"Improved power counting with harmonic polynomials"

Joseph C. Várilly

(Departamento de Matemáticas, Universidad Costa Rica)

A basic task in quantum field theory is the construction of
time-ordered products of two (or more) quantum fields. The
mathematical difficulty is that Heaviside functions do not like to be multiplied with other distributions. This difficulty is best overcome, whenever possible, by the algorithm of power counting.
One of the last works of Raymond Stora (1930-2015) declared that this procedure can be improved if a certain relevant polynomial is harmonic (in the Minkowskian sense). It so happens that harmonic polynomials are also intimately tied up with principal-value regularizations. The emerging improved renormalization procedure will be developed in detail for field strengths with spin or helicity 1 or 2. Its extension to higher spins will also be indicated..

Facultad de Ciencias

Seminario de Física Teórica
Universidad de Zaragoza