Foundations of Quantum Field Theory. Klaus D Rothe
and overlapping divergences
16.41-loop renormalization in QED
16.5Composite operators and Wilson expansion
16.6Criteria for renormalizability
16.8Bogoliubov’s recursion formula
16.10Dispersion relations: a brief view
17Broken Scale Invariance and Callan–Symanzik Equation
17.2Unrenormalized Ward identities of broken scale invariance
17.3Broken scale invariance and renormalized Ward identities
17.5Solution of CS equation in the deep euclidean region
17.6Asymptotic behaviour of r and zeros of the β-function
17.7Perturbative calculation of β(g) and γ(g) in ϕ4 theory
17.8QED β-function and anomalous dimension
17.9QED β-function and leading log summation
17.10Infrared fix point of QED and screening of charge
18.1The Renormalization Group equation
18.2Asymptotic solution of RG equation
19Spontaneous Symmetry Breaking
19.2More about spontaneous symmetry breaking
19.4Realization of Goldstone Theorem in QFT
20.1Generating functional of proper functions
20.3The 1-loop effective potential of ϕ4-theory
20.4WKB approach to the effective potential
20.5The effective potential and SSB
Chapter 1
The Principles of Quantum Physics
Quantum Field Theory is a natural outgrowth of non-relativistic Quantum Mechanics, combining it with the Principles of Special Relativity and particle production at sufficiently high energies. We therefore devote this introductory chapter to recalling some of the basic principles of Quantum Mechanics which are either shared or not shared with Quantum Field Theory.
1.1Principles shared by QM and QFT
We briefly review first the principles which non-relativistic Quantum Mechanics (NRQM), relativistic Quantum Mechanics (RQM) and Quantum Field Theory (QFT) have in common.
(1)Physical states
Physical states live in a Hilbert space
(2)Time development
In the Schrödinger picture, operators OS are independent of time and physical states |Ψ(t)
with H the Hamiltonian.
In the Heisenberg picture physical states |Ψ
The states in the two pictures are related by the unitary transformation
(3)Completeness
Eigenstates |Ψn > of H,
are assumed to satisfy the completeness relation
