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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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What is the i for the S-matrix? (Paperback, 1st ed. 2022)
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What is the i for the S-matrix? (Paperback, 1st ed. 2022)
Series: SpringerBriefs in Physics
Expected to ship within 10 - 15 working days
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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 i 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 i -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. To help with the
investigation of related questions, we introduce a number of tools,
including holomorphic cutting rules, new approaches to dispersion
relations, as well as formulae for local behavior of Feynman
integrals near branch points. This book is well suited for anyone
with knowledge of quantum field theory at a graduate level who
wants to become familiar with the complex-analytic structure of
Feynman integrals.
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