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This book begins with a brief historical review of the early applications of standard dispersion relations in particle physics. It then presents the modern perspective within the Standard Model, emphasizing the relation of analyticity together with alternative tools applied to strong interactions, such as perturbative and lattice quantum chromodynamics (QCD), as well as chiral perturbation theory. The core of the book argues that, in order to improve the prediction of specific hadronic observables, it is often necessary to resort to methods of complex analysis more sophisticated than the simple Cauchy integral. Accordingly, a separate mathematical chapter is devoted to solving several functional analysis optimization problems. Their applications to physical amplitudes and form factors are discussed in the following chapters, which also demonstrate how to merge the analytic approach with statistical analysis tools. Given its scope, the book offers a valuable guide for researchers working in precision hadronic physics, as well as graduate students who are new to the field.

Quantum chromodynamics. --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Particles (Nuclear physics) --- Quantum electrodynamics --- Nuclear physics. --- Mathematical physics. --- Nuclear Physics, Heavy Ions, Hadrons. --- Mathematical Methods in Physics. --- Mathematical Applications in the Physical Sciences. --- Physical mathematics --- Physics --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Mathematics --- Heavy ions. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Ions

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This thesis makes significant advances in the quantitative understanding of two intrinsically linked yet technically very different phenomena in quantum chromodynamics (QCD). Firstly, the thesis investigates the soft probe of strong interaction topological fluctuations in the quark-gluon plasma (QGP) which is made possible via the anomalous chiral transport effects induced by such fluctuations. Here, the author makes contributions towards establishing the first comprehensive tool for quantitative prediction of the chiral magnetic effect in the QGP that is produced in heavy ion collision experiments. Secondly, the thesis deals with the hard probe of strongly coupled QGP created in heavy-ion collisions. In particular, this study addresses the basic question related to the nonperturbative color structure in the QGP via jet energy loss observables. The author further develops the CUJET computational model for jet quenching and uses it to analyze the topological degrees of freedom in quark-gluon plasma. The contributions this thesis makes towards these highly-challenging problems have already generated widespread impacts in the field of quark-gluon plasma and high-energy nuclear collisions.

Quantum chromodynamics. --- Nuclear physics. --- Quantum theory. --- Nuclear Physics, Heavy Ions, Hadrons. --- Elementary Particles, Quantum Field Theory. --- Mathematical Physics. --- Numerical and Computational Physics, Simulation. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Heavy ions. --- Elementary particles (Physics). --- Quantum field theory. --- Mathematical physics. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Ions --- Mathematics