Finite temperature spinor pregeometry

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...

Finite Temperature Effective Theories

High-temperature and dense matter of elementary particles appears in several areas of physics. The rst and most familiar example is the Universe at the early stages of its expansion. The Big Bang theory (for reviews see, e.g. ) states that the Universe was hot and dense in the past, with a temperature ranging from a few eV up to the Planck scale MPl 10 GeV. Another place, where matter exists in...