ar X iv : m at h - ph / 0 50 90 56 v 1 2 6 Se p 20 05

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 : m at h - ph / 0 10 90 32 v 1 2 8 Se p 20 01 No zero energy states for the supersymmetric x 2 y 2 potential

We show that the positive supersymmetric matrix-valued differential operator H = px 2 + py 2 + x2y2 + xσ3 + yσ1 has no zero modes, i.e., Hψ = 0 implies ψ = 0.

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 - l at / 0 50 91 33 v 1 2 6 Se p 20 05 DESY 05 - 169 Edinburgh 2005 / 10 Structure of the Pion from Full Lattice QCD

D. Brömmel∗a,b, M. Diehla, M. Göckelerb, Ph. Häglerc, R. Horsleyd, D. Pleitere, P.E.L. Rakow f , A. Schäferb, G. Schierholza,e and J.M. Zanottie aTheory Group, Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany bInstitut für Theoretische Physik, Universtität Regensburg, 93040 Regensburg, Germany cInstitut für Theoretische Physik T39, Physik-Department der TU München, 85747 Garching, ...

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 ℘ ′ .