Field Theory

A Path Integral Approach (2nd Edition)

By: Ashok Das

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Paperback | 19 June 2006 | Edition Number 2

At a Glance

Paperback
376 Pages

Edition Type
Revised

Dimensions(cm)
22.8 x 15.2 x 2.4

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New Edition: Field Theory (3rd Edition)This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.

Industry Reviews

"This book is well-written and very readable. The book is a self-consistent introduction to the path integral formalism and no prior knowledge of it is required, although the reader should be familiar with quantum mechanics. This book is an excellent guide for the reader who wants a good and detailed introduction to the path integral and most of its important application in physics. I especially recommend it for graduate students in theoretical physics and for researchers who want to be introduced to the powerful path integral methods."Mathematical Reviews"... this volume gives a clear and neat account by way of practical use. Accordingly, it will be a useful compact textbook for graduate students to learn quantum field theory by path integral approach, especially, to get quickly an overview of its technical side so as to know the applicability of its methods to various areas."Zentralblatt MATH

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Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Booktopia Publisher Services World Scientific Publishing

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Preface to the First Edition	p. vii
Preface to the Second Edition	p. ix
Introduction	p. 1
Particles and Fields	p. 1
Metric and Other Notations	p. 2
Functionals	p. 3
Review of Quantum Mechanics	p. 7
References	p. 10
Path Integrals and Quantum Mechanics	p. 11
Basis States	p. 11
Operator Ordering	p. 13
The Classical Limit	p. 20
Equivalence with the Schrodinger Equation	p. 22
Free Particle	p. 25
References	p. 30
Harmonic Oscillator	p. 31
Path Integral for the Harmonic Oscillator	p. 31
Method of Fourier Transform	p. 33
Matrix Method	p. 36
The Classical Action	p. 45
References	p. 51
Generating Functional	p. 53
Euclidean Rotation	p. 53
Time Ordered Correlation Functions	p. 59
Correlation Functions in Definite States	p. 61
Vacuum Functional	p. 64
Anharmonic Oscillator	p. 71
References	p. 73
Path Integrals for Fermions	p. 75
Fermionic Oscillator	p. 75
Grassmann Variables	p. 78
Generating Functional	p. 83
Feynman Propagator	p. 86
The Fermion Determinant	p. 91
References	p. 95
Supersymmetry	p. 97
Supersymmetric Oscillator	p. 97
Supersymmetric Quantum Mechanics	p. 102
Shape Invariance	p. 105
Example	p. 110
Supersymmetry and Singular Potentials	p. 111
Regularized Superpotential	p. 115
Alternate Regularization	p. 117
References	p. 118
Semi-Classical Methods	p. 121
WKB Approximation	p. 121
Saddle Point Method	p. 127
Semi-Classical Methods in Path Integrals	p. 130
Double Well Potential	p. 134
References	p. 142
Path Integral for the Double Well	p. 143
Instantons	p. 143
Zero Modes	p. 150
The Instanton Integral	p. 154
Evaluating the Determinant	p. 158
Multi-Instanton Contributions	p. 163
References	p. 166
Path Integral for Relativistic Theories	p. 167
Systems with Many Degrees of Freedom	p. 167
Relativistic Scalar Field Theory	p. 170
Feynman Rules	p. 181
Connected Diagrams	p. 184
References	p. 186
Effective Action	p. 187
The Classical Field	p. 187
Effective Action	p. 193
Loop Expansion	p. 200
Effective Potential at One Loop	p. 203
References	p. 208
Invariances and Their Consequences	p. 209
Symmetries of the Action	p. 209
Noether's Theorem	p. 212
Example	p. 215
Complex Scalar Field	p. 218
Ward Identities	p. 222
Spontaneous Symmetry Breaking	p. 226
Goldstone Theorem	p. 235
References	p. 236
Gauge Theories	p. 239
Maxwell Theory	p. 239
Non-Abelian Gauge Theory	p. 246
Path Integral for Gauge Theories	p. 255
BRST Invariance	p. 266
Ward Identities	p. 274
References	p. 278
Anomalies	p. 279
Anomalous Ward Identity	p. 279
Schwinger Model	p. 289
References	p. 307
Systems at Finite Temperature	p. 309
Statistical Mechanics	p. 309
Critical Exponents	p. 314
Harmonic Oscillator	p. 318
Fermionic Oscillator	p. 324
References	p. 326
Ising Model	p. 327
One Dimensional Ising Model	p. 327
The Partition Function	p. 332
Two Dimensional Ising Model	p. 337
Duality	p. 339
High and Low Temperature Expansions	p. 343
Quantum Mechanical Model	p. 349
Duality in the Quantum System	p. 356
References	p. 358
Index	p. 359
Table of Contents provided by Ingram. All Rights Reserved.

Field Theory

A Path Integral Approach (2nd Edition)

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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