Fractional Quantum Field Theory, Path Integral, and Stochastic Differential Equation for Strongly Interacting Many-Particle Systems

Abstract

While free and weakly interacting particles are well described by a a second-quantized nonlinear Schrödinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal Lévy walks rather than Gaussian random walks with perturbations.

References in corpus (5)

• Fractional Quantum Mechanics
• Extreme tunability of interactions in a ${}^7$Li Bose-Einstein condensate
• Cold Bosons in Optical Lattices
• Critical Behavior of a Trapped Interacting Bose Gas
• Kinetic theory for non-equilibrium stationary states in long-range interacting systems

Cited by in corpus (7)

• Observational Challenges for the Standard FLRW Model
• On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric
• Green function of the double fractional Fokker-Planck equation: Path integral and stochastic differential equations
• Fractional Effective Action at strong electromagnetic fields
• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• Effective Action and Field Equation for BEC from Weak to Strong Couplings
• Dynamic critical exponent in quantum long-range models