Lehrstuhl für Theoretische Physik III

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Quantum Field Theory II (Harald Grießhammer)

Correction to Problem sheet VI

Eliminate all factors $\mu^{-2\epsilon}$ in the four renormalisation constants! If they were there, the dimensions would not match. The definition of the renormalised coupling in $d$ dimensions in problem b) should read $g_R(\mu):=g_R\;\mu^{\epsilon}$ (sign of exponent wrong).

Zeit, Ort

2 SWS + 1 SWS Übungen
Lecture Wed 10 s.t. to 11:30 in Hörsaal D
Tutorial Tue 17 s.t. to 19 in SR 02.729 (Seminarraum Theorie III)

Art der Vorlesung

Hauptstudium, Physikalisches Wahlpflichtfach

This continuation of "Einführung in die Quantenfeldtheorie" (SS 2005, Prof. Lenz) is intended primarily for students after the 8th semester, and for Doktoranden. Like practically all literature, the lecture will be in English. Questions and comments in English or German encouraged.

Goals

Introduction into non-Abelian gauge theories and the principles of modern elementary particle physics.

Prerequisites

Thorough understanding of all course lectures, in particular second quantisation; "Einführung in die Quantenfeldtheorie" (SS 2005, Prof. Lenz), in particular path integrals; phenomenology of the standard model on the level of "Kern- und Teilchenphysik (Experimentalphysik VI)".

Tutorials

1 SWS. Active participation a must for success.

Contents

Literature/bibliography/conventions: qftIIWS0506.handout.pdf

Date Topic Literature Problem sheets
26.10.05 Review of Quantum Field Theory QFT I script (SS05,Prof. Lenz)
02.11.05
Take crayons with you!		 Classical and Quantised Gauge Theories Global non-Abelian symmetries; Interlude: Lie Algebrae and Lie Groups [2, Chap. 15.4], [3, Chap. 2.3], [12, Chap. 4.4] Problems I
09.11.05
Take crayons with you! 		From global to local symmetries: geometry behind non-Abelian gauge fields; gauge-covariant derivative; field-strength tensor [2, Chap. 15.1], [3, Chap. 3.6], [12, Chap. 8.1 and 8.2]
16.11.05 field-strength tensor as curvature tensor, Yang-Mills action and equations of motion, gauge choices see 9.11.05, and [2, Chap. 15.2 and 4] Problems II
23.11.05 Faddeev-Popov quantisation of non-Abelian gauge theories (I) [3, Chap. 7.2], [12, Chap. 9], [4, Chap. 9]
30.11.05 Faddeev-Popov quantisation of non-Abelian gauge theories (II) see above Problems III
7.12.05 Comments on Faddeev-Popov Quantisation, BRST-Symmetries and Slavnov-Taylor identities see above, [3, Chap. 7.4-6]
14.12.05 Concepts in Regularisation and Renormalisation. A First Look at Renormalisation a la BRST [12, Chap. 2.1], sketches of proofs of renormalisability of non-Abelian gauge theories e.g. in [4, Chap. 13], [14, Chap. 12]
21.12.05 Regularisation: spotting divergences, dimensional regularisation, quark self-energy [3, Chap. 9.1-3 and 9.9], [13, Chap. 2.4], axiomatic approach to dim. reg.: [14, Chap. 4]. One-loop renormalisation of QCD e.g. in [13, Chap. 2.5.5] Problems IV
11.01.06 1-loop regularisation of quark self-energy in dim. reg., BPHZ renormalisation, renormalisability criterion [13, Chaps. 2.4.3, 2.5.5], [11, Chaps. 7.1, 7.2.1] Problems V
18.01.06 No lecture No lecture No lecture
25.01.06 renormalisability criterion (cont'd), Physics behind infinities, Effective Field Theories [4, Chap. 7.2], [6, Vol. I, Chap. 12.2-4, Vol. II, Chap. 18] , [1, Chap. VIII.3], article "What is Renormalisation" by G.P. Lepage (hep-ph/0506330)
01.02.06 Effective Field Theories (cont'd); Renormalisation Group: Group properties of renormalisations, renormalisation group equations, anomalous dimensions [13, Chap. 3.2-5, 5.3] (very useful), [3, Chap. 9.4],[4, Chap. 14.5], [6. Vol. II, Chap 18.3]
08.02.06 running coupling constant, asymptotically free theories see above Problems VI

Bibliography

The "books to the lecture":

Classics and Modern Classics:

"The price is right":

Only in German:

More applied to high-energy Phsyics:

On Renormalisation

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