◽  
pp. 116-116 ◽  
Author(s):  
N. H. March ◽  
W. H. Young ◽  
S. Sampanthar ◽  
Donald H. Kobe
Keyword(s):  
Quantum Mechanics ◽  
Body Problem ◽  
Many Body ◽  
The Many

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.

scholarly journals NEW APPROACH TO N-BODY RELATIVISTIC QUANTUM MECHANICS

2007 ◽  
Vol 22 (11) ◽  
pp. 2007-2019 ◽  
Author(s):  
YING-QIU GU
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Many Body ◽  
New Approach ◽  
Consistent System ◽  
Nonrelativistic Approximation ◽  
Newtonian Dynamics ◽  
Classical Approximation ◽  
Self Consistent

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schrödinger equation for many-body.

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