Phase space quantum mechanics - Direct

Nasiri, S.; Sobouti, Y.; Taati, F.

doi:10.1063/1.2345109

Cited by 14 publications

(12 citation statements)

References 21 publications

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“…The interested reader is invited to consult the original papers [1,2] for further details. In the framework of the proposed formalism, the extended Lagrangian can be written as…”

Section: The Integrals Of Motionmentioning

confidence: 99%

“…Here and will be considered as independent -number operators on the integrable complex function ( , ). One of the key assumptions of extended phase space quantization [1,2] is the differential operators and commutation brackets for and borrowed from the conventional quantum mechanics as follows:…”

Section: The Integrals Of Motionmentioning

confidence: 99%

“…From its historical development, this aspect of statistical quantum mechanics, unfortunately, has attracted little attention. However, much use has been made of the technique of ordering of canonical coordinates ( ) and momenta ( ) in quantum mechanics [1,2]. It was observed that the concept of an extended Lagrangian L( , ,,) in phase space allows a subsequent extension of Hamilton's principle to actions minimum along the actual trajectories in ( , )-, rather than in -space.…”

Section: Introductionmentioning

confidence: 99%

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Classical Analog of Extended Phase Space SUSY and Its Breaking

Ter-Kazarian

2013

ISRN Mathematical Physics

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We derive the classical analog of the extended phase space quantum mechanics of the particle with odd degrees of freedom which gives rise to ( = 2)-realization of supersymmetry (SUSY) algebra. By means of an iterative procedure, we find the approximate ground state solutions to the extended Schrödinger-like equation and use these solutions further to calculate the parameters which measure the breaking of extended SUSY such as the ground state energy. Consequently, we calculate a more practical measure for the SUSY breaking which is the expectation value of an auxiliary field. We analyze nonperturbative mechanism for extended phase space SUSY breaking in the instanton picture and show that this has resulted from tunneling between the classical vacua of the theory. Particular attention is given to the algebraic properties of shape invariance and spectrum generating algebra.

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“…The interested reader is invited to consult the original papers [1,2] for further details. In the framework of the proposed formalism, the extended Lagrangian can be written as…”

Section: The Integrals Of Motionmentioning

confidence: 99%

Section: The Integrals Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Classical Analog of Extended Phase Space SUSY and Its Breaking

Ter-Kazarian

2013

ISRN Mathematical Physics

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“…Each alternative has its own Wigner-type evolution equation which, if Taylor-expanded in powers of the Planck constant, its zeroth order term is the classical Liouville equation. More striking is the fact that for the nD simple harmonic oscillators, Wigner's evolution equation is exactly equation (2.1) and is the phase space transformation of Schroedinger equation for quadratic potentials[7].…”

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confidence: 99%

An oscillator-representation of elementary particles

Sobouti

2018

J. Phys. Commun.

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Two dynamical systems with same symmetry should have features in common, and as far as their shared symmetry is concerned, one may represent the other. The three light quark constituent of the hadrons, (a) have an approximate flavor SU(3) f symmetry, (b) have an exact color SU(3) c symmetry, and (c) as spin 1 2 particles, have a Lorentz SO(3, 1) symmetry. So does a 3D harmonic oscillator. (a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 oscillators are not identical. (b) The 3 directions of oscillation have the permutation symmetry. This enables one to create three copies of unbreakable SU(3) symmetry for each oscillator, and mimic the color of the elementary particles. (c) The Lagrangian of the 3D oscillator has the SO(3,1) symmetry. This can be employed to accommodate the spin of the particles. In this paper we propose a one-to-one correspondence (a) between the eigen modes of the Poisson bracket operator of the 3D oscillator and the flavor multiplets of the particles, and (b) between the permuted modes of the oscillator and the color and anticolor multiplets of the particles. The bi-colored gluons are represented by the generators of the color SU(3) c symmetry of the oscillator. Harmonic oscillators are common place objects and, wherever encountered, are analytically solvable. Elementary particles, on the other hand, are abstract entities far from one's reach. Understanding of one may help a better appreciation of the other.

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“…Carroll [10] has shown that there are generalized quantum theories for which the quantum potential depends on the wave function. Using the extended phase space formulation of quantum mechanics [11,12,13], Nasiri [9] has shown that in the Wigner representation of phase space quantum mechanics [14] the quantum potential is removed from the dynamical equation of a particle in linear and harmonic potentials keeping the Hamilton-Jacobi equation form invariant. It seems that the Husimi representation could be another candidate to release the quantum potential.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation

Bahrami¹

2008

SIGMA

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Abstract. In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function.

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Phase space quantum mechanics - Direct

Cited by 14 publications

References 21 publications

Classical Analog of Extended Phase Space SUSY and Its Breaking

Classical Analog of Extended Phase Space SUSY and Its Breaking

An oscillator-representation of elementary particles

Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation

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