June 6, 2000
RELATIVISTIC QUANTUM MECHANICS
Physics D153
March 28  June 6 2000

Spring Quarter 2000 
TTh 10:3012:00 in Tech F328

Predrag
Cvitanovic' 
Course schedule

They act so cute when they try to understand Quantum Field Theory.

www.phys.nwu.edu/~predrag/NUcourses/D1532000/index.html
NU Registrar course description
www.phys.nwu.edu/~predrag/NUcourses/D1532000/NUD153.html
Start:
Thursday, March 30, 10:30 in Tech F328.
For people following the course, check the
email list.
PROBLEM SETS:
Please deliver solutions to problem sets
to me, or place them in Yuheng Lan's Physics & Astronomy mailbox
(ylan@nwu.edu).

Feynman's Formulation of Quantum Field Theory

QM Amplitudes as a Sum over Paths
Suggested reading:

Peskin: Chap 9  Functional Methods

Brown: Chap 1  Functional integrals
(Very clear)
Exercises, due Tue Apr 18, 2000:

Fresnel integral: problem 1.14
in Predrag's lecture notes (postscript gzipped) on
path integrals

ddimensional Gaussian integral: problem 1.15
in Predrag's path integrals lecture notes.

Greiner & Reinhardt,
example 11.2: Weyl ordering for operators

Greiner & Reinhardt,
exercise 11.1: Path integral for a free particle

Schwinger/Feynman Formulation of Field Theory
If you want to relax by listening to diagrammatic, Predragian
vision of field theory, I will cover the material in chapters 23 of
Field Theory
in n lectures, n unknown.
The exposition assumes no prior knowledge of anything (other
than Taylor expansion of an exponential, taking derivatives,
and inate knack for doodling).
The techniques covered apply to QFT, Stat Mech and stochastic processes.
Suggested reading:

Cvitanovic': Field Theory, chapters 2,3

Peskin: Chap 9  Functional Methods, sects 9.1, 9.2, 9.3, 9.6

Peskin: Chap 11  The Effective Action, sects 11.3, 11.4, 11.5

Cvitanovic': Field Theory, chapter 4: Fermions
Exercises, due Tue Apr 25, 2000:

Predrag's
Field Theory
exercises
2.D.1,
2.D.2,
2.D.3,
2.E.3,
2.F.1
Exercises, due Tue May 2, 2000:

Predrag's
Field Theory
exercises
3.B.1,
3.F.2
Exercises, due Tue May 9, 2000:

Predrag's
chapter 4
exercises
4.E.2,
4.F.1

Renormalization
Suggested reading:

Predrag's
Chapt. 5; pp. 6670;
Chapt. 6; p. 71
,
Chapt. 6; p. 72100

Peskin: Sect 7.2  LSZ reduction, 7.4 WardTakahashi indentities

Greiner & Reinhardt,
Sect 6.4: Vector fields

Peskin: Chap 10  Systematics of Renormalization
Exercise, due Tue May 16, 2000:

Predrag's
chapter 6
exercise
6.A.1: QED Ward identity
No class May 16, 18 and 23.
Assignments for period of May 1623:

Predrag's
exercises
6.E.1, 6.F.2
due Thu May 18, 2000, Y. Lan's mailbox.

Work through
sections
6.G, 6.H and 6.I
Midterm exam (takehome
 including solutions)
Due Thursday, May 25, 2000, 10:30
Overal course grade
will be determined from the homework (40%), midterm (20%), and the final (40%).

NonAbelian Gauge Invariance
Suggested reading:

Peskin: Chap 15  NonAbelian Gauge Invariance

Quantization of NonAbelian Gauge Theories
Suggested reading:

Peskin:
Sects 16.116.4
 Quantization of NonAbelian Gauge Theories,
Final exam: takehome, start May 30.
Required:
perform all calculations outlined in Peskin sect. 16.5, leading to
the gluon 1loop correction to the gluon propagator (16.70).
If you prefer to compute the beta function (16.85) by any other method,
that is even better.
Optional (but it would give you the full satisfaction):
compute the beta function (16.85), read through sect 16.7 (without including
any of it into the exam), derive the QCD running coupling constant
(17.17), and finish off by reading through sect 17.6 (without including
any of it into the exam).
References

An Introduction to Quantum Field Theory,
M.E. Peskin and D.V. Schoeder
(Addison Wesley, Reading MA, 1995).

Field theory,
P. Cvitanovic'.

Lattice
Field Theory,
P. Cvitanovic'.

Group
theory,
P. Cvitanovic'.

Quantum Field Theory,
L.S. Brown
(Cambridge University Press, Cambridge 1992).

Field Quantization,
W. Greiner and J. Reinhardt
(SpringerVerlag, Berlin 1996).