Parametric Integral Formulas and Analytic Properties in Perturbation Theory

Analytic Perturbation Theory and Its Applications

Resummation Approach in QCD Analytic Perturbation Theory

We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start with a simple example of asymptotic power series for a zero-dimensional analog of the scalar g φ4 model. Then we give a short historic preamble of APT and show that renormgroup improvement of the QCD perturbation theory dictates to use the Fractional APT (FAPT). After that we discuss the (F)APT resummation o...

Analytic Perturbation Theory for QCD observables

The connection between ghost–free formulations of RG–invariant perturbation theory in the both Euclidean and Minkowskian regions is investigated. Our basic tool is the “double spectral representation”, similar to the definition of Adler function, that stems from first principles of local QFT. It relates real functions defined in the Euclidean and Minkowskian regions. On this base we establish a...

Topics in Representation Theory: The Weyl Integral and Character Formulas

We have seen that irreducible representations of a compact Lie group G can be constructed starting from a highest weight space and applying negative roots to a highest weight vector. One crucial thing that this construction does not easily tell us is what the character of this irreducible representation will be. The character would tell us not just which weights occur in the representation, but...

Multivariate Integral Perturbation Techniques - I (Theory)

We present a quasi-analytic perturbation expansion for multivariate N dimensional Gaussian integrals. The perturbation expansion is an infinite series of lower-dimensional integrals (one-dimensional in the simplest approximation). This perturbative idea can also be applied to multivariate Student-t integrals. We evaluate the perturbation expansion explicitly through 2 order, and discuss the con...