دانلود کتاب Renormalization: An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion

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contents
1 Introduction
2 Quantum field theory
2.1 Scalar field theory
2.2 Functional-integral solution
2.3 Renormalization
2.4 Ultra-violet regulators
2.5 Equations of motion for Green\'s functions
2.6 Symmetries
2.7 Ward identities
2.8 Perturbation theory
2.9 Spontaneously broken symmetry
2.10 Fermions
2.11 Gauge theories
2.12 Quantizing gauge theories
2.13 BRS invariance and Slavnov-Taylor identities
2.14 Feynman rules for gauge theories
2.15 Other symmetries of (2.11.7)
2.16 Model field theories
3 Basic examples
3.1 One-loop self-energy in phi3 theory
3.1.1 Wick rotation
3.1.2 Lattice
3.1.3 Interpretation of divergence
3.1.4 Computation
3.2 Higher order
3.3 Degree of divergence
3.3.1 phi3 at d = 6
3.3.2 Why may Z be zero and yet contain divergences?
3.3.3 Renormalizability and non-renormalizability
3.4 Renormalization group
3.4.1 Arbitrariness in a renormalized graph
3.4.2 Renormalization prescriptions
3.5 Dimensional regularization
3.6 Minimal subtraction
3.6.1 Definition
3.6.2 d = 6
3.6.3 Renormalization group and minimal subtraction
3.6.4 Massless theories
3.7 Coordinate space
4 Dimensional regularization
4.1 Definition and axioms
4.2 Continuation to small d
4.3 Properties
4.4 Formulae for Minkowski space
4.4.1 Schwinger parameters
4.4.2 Feynman parameters
4.5 Dirac matrices
4.6 gamma_5and epsilon
5 Renormalization
5.1 Divergences and subdivergences
5.2 Two-loop self-energy in (phi3)6
5.2.1 Fig. 5.1.2
5.2.2 Differentiation with respect to external momenta
5.2.3 Fig. 5.1.3
5.3 Renormalization of Feynman graphs
5.3.1 One-particle-irreducible graph with no subdivergences
5.3.2 General case
5.3.3 Application of general formulae
5.3.4 Summary
5.4 Three-loop example
5.5 Forest formula
5.5.1 Formula
5.5.2 Proof
5.6 Relation to L
5.7 Renormalizability
5.7.1 Renormalizability and non-renormalizability
5.7.2 Cosmological term
5.7.3 Degrees of renormalizability
5.7.4 Non-renormalizability
5.7.5 Relation of renormalizability to dimension of coupling
5.7.6 Non-renormalizable theories of physics
5.8 Proof of locality of counterterms; Weinberg\'s theorem
5.8.1 Degree of counterterms equals degree of divergence
5.8.2 \\bar{R}(G) is finite if delta{G) is negative
5.8.3 Asymptotic behavior
5.9 Oversubtractions
5.9.1 Mass-shell renormalization and oversubtraction
5.9.2 Remarks
5.9.3 Oversubtraction on IPR graphs
5.10 Renormalization without regulators: the BPHZ scheme
5.11 Minimal subtraction
5.11.1 Definition
5.11.2 \\bar{MS} renormalization
6 Composite operators
6.1 Operator-product expansion
6.2 Renormalization of composite operators: examples
6.2.1 Renormalization of phi2
6.2.2 Renormalization of (phi)2(x)(phi)2(y)
6.3 Definitions
6.4 Operator mixing
6.5 Tensors and minimal subtraction
6.6 Properties
Property 1. Linearity
Property 2. Differentiation is distributive
Property 3. Simple equation of motion
Property 4. Equation of motion times operator
Property 5. Ward identities
Property 6. Non-renormalization of current
6.7 Differentiation with respect to parameters in L
6.8 Relation of renormalizations of phi2 and m2
7 Renormalization group
7.1 Change of renormalization prescription
7.1.1 Change of parametrization
7.1.2 Renormalization-prescription dependence
7.1.3 Low-order examples
7.2 Proof of RG invariance
7.3 Renormalization-group equation
7.3.1 Renormalization-group coefficients
7.3.2 RG equation
7.3.3 Solution
7.4 Large-momentum behavior of Green\'s functions
7.4.1 Generalizations
7.5 Varieties of high- and low-energy behavior
7.5.1 Asymptotic freedom
7.5.2 Maximum accuracy in an asymptotically free theory
7.5.3 Fixed point theories
7.5.4 Low-energy behavior ofmassless theory
7.6 Leading logarithms, etc.
7.6.1 Renormalization-group logarithms
7.6.2 Non-renormalization-group logarithms
7.6.3 Landau ghost
7.7 Other theories
7.8 Other renormalization prescriptions
7.9 Dimensional transmutation
7.10 Choice of cut-off procedure
7.10.1 Example: phi4 self-energy
7.10.2 RG coefficients
7.10.3 Computation of g0 and Z; asymptotically free case
7.10.4 Accuracy needed for g0
7.10.5 m20
7.10.6 Non-asymptotically free case
7.11 Computing renormalization factors using dimensional regularization
7.12 Renormalization group for composite operators
8 Large-mass expansion
8.1 A model
8.2 Power-counting
8.2.1 Tree graphs
8.2.2 Finite graphs with heavy loops
8.2.3 Divergent one-loop graphs
8.2.4 More than one loop
8.3 General ideas
8.3.1 Renormalization prescriptions with manifest decoupling
8.3.2 Dominant regions
8.4 Proof of decoupling
8.4.1 Renormalization prescription R* with manifest decoupling
8.4.2 Definition of R*
8.4.3 IR finiteness of C*(\\Gamma)
8.4.4 Manifest decoupling for R*
8.4.5 Decoupling theorem
8.5 Renormalization-group analysis
8.5.1 Sample calculation
8.5.2 Accuracy
9 Global symmetries
9.1 Unbroken symmetry
9.2 Spontaneously broken symmetry
9.2.1 Proof of invariance of counterterms
9.2.2 Renormalization of the current
9.2.3 Infrared divergences
9.3 Renormalization methods
9.3.1 Generation of renormalization conditions by Ward identities
10 Operator-product expansion
10.1 Examples
10.1.1 Cases with no divergences
10.1.2 Divergent example
10.1.3 Momentum space
10.1.4 Fig. 10.1.3 inside bigger graph
10.2 Strategy of proof
10.3 Proof
10.3.1 Construction of remainder
10.3.2 Absence of infra-red and ultra-violet divergences in r(\\Gamma).
10.3.3 R(T) — r(T) is the Wilson expansion
10.3.4 Formula for \\bar{C}(U)
10.4 General case
10.5 Renormalization group
11 Coordinate space
11.1 Short-distance singularities of free propagator
11.1.1 Zero temperature
11.1.2 Non-zero temperature
11.2 Construction of counterterms in low-order graphs
11.3 Flat-space renormalization
11.4 Externa] fields
12 Renormalization of gauge theories
12.1 Statement of results
12.2 Proof of renormalizability
12.2.1 Preliminaries
12.2.2 Choice of counterterms
12.2.3 Graphs with external derivatives
12.2.4 Graphs finite by equations of motion
12.2.5 Gluon selfenergy
12.2.6 BRS transformation of A.
12.2.7 Gluon self-interaction
12.2.9 Quark-gluon interaction; introduction of B
12.3 More general theories
12.3.1 Bigger gauge group
12.3.2 Scalar matter
12.3.3 Spontaneous symmetry breaking
12.4 Gauge dependence of counterterms
12.4.1 Change of Xi
12.4.2 Change of Fa
12.5 R-gauge
12.6 Renormalization of gauge-invariant operators
12.6.1 Caveat
12.7 Renormalization-group equation
12.8 Operator-product expansion
12.9 Abelian theories: with and without photon mass
12.9.1 BRS treatment of massive photon
12.9.2 Elementary treatment of abelian theory with photon mass
12.9.3 Ward identities
12.9.4 Counterterms proportional to A2 and d-A2
12.9.5 Relation between e0 and Z3
12.9.6 Gauge dependence
12.9.7 Renormalization-group equation
12.10 Unitary gauge for massive photon
13 Anomalies
13.1 Chiral transformations
13.2 Definition of gamma5
13.3 Properties of axial currents
13.3.1 Non-anomalous currents
13.3.2 Anomalous currents
13.3.3 Chiral gauge theories
13.3.4 Supersymmetric theories
13.4 Ward identity for bare axial current
13.4.1 Renormalization of operators in Ward identities
13.5 One-loop calculations
13.6 Non-singlet axial current has no anomaly
13.6.1 Reduction of anomaly
13.6.2 Renormalized current has no anomalous dimension
13.7 Three-current Ward identity; the triangle anomaly
13.7.1 General form of anomaly
13.7.2 One-loop value
13.7.3 Higher orders
14 Deep-inelastic scattering
14.1 Kinematics, etc.
14.2 Parton model
14.3 Dispersion relations and moments
14.4 Expansion for scalar current
14.5 Calculation of Wilson coefficients
14.5.1 Lowest-order Wilson coefficients
14.5.2 Anomalous dimensions
14.5.3 Solution of RG equation - non-singlet
14.6 OPE for vector and axial currents
14.6.1 Wilson coefficients - electromagnetic case
14.7 Parton interpretation of Wilson expansion
14.8 W4 and W5
References
Index