منابع مشابه
A Grassmann integral equation
The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann (Berezin) integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra Gm (i.e., a sought after element of t...
متن کاملGrassmann Integral Representation for Spanning Hyperforests
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff’s matrix-tree theorem. Furthermore, we show tha...
متن کاملHyperforests on the Complete Hypergraph by Grassmann Integral Representation
We study the generating function of rooted and unrooted hyperforests in a general complete hypergraph with n vertices by using a novel Grassmann representation of their generating functions. We show that this new approach encodes the known results about the exponential generating functions for the different number of vertices. We consider also some applications as counting hyperforests in the k...
متن کاملDirac Equation Path Integral: Interpreting the Grassmann Variables (*)(**)
S u m m a r y . A functional integral for a particle obeying the Dirac equation is presented. In earlier work (reviewed here) we showed that 1) such a particle could be described as a massless particle randomly flipping direction and helicity at a complex rate i/m and 2) its between-flips propagation could be written as a sum over paths for a Grassmann variable valued stochastic process. We her...
متن کاملStylized Caustics: Progressive Rendering of Animated Caustics
In recent years, much work was devoted to the design of light editing methods such as relighting and light path editing. So far, little work addressed the target-based manipulation and animation of caustics, for instance to a differently-shaped caustic, text or an image. The aim of this work is the animation of caustics by blending towards a given target irradiance distribution. This enables an...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 2003
ISSN: 0033-068X,1347-4081
DOI: 10.1143/ptp.110.589