Asymptotic conservation laws for loop level soft photon theorems

Abstract

In the thesis we study new asymptotic conservation laws in electromagnetism that could reproduce the loop effects in the soft expansion of QED amplitudes We also explore interesting properties of asymptotic expansions of the classical as well as quantum gauge field Incorporating the effect of long range electromagnetic force present in four spacetime dimensions acting on the scattered particles we analyse the new modes that arise in the asymptotic radiative field emitted in a generic classical scattering process We show that there exist new asymptotic conservation laws Qm m 1 2 that are obeyed by the classical radiative field Building on the m 1 2 cases we propose that there exists a conservation law for every m The corresponding charges are made of modes of the asymptotic electromagneticfield that appear at O e2m 1 and are expected to be conserved exactly The asymptotic behaviour of the gauge field is modified in the quantum theory due to use of Feynman boundary condition We derive the analogue of the first of above asymptotic conservation laws upon imposing Feynman boundary condition on the radiative field We also discuss purely quantum modes in the Feynman solution which are absent in the classical radiative solution These modes lead to quantum corrections to the asymptotic charges We anticipate that the Qm charges imply existence of m loop soft theorems for every m In particular we show that the Ward identity for the Q1 charge is equivalent to the 1 loop exact subleading soft photon theorem for loop level QED amplitudes We demonstrate this equivalence in the context of massless scalar QED in presence of dynamical gravity This asymptotic charge is directly related to the dressing of fields due to long range forces In presence of gravity the new feature is that the soft photon also acquires a dressing due to longrange gravitational force and contributes to the asymptotic charge We expect this story to hold beyond 1 loop as well The Q2 conser newline newline