ar X iv : m at h - ph / 0 31 00 07 v 1 7 O ct 2 00 3 Green functions of the Dirac equation with magnetic - solenoid field

ar X iv : m at h - ph / 0 11 00 12 v 1 9 O ct 2 00 1 Functional Equations and Poincare Invariant Mechanical Systems

We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincaré algebra:

ar X iv : m at h - ph / 0 31 00 10 v 1 8 O ct 2 00 3 Obstructions , Extensions and Reductions . Some applications of Cohomology ∗

After introducing some cohomology classes as obstructions to orientation and spin structures etc., we explain some applications of cohomology to physical problems, in especial to reduced holonomy in M and F -theories.

ar X iv : h ep - l at / 0 11 00 06 v 2 3 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h - ph / 0 31 10 01 v 3 6 O ct 2 00 4 Clifford Valued Differential Forms , Algebraic Spinor Fields , Gravitation , Electromagnetism and ” Unified ” Theories ∗

ar X iv : m at h - ph / 0 61 00 39 v 1 1 7 O ct 2 00 6 Harmonic analysis on a Galois field and its subfields

Complex functions χ(m) where m belongs to a Galois field GF (p ℓ), are considered. Fourier transforms , displacements in the GF (p ℓ) × GF (p ℓ) phase space and symplectic Sp(2, GF (p ℓ)) transforms of these functions are studied. It is shown that the formalism inherits many features from the theory of Galois fields. For example, Frobenius transformations are defined which leave fixed all funct...