منابع مشابه
Stochastic Calculus and Anticommuting Variables
A theory of integration for anticommuting paths is described. This is combined with standard Itô calculus to give a geometric theory of Brownian paths on curved supermanifolds. This lecture concerns a generalisation of Brownian motion and Itô calculus to include paths in spaces of anticommuting variables. The motivation for this work comes originally from physics, where anticommuting variables ...
متن کاملOn families of anticommuting matrices
Let e1, . . . , ek be complex n× n matrices such that eiej = −ejei whenever i 6= j. We conjecture that • rk(e21) + rk(e 2 2) + · · ·+ rk(e 2 k) ≤ O(n log n). We show that (i). rk(en1 ) + rk(e n 2 ) + · · ·+ rk(e n k ) ≤ O(n log n), (ii). if e21, . . . , e 2 k 6= 0 then k ≤ O(n), (iii). if e1, . . . , ek have full rank, or at least n−O(n/ log n), then k = O(log n). (i) implies that the conjectur...
متن کاملA Feynman-Kac Formula for Anticommuting Brownian Motion
Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Itô integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are cons...
متن کاملZero Derivations
In LI 31.2, J. Rubach proposes a modified version of OT that features derivations. In the present article I argue that, while some modification to the original formulation by Prince and Smolensky is needed, the correct one is not to re-introduce derivations, but rather to take fuller advantage of OT’s inherent parallelism. I propose that outputs must be related not only to inputs, but to other,...
متن کاملDerivations and skew derivations of the Grassmann algebras
Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let Λn = K⌊x1, . . . , xn⌋ be the Grassmann algebra over a commutative ring K with 12 ∈ K, and δ be a skew K-derivation of Λn. It is proved that δ is a unique sum δ = δ ev + δ of an even and odd skew derivation. Explicit formulae are given for δ and δ via the ele...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04642-0