arXiv subjects

Uwe Müller

Publications and source records attributed to Uwe Müller.

4 recordsLinked to original sources

arXiv2026

Worldline representation of multiloop amplitudes in quantum electrodynamics

The worldline approach to quantum electrodynamics allows one to construct integral representations combining large numbers of Feynman diagrams. Here I review the state-of-the-art of a long-term effort to make this fact useful for actual multiloop calculations, such as of the scalar and spinor QED vacuum polarization functions and the electron anomalous magnetic moment. After a short historical introduction, and a discussion of the non-standard mathematical challenges involved, I focus on a recent calculation of the two-loop vacuum polarisation in scalar QED and some master integral formulas obtained in this context.

hep-th↗

arXiv2021

New Techniques for Worldline Integration

The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it allows one to write down integral representations combining the contributions of large classes of Feynman diagrams of different topologies. However, calculating these integrals analytically without splitting them into sectors corresponding to individual diagrams poses a formidable mathematical challenge. We summarize the history and state of the art of this problem, including some natural connections to the theory of Bernoulli numbers and polynomials and multiple zeta values.

hep-th↗

arXiv1997

Analytical Solution of the SL(2,R)/U(1) WZNW Black Hole Model

The gauged SL(2,R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. We have found a Lax pair representation for the non-linear equations of motion, and a B"acklund transformation. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory, and its fundamental solutions describe the general solution of the WZNW model as well. The physical and free fields are related by non-local transformations. The (anti-)chiral component of the energy-momentum tensor which factorizes into conserved quantities satisfying a non-linear algebra characteristic for parafermions assumes the expected canonical free field form. So the black hole model seems to be prepared for an exact canonical quantization.

hep-th↗

arXiv1997

Basis Invariants in Non--Abelian Gauge Theories

A basis of Lorentz and gauge-invariant monomials in non--Abelian gauge theories with matter is described, applicable for the inverse mass expansion of effective actions. An algorithm to convert an arbitrarily given invariant expression into a linear combination of the basis elements is presented. The linear independence of the basis invariants is proven.

hep-th↗