Introduction to the Theory of Quantized Fields

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter

“…[19]) If for some integer j, the series Σ (1) a; b;j (u) is expressible in terms of Remiddi-Vermaseren functions (A.4b) with rational coefficients, then the sums Σ (1) a; b;j+i (u) for positive integers i can also be expressed in terms of functions of this type with rational coefficients.…”

“…Feynman diagrams [1] are a primary tool for calculating radiative corrections to any processes within the Standard Model or its extensions. With increasing of accuracy of measurements, more and more complicated diagrams (with increasing number of loops and legs and increasing numbers of variables associated with different particle masses) must be evaluated.…”

NSVZ scheme with the higher derivative regularization for SQED

“…(12) coincides with the invariant charge α inv [58], related with the polarization operator Π(α 0 , Λ/p) by the equation…”

“…Here we use the following renormalization procedure [58,59]: we define a renormalized coupling constant α(α 0 , Λ/µ), where µ is a renormalization parameter, requiring that the inverse invariant charge d −1 (α 0 (α, Λ/µ), Λ/p) is finite in the limit Λ → ∞ (and, therefore, in this limit depends only on α and µ/p). Then the renormalization constant Z 3 is defined according to the equation…”

On the linearity of the Schrödinger equation

“…This does not mean, however, that one cannot salvage the idea of the linear evolution. All one has to do is to employ the concept of a diffuse time introduced by Stueckelberg and elaborated further by Bogolubov and Shirkov [34]. The evolution equation of the state vector can then still be described by a linear Schrödinger-like equation (5).…”