GEOMETRIC AND KINEMATIC DIMENSIONAL REDUCTION IN QUANTUM-FIELD THEORY

Dimensional reduction in quantum field theory is discussed with emphas is on the difference between ''geometric'' versus ''kinematic'' dimens ional reduction. It is shown how environmentally friendly renormalisat ion can also be applied to the latter case. As concrete examples, fini te temperature lambda phi(4) theory and the Regge limit of phi(2) psi are considered. In the latter, crossover between large and small energ ies at fixed momentum transfer is considered and asymptotic forms of t he crossover scaling functions are exhibited for all two-particle scat tering processes in this channel.