What is the iε for the S-matrix? Holmfridur Sigridar Hannesdottir by Holmfridur Sigridar Hannesdottir, Sebastian Mizera 9783031182570, 303118257X instant download after payment.

This book provides a modern perspective on the analytic structure of
scattering amplitudes in quantum field theory, with the goal of
understanding and exploiting consequences of unitarity, causality, and
locality. It focuses on the question: Can the S-matrix be complexified
in a way consistent with causality? The affirmative answer has been well
understood since the 1960s, in the case of 2→2 scattering of the
lightest particle in theories with a mass gap at low momentum transfer,
where the S-matrix is analytic everywhere except at normal-threshold
branch cuts. We ask whether an analogous picture extends to realistic
theories, such as the Standard Model, that include massless fields,
UV/IR divergences, and unstable particles. Especially in the presence of
light states running in the loops, the traditional iε prescription for
approaching physical regions might break down, because causality
requirements for the individual Feynman diagrams can be mutually
incompatible. We demonstrate that such analyticity problems are not in
contradiction with unitarity. Instead, they should be thought of as
finite-width effects that disappear in the idealized 2→2 scattering
amplitudes with no unstable particles, but might persist at higher
multiplicity. To fix these issues, we propose an iε-like prescription
for deforming branch cuts in the space of Mandelstam invariants without
modifying the analytic properties of the physical amplitude. This
procedure results in a complex strip around the real part of the
kinematic space, where the S-matrix remains causal. We illustrate all
the points on explicit examples, both symbolically and numerically, in
addition to giving a pedagogical introduction to the analytic properties
of the perturbative S-matrix from a modern point of view.