Description of Vorticity by Grassmann Variables and an Extension to Supersymmetry
نویسنده
چکیده
Hagen Kleinert’s early interest in particle physics quantum field theory served him well for his subsequent researches on statistical physics and collective phenomena. Therefore, on the occasion of a significant birthday, I offer him this essay, in which particle physics concepts are blended into a field theory for macroscopic phenomena: Fluid mechanics is enhanced by anticommuting Grassmann variables to describe vorticity, while an additional interaction for the Grassmann variables leads to supersymmetric fluid mechanics. 1 Précis of Fluid Mechanics (With No Vorticity) Let me begin with a précis of fluid mechanical equations [1]. An isentropic fluid is described by a matter density field ρ and a velocity field v, which satisfy a continuity equation involving the current j = ρv: ρ̇+∇ · (ρv) = 0 (1) and a force equation involving the pressure P : v̇ + v ·∇v = − ρ ∇P . (2) (Over-dot denotes differentiation with respect to time.) For isentropic fields, the pressure P is a function only of the density, and the right side of (2) may also be written as −∇V (ρ), where V (ρ) is the enthalpy, P (ρ) = ρV (ρ) − V (ρ), and √
منابع مشابه
Supersymmetric Fluid Mechanics
When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed from the Grassmann variables. Upon adding a further specific interaction with the Grassmann degrees of freedom, the model becomes supersymmetric.
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تاریخ انتشار 2000