By introducing a new kind of variable we find simple Lagrangian and Hamiltonian descriptions of a classical particle interacting with an external non-Abelian gauge field. Both conventional particles and supersymmetric particles carrying pseudoclassical spin are considered. The physical interpretation of these models is discussed. The models are quantized fo!lowing Dirac's procedure. Finally, the isospin representations to which the resulting quantized particles belong are investigated.

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This paper is a sequel to a previous report (Aurell E. & Salomonson P., 1993), where we investigate the functional determinant of the laplacian on piece-wise flat two-dimensional surfaces, with conical singularities in the interior and/or corners on the boundary. Our results extend earlier investigations of the determinants on smooth surfaces with smooth boundaries. The differences to the smooth case are: a) different "interaction energies" between pairs of conical singularities than one would expect from a naive extrapolation of the results for a smooth surface; and b) "self-energies" of the singularities. In this paper we give the results for general simplicial complexes that are conformally related. Special attention is given to the case of disc topology with corners in the interior, and to the topology of a sphere, where we can compare with alternative computations in special cases where the spectra are known. We consider both Dirichlet and Neumann boundary conditions. In the limit when all corners are almost flat we recover the expressions for smooth surfaces with smooth boundaries.

Abstract:We consider a free (2k)-form gauge-field on a Euclidean (4k + 2)-manifold. The parameters needed to specify the action and the gauge-invariant observables take their values in spaces with natural complex structures. We show that the correlation functions can be written as a finite sum of terms, each of which is a product of a holomorphic and an anti-holomorphic factor. The holomorphic factors are naturally interpreted as correlation functions for a chiral (2k)-form, i.e. a (2k)-form with a self-dual (2k + 1)-form field strength, after Wick rotation to a Minkowski signature.

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