Perturbative Evolution and Regge Behaviour

The known analytic properties of the Compton amplitude at small $Q^2$ place significant constraints on its behaviour at large $Q^2$. This calls for a re-evaluation of the role of perturbative evolution in past fits to data.Comment: Revised figures 4 and

Soft and hard pomerons

Regge theory provides an excellent description of small-$x$ structure-function data from $Q^2=0$ up to the highest available values. The large-$Q^2$ data should also be described by perturbative QCD: the two descriptions must agree in the region where they overlap. However, at present there is a serious lack in our understanding of how to apply perturbative QCD at small $x$. The usual lowest-order or next-to-lowest order expansion is not valid, at least not until $Q^2$ becomes much larger than is usually assumed; a resummation is necessary, but as yet we do not know how to do this resummation.Comment: 8 pages, plain tex, with 6 figures embedded using epsf. Lecture at Workshop on New Trends in HERA Physics, Ringberg (june 1999

Photon Radiation in a Heat Bath

We discuss the bremsstrahlung of photons into a heat bath, and calculate from first principles the energy radiated. Even to lowest order the spectrum of the radiation at low frequency is no more singular than at zero temperature. In addition to the obvious contributions, this spectrum includes terms associated with fluctuations. [Revised version has additional explanations]Comment: 7 pages, plus 2 figures in pictex DAMTP 94/

Unusual high-pT jet events at HERA

We calculate the cross-section for events at HERA where the proton loses only a minute fraction of its initial energy, all of which goes into producing a single pair of transverse jets.Comment: 4 pages plus figure