Geometric and Kinematic Dimensional Reduction in Quantum Field Theory

Abstract

Dimensional reduction in quantum field theory is discussed with emphasis on the difference between "geometric" versus "kinematic" dimensional reduction. It is shown how environmentally friendly renormalization can also be applied to the latter case. As concrete examples, finite temperature λϕ4 theory and the Regge limit of ϕ2ψ are considered. In the latter, crossover between large and small energies at fixed momentum transfer is considered and asymptotic forms of the crossover scaling functions are exhibited for all two-particle scattering processes in this channel.