منابع مشابه
Fractional quantum mechanics
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and s...
متن کاملFractional statistical mechanics.
The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generaliz...
متن کاملExtended Fractional Supersymmetric Quantum Mechanics
Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the F th power of a conserved charge: H = Q with F = 2, 3, ... . This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable θ of order F , which satisfies θ = 0. Here, we present an alternative realization of such an algebra in which the int...
متن کاملFractional Supersymmetry and Quantum Mechanics
We present a set of quantum-mechanical Hamiltonians which can be written as the F th power of a conserved charge: H = Q F with [H, Q] = 0 and F = 2, 3, .... This new construction, which we call fractional supersymmetric quantum mechanics, is realized in terms of paragrassmann variables satisfying θ F = 0. Furthermore, in a pseudo-classical context, we describe fractional supersymmetry transform...
متن کاملOn Fractional Supersymmetric Quantum Mechanics: the Fractional Supersymmetric Oscillator
What is supersymmetry ? Roughly speaking SUperSYmmetry or SUSY can be defined as a symmetry between bosons and fermions (as considered as elementary particles or simply as degrees of freedom). In other words, SUSY is based on the postulated existence of operators Qα which transform a bosonic field into a fermionic field and vice versa. In the context of quantum mechanics, such symmetry operator...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2008.03.011