Generalized Yang-Mills actions from Dirac operator determinants

We consider the quantum effective action of Dirac fermions on four dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R^4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present an explicit computation proving this fact, generalized to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.Comment: LaTex, 26 page

On anomalies and noncommutative geometry

I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.Comment: 6 pages, latex, no figures. Proceedings of ``34. Internationale Universit\"atswochen f\"ur Kern- und Teilchenphysik Schladming'', Schladming March 1995, Springer Verlag (to appear

An explicit solution of the (quantum) elliptic Calogero-Sutherland model

We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling constant and particle number. Our solution gives explicit formulas for an elliptic deformation of the Jack polynomials.Comment: 16 pages, Contribution to SPT 2004 in Cala Gonone (Sardinia, Italy) v2 and v3: minor correction

Second quantization of the elliptic Calogero-Sutherland model

We use loop group techniques to construct a quantum field theory model of anyons on a circle and at finite temperature. We find an anyon Hamiltonian providing a second quantization of the elliptic Calogero-Sutherland model. This allows us to prove a remarkable identity which is a starting point for an algorithm to construct eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland Hamiltonian (this algorithm is elaborated elsewhere). This paper contains a detailed introduction, technical details and proofs.Comment: 36 page