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El. knyga: Quantum Field Theory: The Why, What and How

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  • Formatas: PDF+DRM
  • Serija: Graduate Texts in Physics
  • Išleidimo metai: 02-Feb-2016
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319281735
Kitos knygos pagal šią temą:
Quantum Field Theory: The Why, What and HowDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Graduate Texts in Physics
  • Išleidimo metai: 02-Feb-2016
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319281735
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This bookdescribes, in clear terms, the Why, What and the How of Quantum Field Theory.The raison d"etre of QFT is explained by starting from the dynamics of arelativistic particle and demonstrating how it leads to the notion of quantumfields. Non-perturbative aspects and the Wilsonian interpretation offield theory are emphasized right from the start. Several interestingtopics such as the Schwinger effect, Davies-Unruh effect, Casimir effect andspontaneous symmetry breaking introduce the reader to the elegance and breadthof applicability of field theoretical concepts. Complementing the conceptualaspects, the book also develops all the relevant mathematical techniques indetail, leading e.g., to the computation of anomalous magnetic moment of the electronand the two-loop renormalisation of the self-interacting scalar field. Itcontains nearly a hundred problems, of varying degrees of difficulty, making itsuitable for both self-study and classroom use.

From Particles to Fields.- Disturbing the Vacuum.- From Fields to Particles.- Real Life I: Interactions.- Real Life II: Fermions and QED.- A Potpourri of Problems.

Recenzijos

The readership of this book consists of graduate students and researchers alike. Full of valuable insight, this modern treatise is sure to become a classic text on a subject of central importance. (Gert Roepstorff, zbMATH 1338.81002, 2016)

1 From Particles to Fields
1(44)
1.1 Motivating the Quantum Field Theory
1(2)
1.2 Quantum Propagation Amplitude for the Non-relativistic Particle
3(14)
1.2.1 Path Integral for the Non-relativistic Particle
4(2)
1.2.2 Hamiltonian Evolution: Non-relativistic Particle
6(3)
1.2.3 A Digression into Imaginary Time
9(4)
1.2.4 Path Integral for the Jacobi Action
13(4)
1.3 Quantum Propagation Amplitude for the Relativistic Particle
17(3)
1.3.1 Path Integral for the Relativistic Particle
17(3)
1.4 Mathematical Structure of G(x2; x1)
20(9)
1.4.1 Lack of Transitivity
20(1)
1.4.2 Propagation Outside the Light Cone
20(1)
1.4.3 Three Dimensional Fourier Transform of G(x2; x1)
21(3)
1.4.4 Four Dimensional Fourier Transform of G(x2; x1)
24(2)
1.4.5 The First Non-triviality: Closed Loops and G(x; x)
26(1)
1.4.6 Hamiltonian Evolution: Relativistic Particle
27(2)
1.5 Interpreting G(x2; x1) in Terms of a Field
29(10)
1.5.1 Propagation Amplitude and Antiparticles
32(3)
1.5.2 Why do we Really Need Antiparticles?
35(2)
1.5.3 Aside: Occupation Number Basis in Quantum Mechanics
37(2)
1.6 Mathematical Supplement
39(6)
1.6.1 Path Integral From Time Slicing
39(2)
1.6.2 Evaluation of the Relativistic Path Integral
41(4)
2 Disturbing the Vacuum
45(22)
2.1 Sources that Disturb the Vacuum
45(7)
2.1.1 Vacuum Persistence Amplitude and G(x2; X1)
45(5)
2.1.2 Vacuum Instability and the Interaction Energy of the Sources
50(2)
2.2 From the Source to the Field
52(12)
2.2.1 Source to Field: Via Functional Fourier Transform
53(4)
2.2.2 Functional Integral Determinant: A First Look at Infinity
57(6)
2.2.3 Source to the Field: via Harmonic Oscillators
63(1)
2.3 Mathematical Supplement
64(3)
2.3.1 Aspects of Functional Calculus
64(3)
3 From Fields to Particles
67(64)
3.1 Classical Field Theory
68(19)
3.1.1 Action Principle in Classical Mechanics
68(2)
3.1.2 From Classical Mechanics to Classical Field Theory
70(4)
3.1.3 Real Scalar Field
74(3)
3.1.4 Complex Scalar Field
77(1)
3.1.5 Vector Potential as a Gauge Field
78(3)
3.1.6 Electromagnetic Field
81(6)
3.2 Aside: Spontaneous Symmetry Breaking
87(3)
3.3 Quantizing the Real Scalar Field
90(6)
3.4 Davies-Unruh Effect: What is a Particle?
96(5)
3.5 Quantizing the Complex Scalar Field
101(3)
3.6 Quantizing the Electromagnetic Field
104(21)
3.6.1 Quantization in the Radiation Gauge
105(4)
3.6.2 Gauge Fixing and Covariant Quantization
109(6)
3.6.3 Casimir Effect
115(6)
3.6.4 Interaction of Matter and Radiation
121(4)
3.7 Aside: Analytical Structure of the Propagator
125(3)
3.8 Mathematical Supplement
128(3)
3.8.1 Summation of Series
128(1)
3.8.2 Analytic Continuation of the Zeta Function
129(2)
4 Real Life I: Interactions
131(58)
4.1 Interacting Fields
131(8)
4.1.1 The Paradigm of the Effective Field Theory
132(4)
4.1.2 A First Look at the Effective Action
136(3)
4.2 Effective Action for Electrodynamics
139(7)
4.2.1 Schwinger Effect for the Charged Scalar Field
142(1)
4.2.2 The Running of the Electromagnetic Coupling
143(3)
4.3 Effective Action for the λφ4 Theory
146(6)
4.4 Perturbation Theory
152(10)
4.4.1 Setting up the Perturbation Series
153(3)
4.4.2 Feynman Rules for the λφ4 Theory
156(4)
4.4.3 Feynman Rules in the Momentum Space
160(2)
4.5 Effective Action and the Perturbation Expansion
162(2)
4.6 Aside: LSZ Reduction Formulas
164(3)
4.7 Handling the Divergences in the Perturbation Theory
167(9)
4.7.1 One Loop Divergences in the λφ4 Theory
168(3)
4.7.2 Running Coupling Constant in the Perturbative Approach
171(5)
4.8 Renormalized Perturbation Theory for the λφ4 Model
176(4)
4.9 Mathematical Supplement
180(9)
4.9.1 Lea from the Vacuum Energy Density
180(4)
4.9.2 Analytical Structure of the Scattering Amplitude
184(5)
5 Real Life II: Fermions and QED
189(72)
5.1 Understanding the Electron
189(2)
5.2 Non-relativistic Square Roots
191(4)
5.2.1 Square Root of pαpaα and the Pauli Matrices
191(1)
5.2.2 Spin Magnetic Moment from the Pauli Equation
192(1)
5.2.3 How does φ Transform?
193(2)
5.3 Relativistic Square Roots
195(6)
5.3.1 Square Root of pαpα and the Dirac Matrices
195(2)
5.3.2 How does φ Transform?
197(3)
5.3.3 Spin Magnetic Moment from the Dirac Equation
200(1)
5.4 Lorentz Group and Fields
201(11)
5.4.1 Matrix Representation of a Transformation Group
201(1)
5.4.2 Generators and their Algebra
202(1)
5.4.3 Generators of the Lorentz Group
203(2)
5.4.4 Representations of the Lorentz Group
205(1)
5.4.5 Why do we use the Dirac Spinor?
206(2)
5.4.6 Spin of the Field
208(1)
5.4.7 The Poincare Group
209(3)
5.5 Dirac Equation and the Dirac Spinor
212(4)
5.5.1 The Adjoint Spinor and the Dirac Lagrangian
212(1)
5.5.2 Charge Conjugation
213(1)
5.5.3 Plane Wave solutions to the Dirac Equation
214(2)
5.6 Quantizing the Dirac Field
216(16)
5.6.1 Quantization with Anticommutation Rules
216(3)
5.6.2 Electron Propagator
219(3)
5.6.3 Propagator from a Fermionic Path Integral
222(2)
5.6.4 Ward Identities
224(2)
5.6.5 Schwinger Effect for the Fermions
226(5)
5.6.6 Feynman Rules for QED
231(1)
5.7 One Loop Structure of QED
232(18)
5.7.1 Photon Propagator at One Loop
234(11)
5.7.2 Electron Propagator at One Loop
245(3)
5.7.3 Vertex Correction at One Loop
248(2)
5.8 QED Renormalization at One Loop
250(5)
5.9 Mathematical Supplement
255(6)
5.9.1 Calculation of the One Loop Electron Propagator
255(2)
5.9.2 Calculation of the One Loop Vertex Function
257(4)
A Potpourri of Problems 261(18)
Annotated Reading List 279(2)
Index 281
Thanu Padmanabhan, currently Distinguished Professor at the Inter-University Centre for Astronomy and Astrophysics at Pune, India, is a theoretical physicist whose research spans a wide variety of topics in gravitation, cosmology and quantum gravity. He has authored 10 books and about 250 papers and reviews, many of which have had significant impact in their fields.  He was a Sackler Distinguished Astronomer of IoA, Cambridge, the President of the Cosmology Commission of the International Astronomical Union and the Chairman of the Astrophysics Commission of the International Union of Pure and Applied Physics and the recipient of Padma Shri, the Presidential medal which is the fourth highest civilian honor in India.
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