| Description |
1 online resource (vi, 525 p.) : ill |
| Contents |
Cover -- Introduction to Quantum Field Theory with Applications to Quantum Gravity -- Copyright -- Preface -- Contents -- Part I Introduction to Quantum Field Theory -- 1 Introduction -- 1.1 What is quantum field theory, and some preliminary notes -- 1.2 The notion of a quantized field -- 1.3 Natural units, notations and conventions -- Comments -- 2 Relativistic symmetry -- 2.1 Lorentz transformations -- 2.2 Basic notions of group theory -- 2.3 The Lorentz and Poincaŕe groups -- 2.4 Tensor representation -- 2.5 Spinor representation -- 2.6 Irreducible representations of the Poincaré group -- Exercises -- Comments -- 3 Lagrange formalism in field theory -- 3.1 The principle of least action, and the equations of motion -- 3.2 Global symmetries -- 3.3 Noether's theorem -- 3.4 The energy-momentum tensor -- Exercises -- Comments -- 4 Field models -- 4.1 Basic assumptions about the structure of Lagrangians -- 4.2 Scalar field models -- 4.2.1 Real scalar fields -- 4.2.2 Complex scalar fields -- 4.2.3 Sigma model -- 4.3 Spinor field models -- 4.3.1 Equations of motion for a free spinor field -- 4.3.2 Properties of the Dirac spinors and gamma matrices -- 4.3.3 The Lagrangian for a spinor field -- 4.4 Models of free vector fields -- 4.4.1 Massive vector field -- 4.4.2 Massless vector fields -- 4.4.3 The gauge-invariant form of the Proca Lagrangian and Stüeckelberg fields -- 4.5 Scalar and spinor filelds interacting with an electromagnetic field -- 4.6 The Yang-Mills field -- Exercises -- Comments -- 5 Canonical quantization of free fields -- 5.1 Principles of canonical quantization -- 5.2 Canonical quantization in field theory -- 5.3 Canonical quantization of a free real scalar field -- 5.4 Canonical quantization of a free complex scalar field -- 5.5 Quantization of a free spinor field -- 5.6 Quantization of a free electromagnetic field -- Exercises |
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Comments -- 6 The scattering matrix and the Greenfunctions -- 6.1 Particle interactions and asymptotic states -- 6.2 Reduction of the S-matrix to Green functions -- 6.3 Generating functionals of Green functions and the S-matrix -- 6.4 The S-matrix and the Green functions for spinor fields -- 6.4.1 Definition of the spinor field S-matrix and Green functions -- 6.4.2 Generating functional of spinor field Green functions -- Exercises -- Comments -- 7 Functional integrals -- 7.1 Representation of the evolution operator by a functional integral -- 7.1.1 The functional integral for the one-dimensional quantum system -- 7.1.2 The functional integral for quantum system with a finite number of degrees of freedom -- 7.1.3 The functional integral in scalar field theory -- 7.2 Functional representation of Green functions -- 7.3 Functional representation of generating functionals -- 7.4 Functional integrals for fermionic theories -- 7.4.1 Grassmann algebra and anticommuting variables -- 7.4.2 Generating functional of spinor Green functions -- 7.5 Perturbative calculation of generating functionals -- 7.6 Properties of functional integrals -- 7.7 Techniques for calculating functional determinants -- Exercises -- Comments -- 8 Perturbation theory -- 8.1 Perturbation theory in terms of Feynman diagrams -- 8.2 Feynman diagrams in momentum space -- 8.3 Feynman diagrams for the S-matrix -- 8.4 Connected Green functions -- 8.5 Effective action -- 8.6 Loop expansion -- 8.7 Feynman diagrams in theories with spinor fields -- 8.7.1 Feynman diagrams in the theory with Yukawa coupling -- 8.7.2 Feynman diagrams in spinor electrodynamics -- Exercises -- Comments -- 9 Renormalization -- 9.1 The general idea of renormalization -- 9.2 Regularization of Feynman diagrams -- 9.2.1 Cut-off regularization -- 9.2.2 Pauli-Villars regularization -- 9.2.3 Dimensional regularization |
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10.10 Renormalization of Yang-Mills theory -- 10.10.1 Power counting in the Yang-Mills theory -- 10.10.2 Renormalization in the background field method -- 10.10.3 Renormalization in the Lorentz gauge -- Exercises -- Comments -- Part II Semiclassical and Quantum Gravity Models -- 11 A brief review of general relativity -- 11.1 Basic principles of general relativity -- 11.2 Covariant derivative and affine connection -- 11.3 The curvature tensor and its properties -- Exercises -- 11.4 The covariant equation for a free particle: the classical limit -- Exercises -- 11.5 Classical action for the gravity field -- 11.6 Einstein equations and the Newton limit -- Exercises -- 11.7 Some physically relevant solutions and singularities -- 11.7.1 The spherically-symmetric Schwarzschild solution -- 11.7.2 The standard cosmological model -- 11.8 The applicability of GR and Planck units -- Exercises -- 12 Classical fields in curved spacetime -- 12.1 General considerations -- 12.2 Scalar fields -- 12.2.1 Conformal symmetry of the metric-scalar model -- Exercises -- 12.3 Spontaneous symmetry breaking in curved space and induced gravity -- Exercises -- 12.4 Spinor fields in curved space -- 12.4.1 Tetrad formalism and covariant derivatives -- 12.4.2 The covariant derivative of a Dirac spinor -- 12.4.3 The commutator of covariant derivatives -- 12.4.4 Local conformal transformation -- 12.4.5 The energy-momentum tensor for the Dirac field -- Exercises -- 12.5 Massless vector (gauge) fields -- Exercises -- 12.6 Interactions between scalar, fermion and gauge fields -- Exercises -- 13 Quantum fields in curved spacetime: renormalization -- 13.1 Effective action in curved spacetime -- Exercises -- 13.2 Divergences and renormalization in curved space -- 13.2.1 The general structure of renormalization in the matter sector |
| Summary |
This textbook presents a detailed introduction to the general concepts of quantum field theory, with special emphasis on principal aspects of functional methods and renormalization in gauge theories, and includes an introduction to semiclassical and perturbative quantum gravity in flat and curved spacetimes |
| Notes |
Description based on online resource; title from PDF title page (Oxford Scholarship Online, viewed Aug. 4, 2021) |
| Subject |
Quantum field theory.
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Quantum gravity.
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Quantum field theory
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Quantum gravity
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| Form |
Electronic book
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| Author |
Shapiro, I. L. (Ilya Lvovitch)
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| ISBN |
9780192575319 |
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0192575317 |
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9780191874666 |
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0191874663 |
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