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 en
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, a
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 th
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 Alt
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
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
Fiel
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 function
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 th
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
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
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 s
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
magnitud
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 acc
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 matri