Title: Selected topics on the general properties of quantum field theory :
Authors: Strocchi, F.
Date: 1993
Publisher: World Scientific,
Physical description: xii, 173 pages ; 22 cm.
Language: English
Contents: I. General Properties of Relativistic Quantum Field Theory. 1.1. Quantum mechanical properties and relativistic invariance. 1.2. Relativistic covariance, microcausality and ultraviolet singularities. 1.3. Wightman functions and their properties. 1.4. Quantum mechanical interpretation of correlation functions. Reconstruction theorem -- II. Analyticity Properties of Wightman Functions. 2.1. Spectral condition and analytic continuation to the forward tube. 2.2. Lorentz covariance and analyticity in the extended tube. 2.3. Locality and analyticity in the permuted extended tube -- III. Euclidean Quantum Field Theory. 3.1. The Schwinger functions. 3.2. Euclidean invariance and symmetry. 3.3. Reflection positivity. 3.4. Cluster property. 3.5. Laplace transform condition. 3.6. Reconstruction of relativistic QFT from euclidean QFT -- IV. Examples. 4.1. The free scalar field. 4.2. The generalized free field. 4.3. The derivative coupling model. 4.4. The free euclidean field. 4.5. The current operator. Schwinger terms -- V. Some General Results in QFT. 5.1. TCP theorem. 5.2. Spin-Statistics theorem. 5.3. The local structure of QFT. The Reeh-Schlieder theorem -- VI. Local Formulation of Gauge Theories. 6.1. Local and renormalizable gauges. Local charged field algebra. i. Gauss' law and locality. ii. Local and non-local gauges. 6.2. Physical interpretation. Subsidiary condition. 6.3. Hilbert space structure condition. 6.4. Modified Wightman axioms -- Appendix 1. General results on indefinite inner product spaces -- VII. Examples. 7.1. Free quantum electrodynamics. 7.2. The massless scalar field in two dimensions. 7.3. Fermion bosonization. 7.4. The Schwinger model. i. Gauge invariance and mass. ii. Confinement of charged particles. iii. Large gauge transformations and vacuum structure. iv. Breaking of chiral symmetry and mass gap. (Solution of the U(1) problem). 7.5. The Thirring model -- Appendix 2. Remark on the general properties of local formulations of gauge theories. VIII. Exercises.
Notes: "These lecture notes arose from courses given at the International School for Advanced Studies (Trieste) and at the Scuola normale superiore (Pisa) in 1990-91"--P. vii.
Subject headings (LCSH): Quantum field theory.