Below you will find a detailed Course Plan (or Syllabus) for Physics 582. It is
divided in items and there you will find links to my class notes.
I will post them as
they become available.
As you are aware this Fall 2021 this course will be taught in person (and possibly by zoom). If you cannot attend in person it is important that you have access to a computer and good internet access for this to work. My zoom lectures from the Fall 2020 were recorded and subtitled and the recordings are available in MediaSpace
Access to the recorded lectures is available only to registered students.
I strongly recommend that you read the material that will be covered in class from my book.
I also want to encourage you to come with questions and to send me the questions ahead of time by email.
You will also find links to the homework sets and to their
solutions. There will be a total of six homework sets. The homework problem sets are
very important. There you will find many applications to different problems in various
areas of Physics in which Field Theory plays an essential role. You will not be able
to master the subject unless you do (and discuss) the problem sets.
All homework sets
are due on 9:00 pm (US Central Time) of the assigned due date. Below you will find the homework sets that you will need to download with a clearly stated deadline (all times are in US Central Time). You will either have to prepare your solutions using LaTeX (much preferred) or by scanning a clear handwritten version of your solutions. You will have to upload your solutions to a website indicated below. It is fine to upload a scanned file of a handwritten solution provided it is clearly legible. This means that your solutions must not contain anything crossed out and written with dark pen with large enough script on doubly spaced paper with the equations presented (and not written as part of a line text) that it can be easily read. You should not email your solutions! Unreadable solutions will not be graded. The website where you will be able to upload your solutions (and where you will also be able to download the graded set) is accessed through
this link. No late solution sets will be accepted unless you prearrange this beforehand with the TA and with
me. There will be a 20 percent grade penalty for late solution sets.
In addition to my office hours (see above), both TAs will host each an office hour also by zoom. The TAs will send the invitations to each registered student to their office hours zoom meetings by email.
There will not be
a midterm exam but there will be a Take Home Final Exam. You may
prepare your solution set electronically, and you have the choice of either
preparing the solution in LateX (strongly preferred) and to send me the pdf file by
email no later than Friday December 17 at 5:00 pm (CST). Alternatively you may prepare a
handwritten solution. In that case you must write with dark ink and be clearly legible.
You should send me the pdf file of your solution by email.
You should not put your solution neither in the Physics
582 homework box nor in my mail box as I will be out of town. Please recall that the Final Exam is
mandatory and I will have to give an F to any student who does not turn a solution in time. There
will be no extensions as I need to turn the grades in promptly.
The Final grade will be determined by the six homework sets and the Take Home Final Exam. The Take Home Final Exam will carry the same weight as one of the six homework sets. The letter grades will be determined as follows: an A+ will require at least 95% of the grade, an A at least 90 % of the grade, an A- at least 85% of the grade, a B+ at least 80% of the grade, a B at least 75% of the grade, a B- at least 70% of the grade, a C+ at least 65% of the grade, and so on.
Please find below the HW sets for Physics 582. Please notice the clearly shown deadlines. To turn in the pdf file of your work we will follow the following procedure. Upon clicking on this link you will access a website where you can upload your pdf file. To access this secure website you will need to enter your University of Illinois netid and password. Then you will see a menu with the list of homeworks for Physics 582 and you will choose which homework solution you wish to upload. After the homework is graded by the TA you will be able to access and download the graded work by using this same link.
Homework Set No. 1
Posted : Monday August 23, 2021 Due: Friday September 10, 2021, 5 pm (US Central Time)
Solutions to homework set 1;
Posted: Wednesday September 22, 2021.
Homework Set No. 2
Posted: Sunday September 12, 2021 Due: Friday September 24, 2021, 9:00 pm (US Central Time)
Solutions to homework set 2;
Posted: Friday October 1, 2021.
Homework Set No. 3
Posted: Friday September 24, 2021Due: Friday October 8, 2021, 9:00 pm (US Central Time).
Solutions to homework set 3;
Posted: Wednesday October 13, 2021.
Homework Set No. 4;
Posted: Friday October 9, 2021 Due: Friday October 22, 2021, 9:00 pm (US Central Time) New deadline: Monday October 25, 2021, 9:00 pm US Central Time
Solutions to homework set 4;
Posted: Wednesday October 27, 2021.
Homework Set No. 5;
Posted: Monday October 25, 2021 Due: Friday November 12, 2021, 9:00 pm (US Central Time) , replaced with an edited version on Wednesday October 27, 2021
Solutions to homework set 5;
Posted: Thursday November 18, 2021
Homework Set No. 6
Posted: Friday November 12, 2021 Due: Saturday December 4, 2021, 9:00 pm (US Central Time) (new deadline)
Solutions to homework set 6;
Posted: Tuesday December 7, 2021.
Homework Set No. 7/ Final Exam
Posted: Friday Saturday December 4, 2021, Due: Friday December 17, 2021, 9:00 pm (US Central Time). A clearly readable pdf file (composed in LaTeX or a clearly legible handwritten scanned version) should be uploaded to the same website you used for the other problem sets.
This last homework set will be the Take Home Final Exam for Physics 582. No late solutions will be accepted.
Introduction to Quantum Field Theory
Classical Field Theory
Fields, Lagrangians and Hamiltonians. The action. Real and
complex fields. Space-Time and Internal symmetries.
The Least Action Principle. Field Equations. Minkowski
and Euclidean spaces.
The free massive relativistic scalar field. The Klein Gordon Equation, its solutions
and their physical interpretation. Relativistic Covariance.
Statistical Mechanics as a Field Theory. Coarse graining and hydrodynamic picture. The Landau Theory of Phase Transitions and
Landau functionals. Symmetries. Analogy with the Klein-Gordon field.
Field Theory and the Dirac Equation.
The Dirac Equation: The Dirac and the Klein Gordon operators.
Spinors. The Dirac Algebra. Relativistic Covariance. Solutions and their
interpretation. Symmetries. Holes. Massless particles and chirality.
Maxwell's Electrodynamics as a Field Theory. Maxwell's Equations.
Gauge invariance. Solutions and gauge fixing. Helicity.
Classical Field Theory in the Canonical Formalism.
to imaginary time and the connection between Quantum Field Theory
and Classical Statistical
Symmetries and Conservation Laws
Continuous Symmetries, Conservation Laws and
Global Symmetries and Group Representations.
Local Symmetries and Gauge Invariance.
Non-Abelian Gauge Invariance. Minimal Coupling.
The role of topology: the Aharonov-Bohm effect.
Space-Time Symmetries and the Energy-Momentum Tensor.
The Energy-Momentum tensor and the geometry of
Elementary Quantum Mechanics.
Canonical Quantization in Field Theory.
A simple example: Quantized elastic waves.
Quantization of the Free Scalar Field Theory.
Symmetries of the Quantum Theory: the case of the free charged scalar field.
Path Integral Quantization in Quantum Mechanics and in Quantum Field Theory
Path Integrals and Quantum Mechanics. Density matrix.
Evaluating Path Integrals in Quantum Mechanics
Path Integral quantization of the Scalar Field Theory.
Schrödinger, Heisenberg and interaction representations.
The Evolution operator and the S-matrix.
Propagators and path integrals. Propagator for a Relativistic Real and
Complex Scalar Fields. Path-Integral
representation of the S-matrix and Green functions. Imaginary time. Minkowski
space and Euclidean space, and finite temperature; erratum
Non-Relativistic Field Theory
Review of Second Quantization for Many-Particle Systems.
Many-Body Systems as a Field Theory.
Non-Relativistic Fermions at zero temperature: ground
state, spectrum of low-lying excitations.
Propagator for the
Non-Relativistic Fermi Gas. Holes, particles and the analytic properties
of the propagator.
Quantization of the Dirac Theory
Quantization of the Dirac Theory: ground state,
spectrum, quantum numbers of excitations, causality and spin-statistics
Propagator for the Dirac Field Theory.
Coherent State Path Integrals
Coherent State path integral quantization of bosonic and fermionic systems.
Path integrals for spin.
Grassmann variables. Path integral quantization of the Dirac theory.
Fermion and Boson determinants. Zeta function regularization.
Quantization of Gauge Theories
Path-integral quantization of the Maxwell Abelian gauge theory;
quantization and gauge fixing.
Propagator for the free electromagnetic field. The Wilson loop operator.
Path Integral quantization of Yang-Mills non-Abelian Gauge theories.
Gauge fixing, covariant gauges and the Faddeev-Popov construction.
Ghosts. BRST invariance.
Physical Observables and Propagators .
The Propagator in Non-Relativistic Quantum Mechanics:
retarded, advanced and Feynman propagators.
Green Functions in Classical Electrodynamics.
Propagators, Time-Ordered Products and Green
Functions in Quantum Field Theory.
S-matrix elements and Green functions. Analytic
properties. Lehman representation. Spectrum.
Cross-sections and and the S-matrix.
Linear Response Theory. Measurements and correlation
functions. Application to the electromagnetic response of a metal. Sum
(See my additional notes from Physics 561 on
Linear Response Theory)
Perturbation Theory and Feynman Rules
Wick's Theorem, generating functional and perturbation
Perturbation expansion for vacuum amplitudes and Green functions. Feynman
Examples of Feynman Rules: φ^4 theory and QED,
non-relativistic Fermi gas at zero
temperature, and Landau Theory of Phase transitions.