At the fundamental level, the interactions of elementary
particles are described by quantum gauge field theory. The
quantitative implications of these interactions are captured by
scattering amplitudes, traditionally computed using Feynman
diagrams. In the past decade tremendous progress has been made in
our understanding of and computational abilities with regard to
scattering amplitudes in gauge theories, going beyond the
traditional textbook approach. These advances build upon on-shell
methods that focus on the analytic structure of the amplitudes, as
well as on their recently discovered hidden symmetries. In fact,
when expressed in suitable variables the amplitudes are much
simpler than anticipated and hidden patterns emerge.
These modern methods are of increasing importance in
phenomenological applications arising from the need for
high-precision predictions for the experiments carried out at the
Large Hadron Collider, as well as in foundational mathematical
physics studies on the S-matrix in quantum field theory.
Bridging the gap between introductory courses on quantum field
theory and state-of-the-art research, these concise yet
self-contained and course-tested lecture notes are well-suited for
a one-semester graduate level course or as a self-study guide for
anyone interested in fundamental aspects of quantum field theory
and its applications.
The numerous exercises and solutions included will help readers
to embrace and apply the material presented in the main text.
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