ar X iv : m at h - ph / 0 50 90 42 v 1 1 9 Se p 20 05 1 GENERALIZATION OF CONFORMAL TRANSFORMATIONS

ar X iv : m at h - ph / 0 50 90 39 v 1 1 9 Se p 20 05 JACK POLYNOMIALS IN SUPERSPACE : COMBINATORIAL ORTHOGONALITY

Jack polynomials in superspace, orthogonal with respect to a " combinatorial " scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace, orthogonal with respect to a " physical " scalar product, introduced in [5] as eigenfunctions of a supersymmetric quantum mechanical many-body problem. The results of this article rely on generalizing (to include an e...

ar X iv : 0 80 9 . 42 29 v 1 [ m at h - ph ] 2 4 Se p 20 08 Thermodynamic Limit for Spin Glasses . Beyond the Annealed Bound

Using a correlation inequality of Contucci and Lebowitz for spin glasses, we demonstrate existence of the thermodynamic limit for short-ranged spin glasses, under weaker hypotheses than previously available, namely without the assumption of the annealed bound.

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric

ar X iv : h ep - t h / 95 05 05 9 v 1 1 0 M ay 1 99 5 orthochronous The Conformal Spin and Statistics Theorem

ar X iv : m at h - ph / 0 40 90 33 v 1 1 5 Se p 20 04 HYPERELLIPTIC ADDITION LAW

We construct an explicit form of the addition law for hyperelliptic Abelian vector functions ℘ and ℘ ′. The functions ℘ and ℘ ′ form a basis in the field of hyperelliptic Abelian functions, i.e., any function from the field can be expressed as a rational function of ℘ and ℘ ′ .