THE FADDEEV–POPOV METHOD FOR THE RELATIVISTIC LANDAU PROBLEM

1992 ◽  
Vol 07 (12) ◽  
pp. 2825-2839
Author(s):  
C. FARINA ◽  
J. GAMBOA
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Conservation Laws ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Proper Time ◽  
Landau Levels ◽  
Integral Approach ◽  
Relativistic Problem ◽  
Popov Method

We use the Faddeev–Popov method to calculate explicitly the path integral propagator for a relativistic spinless charged particle in the presence of a constant magnetic field. We obtain the conservation laws in the path integral approach. We also establish the equivalence between the Faddeev–Popov method and the Fock–Schwinger proper time approach. Finally, after proposing a suitable regularization prescription for the non-relativistic problem, we obtain the Landau levels directly from the path integral result.

THE RELATIVISTIC LANDAU PROBLEM FOR FERMIONS

1992 ◽  
Vol 07 (29) ◽  
pp. 2731-2739
Author(s):  
J. GAMBOA
Keyword(s):  
Magnetic Field ◽  
Conservation Laws ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Exact Expression ◽  
Integral Formalism ◽  
Planar Case ◽  
Spinning Particle ◽  
Relativistic Models ◽  
Popov Method

Using the Faddeev-Popov method an exact expression for the propagator of a relativistic spinning particle in a constant magnetic field is found. The conservation laws and the generators of the magnetic group are obtained in the path integral formalism. Both the relativistic and non-relativistic models are discussed in the planar case.

scholarly journals LANDAU LEVELS: TRANSLATIONS AND ROTATIONS IN A CONSTANT ELECTROMAGNETIC FIELD

1990 ◽  
Vol 05 (18) ◽  
pp. 3533-3548 ◽  
Author(s):  
S. FUBINI
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Charged Particle ◽  
Constant Magnetic Field ◽  
Constant Electric Field ◽  
Landau Levels ◽  
Translation Invariant ◽  
Constant Electromagnetic Field ◽  
Relative Coordinates ◽  
Charged System

The spectrum of a charged particle in a constant magnetic field consists of equally-spaced Landau levels En = ℏω (n +½) which are infinitely degenerate. Using the magnetic group we show that this structure is present for any charged system which is rotation-translation invariant. The result is extended to the case of a constant electric field. The separation between baricentric and relative coordinates is discussed.

Uncertainty relation for a charged particle in a constant magnetic field

1987 ◽  
Vol 55 (4) ◽  
pp. 375-376 ◽  
Author(s):  
Walter C. Henneberger ◽  
Mojtaba Jafarpour
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Constant Magnetic Field ◽  
Uncertainty Relation

Extended Vacuum Solutions and their Elementary Excitations of the Yang–Mills Gauge Theory

1997 ◽  
Vol 12 (27) ◽  
pp. 2037-2045
Author(s):  
T. Tajima ◽  
Q. Niu
Keyword(s):  
Magnetic Field ◽  
Gauge Theory ◽  
Constant Magnetic Field ◽  
Vacuum Solution ◽  
Landau Levels ◽  
The Other ◽  
Elementary Excitations ◽  
Circularly Polarized ◽  
Yang Mills ◽  
Vacuum Solutions

A number of nontrivial vacua of the Yang–Mills gauge theory which are extended in space are derived. For the vacuum solution with a constant "magnetic" field of one color species, the elementary excitations of the other species are circularly polarized, with a spectrum much like the Landau levels of nonrelativistic electrons in a constant magnetic field.

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