Lectures on Particles' and Field Theory

✍ Scribed by Brandeis University. Summer Institute in Theoretical Physics

• Publisher: M.I.T. Press
• Year: 1969
• Tongue: English
• Leaves: 600
• Category: Library

✦ Table of Contents

Instead of cover
Editors and authors
Title page
Date-line
CONTENTS
Foreword
Perturbation Theory Anomalies (Stephen L. Adler)
CONTENTS
1. Introduction and review of perturbation theory
1.1 Review of quantum electrodynamics and renormalization theory
2. The VVA triangle anomaly
2.1 Ward identity in perturbation theory
2.2 Impossibility of eliminating the anomaly by a subtraction
2.3 Anomaly for general axial-vector current matrix element
2.4 Coordinate space calculation
3. Consequences of the triangle anomaly
3.1 Renormalization of the axial-vector vertex
3.2 Radiative corrections to $\nu_l l$ scattering
3.3 Connection between $\gamma_5$ invariance and a conserved axial-vector current in massless electrodynamics
3.4 Low energy theorem for $2 \mbox{im}_0 j^5(x)$
4. Absence of radiative corrections
4.1 General argument
4.2 Explicit second order calculation
5. Generalizations of our results: $\pi^0$ decay; otherWard identity anomalies
5.1 The $\sigma$-models
5.2 Low energy theorem for $\pi_0$ decay
5.3 Other Ward identity anomalies
6. Connection between Ward identity anomalies and commutator (Bjorken-limit) anomalies
6.1 Schwinger terms, seagulls, the reduction formula and $T$ and $T^\ast$ products in QED
6.2 The Bjorken-Johnson-Low method
6.3 Anomalous commutators associated with the VVA triangle anomaly
7. Applications of the Bjorken limit
7.1 Radiative corrections to hadronic $\beta$ decay
7.2 Asymptotic sum rules and asymptotic cross section relations
8. Breakdown of the Bjorken limit in perturbation theory
8.1 Computational results
8.2 Discussion
References
Dynamical Applications of the Veneziano Formula (Stanley Mandelstam)
CONTENTS
1. Considerations motivating the Veneziano formula
2. The Veneziano formula for the four-point scalar amplitude
3. The Veneziano formula for the $n$-point scalar amplitude
Requirements of the model
Projective transformations
The Koba-Nielsen formalism
Alternative expression for the Koba-Nielsen formula
4. Factorization
Single factorization
Ghosts and Ward identities
Multiple factorizations
5. The operator formalism
Principles of the formalism
Projective transformations
Linear dependences
The twist operator
The Sciuto vertex
6. Veneziano-type quark models
Meson-meson and meson-baryon amplitudes
Exotic resonances
Non-planar multi-particle Veneziano amplitude
7. Higher-order Feynman-like diagrams
Formula for the single-loop planar diagram
Derivation from unitarity
Non-planar diagrams
The divergence problem
References
Dynamic and Algebraic Symmetries (Steven Weinberg)
CONTENTS
1. Introduction
2. Hadron electrodynamics
A. Gauge invariance of the first kind
B. Gauge invariance of the second kind
C. The LSZ theorem — a review
D. Charge non-renormalization
E. Zero mass photons
F. Lorentz invariance — a review
G. Soft photon vertices
H. Elastic photon scattering: general properties
I. Elastic photon scattering: low energy limits
J. The Drell-Hearn sum rule
K. Other soft photon theorems and sum rules
L. Algebraization
3. Local symmetries
A. General realizations
B. Currents
C. Goldstone bosons
D. Non-linear realizations for Goldstone bosons
4. Chirality
A. The pion as a Goldstone boson
B. One soft pion
C. Chirality and weak interactions
D. Two soft pions —pion scattering lengths
E. The Adler-Weisberger sum rule
F. The $x$-matrix
G. Algebraization
H. Chiral dynamics
I. Summing soft pions
References
Local Operator Products and Renormalization in Quantum Field Theory (Wolfhart Zimmermann)
TABLE OF CONTENTS
I. Introduction
II. Renormalization
1. Definition of the finite part of a Feynman integral by Bogoliubov's method
2. Explicitform of the renormalized integrand
3. Convergence of renormalized integrals
4. Bogoliubov's method of renormalization in coordinate space
5. Feynman rules for $A^4$-coupling
6. Unitarity equations
III. Operator product expansions
1. General derivation
2. Notation of Green's functions
3. Normal operator products
4. Algebraic identities
5. Singularities of $TA(x_1)A(x_2)$ at short distances
6. Expansion of $TA(x_1)A(x_2)$ with respect to normal products of constant degree
7. Wilson's expansion of $TA(x_1)A(x_2)$ and derivatives. Light cone singularities
8. Singularities of $TA(x_1)A(x_2)A(X_3)$
IV. Local field equations
1. General remarks
2. $A^4$ coupling
2a. Field equations in general form
2b. Renormalization conditions
2c. The current operator
2d. Discussion of the field equation
3. Pseudoscalar meson-nucleon interaction
3a. Formal Lagrangian
3b. Effective Lagrangian. Local operator products and operator product expansions
3c. Field equations and renormalization conditions
3d. Nucleon field equation and current operator
3e. Meson field equation and current operator
3f. Comparison with formal field equations
4. Neutral vector meson theory
4a. Formal Lagrangian
4b. Effective Lagrangian and renormalization conditions
4c. Dirac equation
4d. Vector meson field equation and Brandt's form of the current operator
5. Quantum electrodynamics
6. Further problems concerning current operators in renormalized perturbation theory
Acknowledgments
Footnotes and references
Index