Spinor Pregeometry at Finite Tempereture

Invariant spinor representations of finite rotation matrices

Multiboundary Algebra as Pregeometry

It is well known that the Clifford Algebras, and their quaternionic and octonionic subalgebras, are structures of fundamental importance in modern physics. Geoffrey Dixon has even used them as the centerpiece of a novel approach to Grand Unification. In the spirit of Wheeler’s notion of ”pregeometry” and more recent work on quantum set theory, the goal of the present investigation is to explore...

Algebraic Quantum Mechanics and Pregeometry

We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the al...

Random ℓ-colourable structures with a pregeometry

We study nite l-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are rst randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satis ed but apart from this in a rando...

BLOW-UPS OF P AT n POINTS AND SPINOR VARIETIES

Abstract. Work of Dolgachev and Castravet-Tevelev establishes a bijection between the 2 weights of the half-spin representations of so2n and the generators of the Cox ring of the variety Xn which is obtained by blowing up P n−3 at n points. We derive a geometric explanation for this bijection, by embedding Cox(Xn) into the even spinor variety (the homogeneous space of the even half-spin represe...