Physical Review A

Quantization of a particle with a force quadratic in the velocity

J. Sá Borges, L.N. Epele, Huner Fanchiotti A, Carlos A. García Canal, F. R. A. Sim�o

Published Sep 1, 1988• 21 citations

Abstract

The quantization of a system subject to a force quadratic in the velocity and position dependence is carried out in the phase-space path-integral framework. The resulting Hamiltonian coincides with that obtained by using the Weyl-ordering canonical prescription.

DOI: 10.1103/physreva.38.3101

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Physical Review A

Quantization of a particle with a force quadratic in the velocity

J. Sá Borges, L.N. Epele, Huner Fanchiotti A, Carlos A. García Canal, F. R. A. Sim�o

Published Sep 1, 1988• 21 citations

Publisher

Abstract

DOI: 10.1103/physreva.38.3101

Related papers

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This article uses the phse space path integral method to find the propagator for a particle with a force quadratic in velocity. Two specific canonical transformations has been used for this purpose.

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We consider the Weyl quantized relativistic Hamiltonian H = H A ∔Ф defined through the quadratic form corresponding to the classical symbol $\sqrt {{{{{\left( {p - A\left( x \right)} \right)}}^{2}} + {{m}^{2}}}} + \Phi \left( x \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {p,x} \right) \in {{\mathbb{R}}^{d}} \times {{\mathbb{R}}^{d}},$ (1.1)of a spinless particle with mass m ≥ 0 in an electromagnetic field (e.g. Landau-Lifschitz [9]), where the light velocity c is taken to be equal to 1.We consider the Weyl quantized relativistic Hamiltonian H = H A ∔Ф defined through the quadratic form corresponding to the classical symbol $ \sqrt {{{{{\left( {p - A\left( x \right)} \right)}}^{2}} + {{m}^{2}}}} + \Phi \left( x \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {p,x} \right) \in {{\mathbb{R}}^{d}} \times {{\mathbb{R}}^{d}}, $ (1.1)of a spinless particle with mass m ≥ 0 in an electromagnetic field (e.g. Landau-Lifschitz [9]), where the light velocity c is taken to be equal to 1.

Birkhäuser Basel eBooksJan 1, 19952 citations

Quantization in nonlinear coordinates via Hamiltonian path integrals

Ashok Kumar Kapoor

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsMay 15, 198413 citations

We consider the Weyl quantized relativistic Hamiltonian H = H A ∔Ф defined through the quadratic form corresponding to the classical symbol

\sqrt {{{{{\left( {p - A\left( x \right)} \right)}}^{2}} + {{m}^{2}}}} + \Phi \left( x \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {p,x} \right) \in {{\mathbb{R}}^{d}} \times {{\mathbb{R}}^{d}},

(1.1)of a spinless particle with mass m ≥ 0 in an electromagnetic field (e.g. Landau-Lifschitz [9]), where the light velocity c is taken to be equal to 1.