1
Anharmonic Oscillator Ground State
The anharmonic oscillator is a eld theory in 1 spacetime dimension with a single degree of freedom or
Fourier mode. The perturbation series for its ground state energy illustrates most of the important concepts
of Wick
1
The Quantum Anharmonic Oscillator
Perturbation theory based on Feynman diagrams can be used to calculate observables in Quantum Electrodynamics, like the anomalous magnetic moment of the electron, and the predictions agree with experiment
with impressiv
1
Interaction of Quantum Fields with Classical Sources
A source is a given external function on spacetime t, x that can couple to a dynamical variable like a
quantum eld. Sources are fundamental in the functional and path integral formulations of eld theo
Lecture 3
Friday, August 30
Contents
1
The Klein-Gordon Field
2
2
Green Functions and Klein-Gordon Radiation
5
3
The Electromagnetic Field
8
1
1
The Klein-Gordon Field
To simplify formulas, follow Altland-Simons (pages 16, 22) and Peskin-Schroeder (page x
1
Canonical Quantization of the Electromagnetic Field
Peskin-Schroeder state the Feynman Rules for the photon eld in 4.8:
and postpone the proof to Chapter 9 Functional Methods.
1
Altland-Simons state the results of quantizing the photon eld using non-cov
Lecture 2
Wednesday, August 28
Contents
1
Fermis Method
2
2
Lattice Oscillators
3
3
The Sine-Gordon Equation
8
1
1
Fermis Method
Feynmans Quantum Electrodynamics refers on the rst page of the rst lecture to Fermis method, and
calls it one of the simplest
Lecture 4
Wednesday, September 4
Contents
1
Transformations and Symmetries
2
2
Representations of the Lorentz Group
4
3
Representations of the Poincar Group
e
9
1
1
Transformations and Symmetries
Fields are functions of spacetime points x. A spacetime poi
1
Equal-time and Time-ordered Green Functions
Predictions for observables in quantum eld theories are made by computing expectation values of products
of eld operators, which are called Green functions or correlation functions.
The two most important type
Topic 3
Spinors, Fermion Fields, Dirac Fields
Lecture 16
The Quantum Heisenberg Ferromagnet
Soon after Schrdinger discovered the wave equation of quantum mechanics, Heisenberg and Dirac
o
developed the rst successful quantum theory of ferromagnetism W. He
1
Vacuum Energy and Cosmology
The Fock-space representation of the Hamiltonian operator
H=
E2 + B2
=
dx
2
2
3
=1
d3k
1
a(k, )(k, ) +
a
(2)3
2
d3x ,
= |k|
has vaccum expectation value
2
0|H|0 = V
=1
V
d3k
=
lim |k|4 ,
3 2
(2)
8 |k|max max
V =
d3x
This i
Topic 3
Spinors, Fermion Fields, Dirac Fields
Lecture 15
Dirac Electrons in Graphene
This phenomenon was discovered by K.S. Novoselov, A.K. Geim, et al., Two-dimensional gas of
massless Dirac fermions in graphene, Nature 438, 197-200 (2005). Novoselov and
Topic 3
Spinors, Fermion Fields, Dirac Fields
Lecture 13
The Dirac Equation
Diracs discovery of a relativistic wave equation for the electron was published in 1928 soon after the
concept of intrisic spin angular momentum was proposed by Goudsmit and Uhlen
Topic 3
Spinors, Fermion Fields, Dirac Fields
Lecture 17
The Spin-Statistics Connection
All experimental evidence on sub-atomic particles indicates that systems of particles with integer spin
magnitude S = 0, 1, 2, . . . obey the laws of Bose-Einstein sta
Lecture 6
Monday, September 6
Contents
1
Dierential Geometry
2
2
Dierential Forms
5
1
1
Dierential Geometry
Vectors in real space have magnitude and direction. They transform under rotations in R3 according to an
irreducible 3-dimensional representation o
Topic 3
Spinors, Fermion Fields, Dirac Fields
Lecture 14
Lorentz Transformations and Dirac Matrices
Lorentz transformations of x are dened in Jackson Chapter 11
(, ) = exp [J K ] ,
where the six matrices J, K are the generators of the Lie algebra of the g