Springer International Publishing Switzerland 2014. — 556 pp. — (Mathematical Physics Studies). — ISBN: 978-3-319-09948-4 (Print) 978-3-319-09949-1 (Online).Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.Leading experts in the field present the latest advances in quantum field theories Reflecting the diversity of approaches and tools developed in the last years With a part dedicated to (semi-)classical field theoriesA Derived and Homotopical View on Field Theories Perturbative Algebraic Quantum Field Theory Lectures on Mathematical Aspects of (twisted) Supersymmetric Gauge Theories Snapshots of Conformal Field Theory Faddeev’s Quantum Dilogarithm and State-Integrals on Shaped Triangulations A Higher Stacky Perspective on Chern–Simons Theory Factorization Homology in Deligne-Beilinson Cohomology in U(1) Chern-Simons Theories Semiclassical Quantization of Classical Field Theories Local BRST Cohomology for AKSZ Field Theories: A Global Approach Symplectic and Poisson Geometry of the Moduli Spaces of Flat Connections Over Quilted Surfaces Groupoids, Frobenius Algebras and Poisson Sigma Models Notes on Factorization Algebras, Factorization Homology and Applications
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