Supermultiplets and relativistic problems: I. The free particle with arbitrary spin in a magnetic field

1996 ◽  
Vol 29 (18) ◽  
pp. 6027-6042 ◽  
Author(s):  
M Moshinsky ◽  
Yu F Smirnov
Keyword(s):  
Magnetic Field ◽  
Free Particle ◽  
Arbitrary Spin

scholarly journals Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution

2014 ◽  
Vol 29 (29) ◽  
pp. 1450148
Author(s):  
Eva Gevorgyan ◽  
Armen Nersessian ◽  
Vadim Ohanyan ◽  
Evgeny Tolkachev
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Free Particle ◽  
Two Dimensional ◽  
Qualitative Character ◽  
Surface Of Revolution ◽  
Paraboloid Of Revolution ◽  
Kepler System ◽  
The Magnetic Field ◽  
Dimensional Surface

We define the Landau problem on two-dimensional ellipsoid, hyperboloid and paraboloid of revolution. Starting from the two-center McIntosh–Cisneros–Zwanziger (MICZ)–Kepler system and making the reduction into these two-dimensional surfaces, we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution in the magnetic field conserving the symmetry of the two-dimensional surface (Landau problem). For each case we figure out the values of parameter for which the qualitative character of the motion coincides with that of a free particle moving on the same two-dimensional surface. For the case of finite trajectories we construct the action-angle variables.

scholarly journals Times of arrival and gauge invariance

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210101
Author(s):  
Siddhant Das ◽  
Markus Nöth
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Arrival Time ◽  
Free Particle ◽  
Natural Generalization ◽  
Arrival Times ◽  
Quantum Flux ◽  
Freely Moving ◽  
Set Up ◽  
Aharonov Bohm

We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov–Bohm–Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski’s result is pointed out, along with an inescapable consequence of the ‘negative arrival times’ inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time set-up featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution, which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect notwithstanding).

scholarly journals VACUUM BIREFRINGENCE CAUSED BY ARBITRARY SPIN PARTICLES

2008 ◽  
Vol 23 (04) ◽  
pp. 245-248 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Laser Beam ◽  
Transverse Magnetic Field ◽  
Vacuum Polarization ◽  
Transverse Magnetic ◽  
Arbitrary Spin ◽  
Effective Lagrangian ◽  
Linearly Polarized ◽  
Higher Spin

We study the propagation of a linearly polarized laser beam in the external transverse magnetic field taking into consideration the vacuum polarization by arbitrary spin particles. Induced ellipticity of the beam is evaluated using the effective Lagrangian. With the help of the PVLAS experimental data, we obtain bounds on masses of charged higher spin particles contributed to ellipticity.

scholarly journals (j, 0) ⊕ (0, j) COVARIANT SPINORS AND CAUSAL PROPAGATORS BASED ON WEINBERG FORMALISM

1993 ◽  
Vol 02 (02) ◽  
pp. 397-422 ◽  
Author(s):  
D.V. AHLUWALIA ◽  
D.J. ERNST
Keyword(s):  
Perturbation Theory ◽  
Wave Equations ◽  
Lorentz Invariance ◽  
Free Particle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Arbitrary Spin ◽  
Definition Of ◽  
The Individual ◽  
Particle Propagator

A pragmatic approach to constructing a covariant phenomenology of the interactions of composite high-spin hadrons is proposed. Because there are no known wave equations without significant problems, we propose to construct the phenomenology without explicit reference to a wave equation. This is done by constructing the individual pieces of a perturbation theory and then utilizing the perturbation theory as the definition of the phenomenology. The covariant spinors for a particle of spin j are constructed directly from Lorentz invariance and the basic precepts of quantum mechanics following the logic put forth originally by Wigner and developed by Weinberg. Explicit expressions for the spinors are derived for j=1, 3/2 and 2. Field operators are constructed from the spinors and the free-particle propagator is derived from the vacuum expectation value of the time-order product of the field operators. A few simple examples of model interactions are given. This provides all the necessary ingredients to treat at a phenomenological level and in a covariant manner particles of arbitrary spin.

LANDAU LEVELS AND GEOMETRIC QUANTIZATION

1989 ◽  
Vol 04 (15) ◽  
pp. 3939-3949 ◽  
Author(s):  
J. R. KLAUDER ◽  
E. ONOFRI
Keyword(s):  
Magnetic Field ◽  
Landau Level ◽  
Free Particle ◽  
Geometric Quantization ◽  
Point Of View ◽  
Geometrical Approach ◽  
Higher Dimensional ◽  
Definition Of ◽  
The Magnetic Field ◽  
Quantum Counterpart

The geometrical approach to phase-space quantization introduced by Klauder [KQ] is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher dimensional configuration space; quantization corresponds to freezing the particle to its first Landau level. The Geometric Quantization [GQ] scheme appears as the natural technique to define the interaction with the magnetic field for a particle on a general Riemannian manifold. The freedom of redefining the operators' ordering makes it possible to select that particular definition of the Hamiltonian which is adapted to a specific polarization; in this way the first Landau level acquires the expected degeneracy. This unification with GQ makes it clear how algebraic relations between classical observables are or are not preserved under quantization. From this point of view all quantum systems appear as the low energy sector of a generalized theory in which all classical observables have a uniquely assigned quantum counterpart such that Poisson bracket relations are isomorphic to the commutation relations.

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