The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the correspondingn-point distributions, called microlocal spectrum condition (SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.     

Crossover from Mott to Efros-Shklovskii variable range-hopping in Si:P

The low-temperature conductivity of uncompensated insulating Si:P with P concentration just below the metal-insulator (MI) transition shows with decreasingN a crossover from Mott variable range hopping (VRH) to Efros-Shklovskii VRH. From the concentration dependence of the Mott temperatureT _M a correlation-length exponent ν=1.1 is obtained which is compatible with the conductivity exponent μ=1.3 for metallic samples.