Exact Solutions of Spin (Rabi) Precession, Transmission and Reflection in the Eckhart Potential

Barut, A. O.; Beker, H.

doi:10.1209/0295-5075/14/3/002

Cited by 8 publications

(2 citation statements)

References 5 publications

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“…• Pin structures [4,24,25,29,53] • Spinors on non-trivial manifolds [11,47,51,55] • Solution of the Dirac equation in electromagnetic fields [9,10] • CP T theorem [42,56,68,69,85,101] • Carruther's theorem [21,22,43,61,77,79,80,102,127] • CP T and cosmology [93,94,95] • Solar neutrinos [7] • Interference and CP T in neutron physics [117] • Majorana neutrinos and double lepton decay [35,59,67,71,109] • Non-trivial manifolds in condensed matter physics [73,76,110] • Phase factor observation [13,91,116] • Space and time reversal in atomic and molecular processes [16,17,70,72]…”

Section: E Collected Referencesmentioning

confidence: 99%

The Pin Groups in Physics: C, P and T

et al. 2001

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A simple, but not widely known, mathematical fact concerning the coverings of the full Lorentz group sheds light on parity and time reversal transformations of fermions. Whereas there is, up to an isomorphism, only one Spin group which double covers the orientation preserving Lorentz group, there are two essentially different groups, called Pin groups, which cover the full Lorentz group. Pin(1,3) is to O (1,3) what Spin(1,3) is to SO (1,3). The existence of two Pin groups offers a classification of fermions based on their properties under space or time reversal finer than the classification based on their properties under orientation preserving Lorentz transformations -provided one can design experiments that distinguish the two types of fermions. Many promising experimental setups give, for one reason or another, identical results for both types of fermions. These negative results are reported here because they are instructive. Two notable positive results show that the existence of two Pin groups is relevant to physics:• In a neutrinoless double beta decay, the neutrino emitted and reabsorbed in the course of the interaction can only be described in terms of Pin(3,1).• If a space is topologically nontrivial, the vacuum expectation values of Fermi currents defined on this space can be totally different when described in terms of Pin(1,3) and Pin(3,1).Possibly more important than the two above predictions, the Pin groups provide a simple framework for the study of fermions; it makes possible clear definitions of intrinsic parities and time reversal; it clarifies colloquial, but literally meaningless, statements. Given the difference between the Pin group and the Spin group it is useful to distinguish their representations, as groups of transformations on "pinors" and "spinors", respectively.The Pin(1,3) and Pin(3,1) fermions are twin-like particles whose behaviors differ only under space or time reversal.A section on Pin groups in arbitrary spacetime dimensions is included.

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Section: E Collected Referencesmentioning

confidence: 99%

The Pin Groups in Physics: C, P and T

et al. 2001

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“…Apart from this type of interaction and some ones relating to it [2], there exist few analytical and exact calculations treating this spin-¢eld interaction. Furthermore, if we replace the time dependence by a space one this list becomes more restricted [3].…”

Section: Introductionmentioning

confidence: 99%

Exact Path Integral for Neutral Spinning Particle in Interaction with Helical Magnetic Field

2001

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In this paper we consider a neutral spinning particle in interaction with a helical magnetic field using the path integral formalism. The spin matrices are replaced by two fermionic oscillators via the Schwinger model. The calculations are done explicitly with the help of an identity over two auxiliary fields. The propagator is exactly evaluated and the energy spectrum and the corresponding wave functions are then deduced.

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Spinning Particle in Interaction with a Time Dependent Magnetic Field: A Path Integral Approach

Benkhelil¹,

Aouachria²

2016

Intelligent Mathematics II: Applied Mathematics and Approximation Theory

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Exact Solutions of Spin (Rabi) Precession, Transmission and Reflection in the Eckhart Potential

Abstract: The bell-shaped Eckhart potential allows one to discuss the passage of neutrons, atoms, and other particles through various fields in a continuous manner. Here the exact formulae for the spin (or Rabi) precession, and for the coefficients of reflection and transmission are derived.

Cited by 8 publications

References 5 publications

The Pin Groups in Physics: C, P and T

The Pin Groups in Physics: C, P and T

Exact Path Integral for Neutral Spinning Particle in Interaction with Helical Magnetic Field

Spinning Particle in Interaction with a Time Dependent Magnetic Field: A Path Integral Approach

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