ZETA-FUNCTION FOR THE LAPLACE OPERATOR ACTING ON FORMS IN A BALL WITHGAUGE BOUNDARY-CONDITIONS

The Laplace operator acting on antisymmetric tensor fields in a D-dime nsional Euclidean ball is studied, Gauge-invariant local boundary cond itions (absolute and relative ones, in the language of Gilkey) are con sidered, The eigenfuctions of the operator are found explicitly for al l values of D. Using in a row a number of basic techniques, as Mellin transforms, deformation and shifting of the complex integration contou r and pole compensation, the zeta function of the operator is obtained . From its expression, in particular, zeta(0) and zeta'(0) are evaluat ed exactly, A table is given in the paper for D = 3,4,..., 8. The func tional determinants and Casimir energies are obtained for D = 3, 4,... ,6.