212 research outputs found
Fractional Generalization of Liouville Equations
In this paper fractional generalization of Liouville equation is considered.
We derive fractional analog of normalization condition for distribution
function. Fractional generalization of the Liouvile equation for dissipative
and Hamiltonian systems was derived from the fractional normalization
condition. This condition is considered considered as a normalization condition
for systems in fractional phase space. The interpretation of the fractional
space is discussed.Comment: 9 pages, LaTe
Review of Some Promising Fractional Physical Models
Fractional dynamics is a field of study in physics and mechanics
investigating the behavior of objects and systems that are characterized by
power-law non-locality, power-law long-term memory or fractal properties by
using integrations and differentiation of non-integer orders, i.e., by methods
of the fractional calculus. This paper is a review of physical models that look
very promising for future development of fractional dynamics. We suggest a
short introduction to fractional calculus as a theory of integration and
differentiation of non-integer order. Some applications of
integro-differentiations of fractional orders in physics are discussed. Models
of discrete systems with memory, lattice with long-range inter-particle
interaction, dynamics of fractal media are presented. Quantum analogs of
fractional derivatives and model of open nano-system systems with memory are
also discussed.Comment: 38 pages, LaTe
Fractional Derivative Regularization in QFT
In this paper, we propose new regularization, where integer-order
differential operators are replaced by fractional-order operators.
Regularization for quantum field theories based on application of the Riesz
fractional derivatives of non-integer orders is suggested. The regularized loop
integrals depend on parameter that is the order alpha>0 of the fractional
derivative. The regularization procedure is demonstrated for scalar massless
fields in phi^4-theory on n-dimensional pseudo-Euclidean space-time.Comment: 15 pages, LaTe
- …