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 superior properties organization string theory. In particular, it allows one write down integral representations combining contributions large classes different topologies. However, calculating these integrals analytically without splitting them into sectors corresponding individual poses a formidable mathematical challenge. We summarize history state art this problem, including natural connections theory Bernoulli numbers polynomials multiple zeta values.