Last update 22nd July 2004.
My thanks to all of you who
attended. Don't forget that QFT is
learned by doing calculations, not by listening to lectures.
I hope to see you soon again with your critiques, comments and
questions. My door is always open for you.
By the way, with the knowledge acquired,
you can now try to
understand a good deal of Hawking's
abstract at a recent conference in Dublin, where he supposes
that
no information is lost when you fly into a Black Hole.
Prerequisites: Quantum Mechanics, Relativistic Quantum Mechanics, outline of Quantum Field Theory on the level of ``Quantenmechanik I & II''; particle phenomenology on the level of ``Kerne und Teilchen I & II''; Classical Field Theory and Special Relativity.
Lecture hours:
Mondays
11:00 s.t. to
12:00 s.t. hrs.
Wednesdays
13:40 to 15:10 hrs.
No lectures in weeks 3rd to 14th
May and 31st May to 4th
June.
Co-ordinated with ``Theoretische Hochenergiephysik'' (A. Buras, Tue 11-13 and Thu 10-12), ``Effektive Feldtheorie'' (A. Hoang, Mon 9-11 and Wed 11-13).
Office hours: You are always welcome with questions, discussions, comments and critique, in particular Friday 10-12 in my office: room 3209, Tel. 289-14403, Email hgrie<at>ph.tum.de
Suggested Rough Outline
Why QFT? - Conventions - Historic overview - Review of Classical Field Theory
Scalar & Dirac field
Motivation from Quantum Mechanics - PIs in QFT - generating functional - Wick's theorem and Feynman rules - Faddeev-Popov quantisation of gauge theories - ghosts and gauge invariance
Detailled Plan:
| Lecture date | Topic | Suggested
preparatory reading |
| Mon, 19.4. |
Introduction:
Setting the value | |
| Wed, 21.4.
(only 1 hour) | Introduction:
Historical note; Notation | |
| Mon, 26.4. | Introduction: Classical Field Theory: equations of motion | Ryder Chap. 3.1 to 3.3; Kaku Chap. 1 Ramond Chap. 1.5 |
| Wed, 28.4. SPECIAL PLACE: SR 3343 (Handbibliothek Physik) | Introduction:
Classical Field Theory: Noether theorem; conserved charges; energy-momentum tensor; solutions for the Klein-Gordon and Dirac fields | dito; Ramond Chap. 1.6 and 1.7 |
| 3.
- 14. May no lectures | ||
| Wed, 19.5.,
13:30hrs (see above)
again in SR1141 | Canonical
quantisation: How to Quantise; free, real scalar fields;
Casimir effect | Ryder Chap. 4.1 Kaku Chap. 3.1 and 3.2 Zee Chap I.8 (Casimir effect) |
| Mon 24.5. |
Canonical
quantisation: Complex scalar field and Dirac field | Ryder Chap.
4.2 and 4.3 Kaku Chap 3.3, 3.5 and 3.6 Kugo Chap 2.1 and 2.2 |
| Wed 26.5. |
Canonical quantisation: Schroedinger Picture; Mathematical Interlude on Functions, Functionals and Functional Differentiation; Wave Function of the Free Scalar Field | Ryder
Chap. 5.4 The Schroedinger-picture is hard to find in textbooks... |
| 31.5.
- 4.6. no lectures | ||
| Mon 7.6.,
11:00 hrs s.t. (see above); take crayons with you! | Gauge
Theories: Introducing Lie Groups: Flavour-SU(2) revisited | Ryder Chap.
2.3 Chen/Li Chap 4.4 Peskin/Schroeder Chap 15.4 Kugo Chap. 5.1 repeat flavour-symmetry from Kerne-und-Teilchen-lecture! |
| Wed 9.6., 13:40 hrs s.t. | Gauge Theories: Quantum Generators of classical symmetries; Mathematical Interlude on Lie Groups and Lie Algebras | see Mon, 7.6. |
| Mon
14.6., 11:00 hrs s.t. take crayons with you! | Gauge
Theories: From global to local symmetries: the geometry
behind
non-Abelian gauge fields; Mathematical Interlude on fibre bundles and
connections | Ryder
Chap. 3.6 Cheng/Li Chap 8.1 and 2 Peskin/Schroeder Chap 15.1 Kugo Chap 5.1 |
| Wed 16.6., 13:40 hrs s.t. take crayons with you! | Gauge Theories: curvature, field strength and equations of motion; Mathematical Interlude on fibre bundles and connections | see
Mon, 14.6. |
| Mon 21.6., 11:00 hrs s.t. | Gauge
Theories: a dictionary between Physics, Differential
Geometry
and General Relativity; canonical (constraint) quantisation of Gauge
Theories |
Kaku Chap. 4.1, 2 and 3; also in Ryder Chap. 4.4, but we do it differently. Kugo Chap. 5.2 and 5.5 for the die-hards |
| Wed 23.6., 13:40 hrs s.t. | Gauge
Theories: Canonical (constraint) quantisation
of QED, and
why it does not work for QCD Path Integrals: Philosophical Background | see
Mon, 21.6. Zee Chap. 1.2 |
| No
lecture Mon 28.6., 11:00 hrs s.t. (taken over by Buras:
Theoretische Hochenergiephysik) see Thu, 1.7. | ||
| Wed 30.6., 13:40 hrs s.t. | Path
Integrals: No derivation of path integrals in Quantum
Mechanics: motivation; expectation values; sources |
Sakurai: Modern QM, Chap.
2.5 The following presentations do not differ too much from each other: Ryder Chap. 5; Kaku Chap. 8.1 and 2; Ramond Chap. 2.2; Peskin/Schroeder Chap. 9.1 and for the die-hards: Kleinert: Pfadintegrale; Rivers: Path Integral Methods in Quantum Field Theory. |
| Thu, 1.7., 10:15-11:45 s.t. special date (taken over from Buras: Theoretische Hochenergiephysik) | Path
Integrals: No derivation of path integrals in Quantum
Mechanics
(cont'd): Wick rotations and Euclidean time, scattering states | see Wed,
30.6. Kugo Chap. 4.2 |
| Mon 5.7., 11:00 hrs s.t. | Path
Integrals: PIs in QFT; third mathematical interlude:
Gaussian
Functional Integration | Kaku Chap. 8.3 Kugo Chap. 4.2 Ryder Chap. 6.2 |
| Wed 7.7., 13:40 hrs s.t. | Path
Integrals: Generating Functional, free two-point function,
deriving Feynman rules; generating functional of connected diagrams | any of the
textbooks; you should
do exemplary calculations of two-and four-point functions to first
order in the coupling in Phi^4-theory. Follow the steps e.g. in Ryder
Chap. 6.5; see also Ramond Chap. 4.1 for a true proof that Feynman rules are rules of differentiation. That W[J] generates only connected graphs is best shown in Kugo Chap. 4.3.1 |
| Mon 12.7., 11:00 hrs s.t. | Path
Integrals: deriving Feynman rules (cont'd),
LSZ-reduction;
Fourth mathematical Interlude; Grassmann variables, differentiation and
integration | Ryder
Chap. 6.8 Ryder Chap. 6.7 Kaku Chap. 8.6; Ramond Chap. 5.1 |
| Wed 14.7., 13:40 hrs s.t. | Path Integrals: Generating Functional for fermions, Faddeev-Popov Quantisation of Non-Abelian gauge Theories | Ramond Chap. 5.2 and 3; Ryder
Chap. 6.7 Cheng/Li Chap. 9; Ryder Chap. 7.2 |
| Mon 19.7., 11:00 hrs s.t. | Path Integrals:Faddeev-Popov Quantisation of Non-Abelian gauge Theories (cont'd) | see above |
| Wed 21.7., 13:40 hrs s.t. | Path Integrals: BRST-symmetry/Slavnov-Taylor identities | Ryder Chap. 7.4,5 and 6 |
Some Books: