The quantization of systems with firstand second-class constraints within the coherentstate path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral measures for Lagrange multipliers, which in this case are in general expected to be elements of a Grassmann algebra, is explicated. Several examples with firstan...

Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann variety with its Plücker embedding. When the base field is finite, we consider the more general question of determining the maximum number of points on sect...

0039-3681/$ see front matter 2012 Elsevier Ltd. A http://dx.doi.org/10.1016/j.shpsa.2012.07.011 E-mail address: [email protected] This paper traces what I see as a Leibniz-inspired constructivist program through the eyes of the 19th century philosopher-mathematicians Herbart, Riemann and Grassmann, and then uses Grassmann’s algebra of points to build up levels of extension algebraically. Th...

We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representations of the spin algebra is discussed in the path integral setting. Finally it is shown how a 'fre...

This paper presents SinguLab, a graphical user interface for the singularity analysis of parallel robots. The algorithm is based on Grassmann-Cayley algebra. The proposed tool is interactive and introduces the designer to the singularity analysis performed by this method, showing all the stages along the procedure and eventually showing the solution algebraically and graphically, allowing as we...

In the so-called conformal model of Euclidean space of geometric algebra, circles receive a very elegant description by the outer product of three general points of that circle, forming what is called a tri-vector. Because circles are a special kind of conic section, the question arises, whether in general some kind of third order outer product of five points on a conic section (or certain line...

This is a continuation of the preceding paper (hep–ph/0108219). First of all we make a brief review of generalized coherent states based on Lie algebra su(1,1) and prove that the resolution of unity can be obtained by the curvature form of some bundle. Next for a set of generalized coherent states we define a universal bundle over the infinite–dimensional Grassmann manifold and construct the pu...