Mathematics of quantization and quantum fields/ Jan Derezinski, Christian Gerard

Includes bibliography and index

Introduction -- Vector spaces -- operators in Hilbert spaces -- tensor algebras -- Analysis in L square -- measures -- Algebras -- Anti-symmetric calculus -- Canonical communitation relations -- CCR on Fock space -- Symplectic invariance of CCR in finite-dimensions -- Symplectic invariance of the CCR on Fock spaces -- Canonical anti-commutation relations -- CAR on Fock spaces -- Orthogonal invariance of CAR algebras -- Clifford relations -- Orthogonal invariance of the CAR on FOCK spaces -- Quasi-free states -- Dynamics of quantum fields -- Quantum fields on space-time -- Diagrammatics -- Euclidean approach for bosons -- Interacting bosonic fields

nifying topics that are scattered throughout the literature, this book offers a definitive review of mathematical aspects of quantization and quantum field theory. It presents both basic and advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. It begins with a discussion of the mathematical structures underlying free bosonic or fermionic fields: tensors, algebras, Fock spaces, and CCR and CAR representations. Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and researchers in mathematics and physics. This title, first published in 2013, has been reissued as an Open Access publication on Cambridge Core.