  The quantization of gauge fields and gravitation on manifolds with boundary
makes it necessary to study boundary conditions which involve both normal and
tangential derivatives of the quantized field. The resulting one-loop
divergences can be studied by means of the asymptotic expansion of the heat
kernel, and a particular case of their general structure is here analyzed in
detail. The interior and boundary contributions to heat-kernel coefficients are
written as linear combinations of all geometric invariants of the problem. The
behaviour of the differential operator and of the heat kernel under conformal
rescalings of the background metric leads to recurrence relations which,
jointly with the boundary conditions, may determine these linear combinations.
Remarkably, they are expressed in terms of universal functions, independent of
the dimension of the background and invariant under conformal rescalings, and
new geometric invariants contribute to heat-kernel asymptotics. Such technique
is applied to the evaluation of the A(1) coefficient when the matrices
occurring in the boundary operator commute with each other. Under these
assumptions, the form of the A(3/2) and A(2) coefficients is obtained for the
first time, and new equations among universal functions are derived. A
generalized formula, relating asymptotic heat kernels with different boundary
conditions, is also obtained.

High Energy Physics - Theory