GREEN'S FUNCTIONS AND ORDERED EXPONENTIALS
CONTENTS INTRODUCTION HISTORICAL REMARKS LINEAR PHYSICS ORDERED EXPONENTIALS NOTES ELEMENTARY FUNCTIONAL METHODS FUNCTIONAL DIFFERENTIATION LINEAR TRANSLATION QUADRATIC (GAUSSIAN) TRANSLATION FUNCTIONAL INTEGRATION EXAMPLES DRAWN FROM QUANTUM ?ELD THEORY CLUSTER DECOMPOSITION SCHWINGER–FRADKIN METHODS PROPER-TIME REPRESENTATIONS OF SCHWINGER AND FRADKIN FRADKIN REPRESENTATIONS FOR QED AND QCD GAUGE STRUCTURE IN QED AND QCD SOLUBLE EXAMPLES: QUADRATIC FORMS AND PERTURBATIVE APPROXIMATIONS PAIR PRODUCTION IN GENERALIZED ELECTRIC ?ELDS LASERS AND CROSSED LASERS CLASSICAL CHARGED-PARTICLE PROPAGATION IN A LASER (EPW) ?ELD THE “SCALAR” LASER SOLUTION FOR GC[A] THE QED LASER SOLUTIONS FOR GC[A] AND L[A] PAIR PRODUCTION VIA CROSSED LASERS SPECIAL VARIANTS OF THE FRADKIN REPRESENTATION EXACT REPRESENTATIONS FOR SCALAR INTERACTIONS FINITE-QUADRATURE APPROXIMATIONS EXACT AND APPROXIMATE VECTORIAL INTERACTIONS THE STOJKOV VARIATION QUANTUM CHAOS AND VECTORIAL INTERACTIONS FIRST-QUANTIZATION CHAOS CHAOS SUPPRESSION IN SECOND QUANTIZATION FLUCTUATION-INDUCED CHAOS SUPPRESSION INFRARED APPROXIMATIONS THE BLOCH–NORDSIECK APPROXIMATION IR DAMPING AT LARGE MOMENTUM TRANSFERS EIKONAL SCATTERING AMPLITUDES IN PARTICLE PHYSICS IR APPROXIMATIONS AND RESCALING CORRECTIONS TO NON-LINEAR ODES MODELS OF HIGH-ENERGY, NON-ABELIAN SCATTERING AN ABELIAN SEPARATION THE QUASI-ABELIAN LIMIT LOOP, LADDER AND CROSSED-LADDER APPROXIMATIONS SUMMING ALL THE EIKONAL GRAPHS UNITARY ORDERED EXPONENTIALS ALGEBRAIC AND DIFFERENTIAL STRUCTURE THE SU(2) ADIABATIC LIMIT THE STOCHASTIC LIMIT FUNCTIONAL INTEGRATION OVER THE STOCHASTIC LIMIT 4? D3R ? |R ?R?|??2V (R?) + 4? DS? · |R ?R?|??V (R?) ?V (R?)?? |R ?R?| (13)