Semiclassical Methods in Quantum Field Theory

Composite Operators, Critical Phenomena, and the Dynamics of Emergence
Erscheinungsjahr 2027
ISBN: 978-3-032-46101-8
Verlag: Springer

Buch, Englisch, Format (B × H): 155 mm x 235 mm

Reihe: Lecture Notes in Physics

This book explains how semiclassical methods can be used to calculate the scaling dimensions of heavy composite operators—operators built from many copies of a quantum field—when conventional fixed-order perturbation theory becomes inadequate.

Starting from standard graduate-level quantum field theory, the text develops all necessary concepts from first principles, including conformal symmetry, primary operators, radial quantization, the state-operator correspondence, and operator mixing. The semiclassical framework is introduced through the free theory, where key results are derived in three independent ways, before being extended to interacting theories using tools such as Floquet theory, fluctuation determinants, the Gel’fand–Yaglom method, and the Gutzwiller trace formula.

A detailed case study of the critical O(N) model at the Wilson–Fisher fixed point illustrates the method in practice and compares its predictions with leading analytical and numerical results. Numerous worked examples, consistency checks, and appendices make the derivations transparent and reproducible.

This self-contained book is intended for graduate students, advanced researchers, and practitioners in theoretical and mathematical physics. Readers should have a standard background in graduate quantum field theory; no prior expertise in conformal field theory or semiclassical methods is assumed.

Zielgruppe

Graduate

Autoren/Hrsg.

Sannino, Francesco

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie

Inhaltsverzeichnis

Quantum Fields, Criticality, and Phases of Matter.- Conformal Symmetry and Primary Operators.- State Operator Correspondence.- Composite Operators and Mixing.- Free Theory: Three Roads to ??.- The Interacting Theory Blueprint.- Semiclassical Quantisation: Periodic Saddles, Fluctuations, and Floquet Theory.- The Four Dimensional O(N) f4 Theory.- Conclusions and Outlook.

Über Autor(innen)

Francesco Sannino is Professor of Theoretical Physics at the University of Southern Denmark, where he recently founded and now directs the Quantum Theory Center (hQTC). He also founded the Danish Institute for Advanced Study. He is Professor of Theoretical Physics at the University of Naples Federico II and Visiting Professor at the Institute for Particle Physics Phenomenology, Durham University. He pioneered studies of the conformal window and minimal walking technicolor, developed the first controlled four-dimensional asymptotically safe gauge–Yukawa theories, and advanced semiclassical methods for composite operators. He developed model-independent effective metric descriptions of quantum black holes and their observable signatures. He also established infinite heat order in ultraviolet-complete four-dimensional theories, where symmetry breaking persists at arbitrarily high temperatures. Beyond fundamental physics, he has applied renormalisation-group methods to pandemic dynamics and information theory to epidemiology and population dynamics. He was the founding director of CP³-Origins, a Danish National Research Foundation Centre of Excellence, and is Editor-in-Chief of . He is an elected member of the Royal Danish Academy of Sciences and Letters and the Finnish Academy of Science and Letters, and has received the Danish Elite Research Prize and a Carlsberg Foundation Semper Ardens: Advance grant. He has authored several hundred scientific publications and lectured widely on quantum field theory.