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Path integral quantization of the dynamics of a classical point particle with intrinsic spin

Patrick L. Nash

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BAug 1, 19951 citation

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

Hilal Benkhelil, Mekki Aouachria

Advances in intelligent systems and computingJan 1, 20160 citations

Path integral treatment for relativistic particles in external fields and quantized plane wave

Baya Bentag, Tahar Boudjedaa, L. Chétouani

Abstract The dynamics of relativistic particles of spin 0 and 1/2, interacting with an external electromagnetic field and a quantized plane wave, is studied using the path integral framework. We take advantage of the existing properties of the interaction to introduce a delta functional in order to calculate Green's functions. This simply reduces the problem to two coupled oscillators. The energy spectrum and wave functions are calculated for the spin 0 case and the analogy with Jaynes‐Cummings model is made to derive the energy spectrum for the spin 1/2 case.Abstract The dynamics of relativistic particles of spin 0 and 1/2, interacting with an external electromagnetic field and a quantized plane wave, is studied using the path integral framework. We take advantage of the existing properties of the interaction to introduce a delta functional in order to calculate Green's functions. This simply reduces the problem to two coupled oscillators. The energy spectrum and wave functions are calculated for the spin 0 case and the analogy with Jaynes‐Cummings model is made to derive the energy spectrum for the spin 1/2 case.

Annalen der PhysikFeb 1, 20000 citations

A path integral for a nonrelativistic spinor particle

Takashi Miura

By formulating a path integral in the SU(2) fiber bundle space, a nonrelativistic spinor particle moving in external electromagnetic fields is studied. This formulation is a direct extension of Schulman’s [Phys. Rev. 176, 1588 (1968)] continuous treatment for spin; it unifies all spin states to a spherical top model. This theory enjoys a definite classical theory with spin–orbital interactions and the corresponding semiclassical approximation for the path integral. This method is also applicable to a particle moving in a more general Yang–Mills field.By formulating a path integral in the SU(2) fiber bundle space, a nonrelativistic spinor particle moving in external electromagnetic fields is studied. This formulation is a direct extension of Schulman’s [Phys. Rev. 176, 1588 (1968)] continuous treatment for spin; it unifies all spin states to a spherical top model. This theory enjoys a definite classical theory with spin–orbital interactions and the corresponding semiclassical approximation for the path integral. This method is also applicable to a particle moving in a more general Yang–Mills field.

Journal of Mathematical PhysicsMay 1, 19901 citation

The Path Integral Formalism

is discussed. A new method is proposed for approximations of the corresponding path integral. It is shown that calculation of this integral does not give the Green's function of the Klein-Gordon equation but leads to the propagator of a scalar field in the twocomponent Feshbach-Villars formalism. The difficulties in calculating path integrals in the presence of nontrivial external fields are discussed. 1. In the present paper, we consider some methodological questions of relativistic quantum mechanics associated with quantization of the classical Hamtltonian of a relativistic charged particle with rest mass m in external fields: electromagnetic Au(r, t) (p = 0, 1, 2, 3) and scalar V(r, t):is discussed. A new method is proposed for approximations of the corresponding path integral. It is shown that calculation of this integral does not give the Green's function of the Klein-Gordon equation but leads to the propagator of a scalar field in the twocomponent Feshbach-Villars formalism. The difficulties in calculating path integrals in the presence of nontrivial external fields are discussed. 1. In the present paper, we consider some methodological questions of relativistic quantum mechanics associated with quantization of the classical Hamtltonian of a relativistic charged particle with rest mass m in external fields: electromagnetic Au(r, t) (p = 0, 1, 2, 3) and scalar V(r, t):

WORLD SCIENTIFIC eBooksSep 1, 20120 citations

Path Integral Quantization of the Sphere

Walter Reartes

Springer eBooksJan 1, 20043 citations

Path integral quantization of spinning particles interacting with crossed external electromagnetic fields

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