Infinite rank spinor and oscillator representations

Spinor Types in Infinite Dimensions

The Cartan Dirac classification of spinors into types is generalized to infinite dimensions. The main conclusion is that, in the statistical interpretation where such spinors are functions on Z2 , any real or quaternionic structure involves switching zeroes and ones. There results a maze of equivalence classes of each type. Some examples are shown in L2(T) . The classification of spinors leads ...

Invariant spinor representations of finite rotation matrices

On infinite rank integral representations of groups and orders of finite lattice type

Let = ZG be the integer group ring of a group, G, of prime order. A main result of this note is that every -module with a free underlying abelian group decomposes into a direct sum of copies of the well-known indecomposable -lattices of finite rank. The first part of the proof reduces the problem to one about countably generated modules, and works in a wider context of suitably restricted modul...

Scalarproducts of Spinor Field Functionals and State Representations in Nonlinear Spinor Field Quantum Theory

In preceding papers it was shown that in nonlinear spinor theory cross-sections of elementary particle scattering processes can be calculated only if the state representations and their scalar products are explicitly known. To obtain these quantities, functional quantum theory of the nonlinear spinor field was introducedIn this paper it is demonstrated that the introduction of functional scalar...

Infinite-dimensional Group Representations