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E-raamat: Field Theory: A Path Integral Approach (Third Edition)

(Univ Of Rochester, Usa & Saha Inst Of Nuclear Physics, India & Institute Of Physics, Bhubaneswar, India)
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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. All the existing chapters of the previous edition have been expanded for more clarity. The chapter on anomalies and the Schwinger model has been completely rewritten for better logical clarity. Two new chapters have been added at the request of students and faculty worldwide. The first describes Schwinger's proper time method with simple examples both at zero and at finite temperature while the second develops the idea of zeta function regularization with simple examples. This latest edition is a comprehensive and much expanded version of the original text.

Preface to the First Edition vii
Preface to the Second Edition ix
Preface to the Third Edition x
1 Introduction
1(12)
1.1 Particles and fields
1(1)
1.2 Metric and other notations
1(2)
1.3 Functional
3(4)
1.4 Review of quantum mechanics
7(4)
1.5 References
11(2)
2 Path integrals and quantum mechanics
13(22)
2.1 Basis states
13(2)
2.2 Operator ordering
15(3)
2.3 Feynman path integral
18(5)
2.4 The classical limit
23(2)
2.5 Equivalence with the Schrodinger equation
25(4)
2.6 Free particle
29(4)
2.7 References
33(2)
3 Harmonic oscillator
35(24)
3.1 Path integral for the harmonic oscillator
35(4)
3.2 Method of Fourier transform
39(3)
3.3 Matrix method
42(9)
3.4 The classical action
51(7)
3.5 References
58(1)
4 Generating functional
59(26)
4.1 Euclidean rotation
59(7)
4.2 Time ordered correlation functions
66(2)
4.3 Correlation functions in definite states
68(4)
4.4 Vacuum functional
72(8)
4.5 Anharmonic oscillator
80(3)
4.6 References
83(2)
5 Path integrals for fermions
85(24)
5.1 Fermionic oscillator
85(4)
5.2 Grassmann variables
89(5)
5.3 Generating functional for fermions
94(4)
5.4 Feynman propagator
98(5)
5.5 The fermion determinant
103(4)
5.6 References
107(2)
6 Supersymmetry
109(26)
6.1 Supersymmetric oscillator
109(6)
6.2 Supersymmetric quantum mechanics
115(4)
6.3 Shape invariance
119(5)
6.4 Example
124(1)
6.5 Supersymmetry and singular potentials
125(8)
6.5.1 Regularized superpotential
130(2)
6.5.2 Alternate regularization
132(1)
6.6 References
133(2)
7 Semi-classical methods
135(24)
7.1 WKB approximation
135(6)
7.2 Saddle point method
141(4)
7.3 Semi-classical methods in path integrals
145(5)
7.4 Double well potential
150(8)
7.5 References
158(1)
8 Path integral for the double well
159(26)
8.1 Instantons
159(8)
8.2 Zero modes
167(4)
8.3 The instanton integral
171(4)
8.4 Evaluating the determinant
175(6)
8.5 Multi-instanton contributions
181(3)
8.6 References
184(1)
9 Path integral for relativistic theories
185(22)
9.1 Systems with many degrees of freedom
185(4)
9.2 Relativistic scalar field theory
189(11)
9.3 Feynman rules
200(2)
9.4 Connected diagrams
202(3)
9.5 References
205(2)
10 Effective action
207(24)
10.1 The classical field
207(6)
10.2 Effective action
213(8)
10.3 Loop expansion
221(3)
10.4 Effective potential at one loop
224(6)
10.5 References
230(1)
11 Invariances and their consequences
231(32)
11.1 Symmetries of the action
231(3)
11.2 Nother's theorem
234(7)
11.2.1 Example
238(3)
11.3 Complex scalar field
241(4)
11.4 Ward identities
245(5)
11.5 Spontaneous symmetry breaking
250(9)
11.6 Goldstone theorem
259(2)
11.7 References
261(2)
12 Gauge theories
263(44)
12.1 Maxwell theory
263(8)
12.2 Non-Abelian gauge theory
271(10)
12.3 Path integral for gauge theories
281(12)
12.4 BRST symmetry
293(9)
12.5 Ward identities
302(3)
12.6 References
305(2)
13 Anomalies
307(34)
13.1 Anomalous Ward identity
307(11)
13.2 Schwinger model
318(22)
13.3 References
340(1)
14 Systems at finite temperature
341(20)
14.1 Statistical mechanics
341(5)
14.2 Critical exponents
346(5)
14.3 Harmonic oscillator
351(6)
14.4 Fermionic oscillator
357(2)
14.5 References
359(2)
15 Ising model
361(36)
15.1 One dimensional Ising model
361(6)
15.2 The partition function
367(5)
15.3 Two dimensional Ising model
372(2)
15.4 Duality
374(5)
15.5 High and low temperature expansions
379(6)
15.6 Quantum mechanical model
385(8)
15.7 Duality in the quantum system
393(3)
15.8 References
396(1)
16 Proper time formalism
397(34)
16.1 Scalar propagator in D dimensions
397(8)
16.2 Evaluating determinants
405(10)
16.2.1 Bosonic oscillator
406(6)
16.2.2 Fermionic oscillator
412(3)
16.3 Effective actions
415(14)
16.3.1 Zero temperature
418(6)
16.3.2 Finite temperature
424(5)
16.4 References
429(2)
17 Zeta function regularization
431(40)
17.1 Riemann zeta function
431(9)
17.1.1 Euler's zeta function
431(5)
17.1.2 Riemann's zeta function
436(4)
17.2 Zeta function regularization
440(4)
17.2.1 Partition function for the bosonic oscillator
442(2)
17.3 Heat kernel method
444(9)
17.3.1 Bosonic propagator in flat space-time
449(4)
17.4 Expansion of the heat kernel
453(7)
17.5 Schwinger model in curved space-time
460(9)
17.6 References
469(2)
Index 471
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