Time fractional quantum mechanics

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...

Extended 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...

Fractional 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...

On 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...

Arrival Time in Quantum Mechanics