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Effektive Feldtheorien
Effective Field Theories

Modul PH2122

Diese Modulbeschreibung enthält neben den eigentlichen Beschreibungen der Inhalte, Lernergebnisse, Lehr- und Lernmethoden und Prüfungsformen auch Verweise auf die aktuellen Lehrveranstaltungen und Termine für die Modulprüfung in den jeweiligen Abschnitten.

Modulversion vom WS 2018/9 (aktuell)

Von dieser Modulbeschreibung gibt es historische Versionen. Eine Modulbeschreibung ist immer so lange gültig, bis sie von einer neuen abgelöst wird.

verfügbare Modulversionen
WS 2018/9SS 2018WS 2016/7SS 2011


PH2122 ist ein Semestermodul in Englisch auf Master-Niveau das im Wintersemester angeboten wird.

Das Modul ist Bestandteil der folgenden Kataloge in den Studienangeboten der Physik.

  • Allgemeiner Spezialfachkatalog Physik
  • Spezifischer Spezialfachkatalog Kern-, Teilchen- und Astrophysik

Soweit nicht beim Export in einen fachfremden Studiengang ein anderer studentischer Arbeitsaufwand ("Workload") festgelegt wurde, ist der Umfang der folgenden Tabelle zu entnehmen.

GesamtaufwandPräsenzveranstaltungenUmfang (ECTS)
300 h 90 h 10 CP

Inhaltlich verantwortlich für das Modul PH2122 ist Nora Brambilla.

Inhalte, Lernergebnisse und Voraussetzungen


The lecture course will provide an introduction to effective field theories (EFTs) and renormalization techniques with applications ranging from high energy to atomic physics. The following topics will be covered:

  • Principles of EFTs
    • Scales and systems in nature
    • What is an EFT and how to construct it
    • Example: the Euler-Heisenberg Lagrangian
    • Example: the Fermi theory of weak interactions at tree level
    • Example: the Rayleigh scattering
    • Relevant, irrelevant and marginal operators
    • Quantum loops of irrelevant operators
    • Mass-dependent vs mass-independent regularization schemes
    • Dimensional regularization
    • Quantum loops of marginal operators
    • Example: β function and running coupling constant in QED and QCD
    • Decoupling theorem
    • Example: the one and two loop matching of the QCD strong-coupling constant in MSbar
    • Renormalization group equations in QFTs and EFTs
    • Anomalous dimensions
    • Mixing
    • Example: ΔS = 2 transition amplitude in the Fermi theory of weak interactions
  • Heavy quark effective theory
    • Heavy-light meson spectrum
    • Heavy-quark spin-flavour symmetry
    • Static Lagrangian
    • Spectroscopy implications
    • Heavy meson decay constants
    • Transition form factors: Isgur-Wise functions
    • Example: B → D transitions and calculation of dΓ(B → D e ν)/dq²
    • Renormalization of composite operators
    • Example: heavy-light currents and heavy-heavy currents
    • Heavy meson decay constants at LL and NLO
    • The 1/m expansion of the HQET Lagrangian
    • Reparameterization invariance
    • Chromomagnetic coupling and hyperfine splitting at LL
    • Decoupling in the HQET
    • B → D e ν and Luke's theorem
  • Applications to atomic physics
    • Bound states in QED: physical picture, scales, degrees of freedom
    • NRQED: Lagrangian, power counting, matching
    • Four-fermion operators
    • Example: matching of dimension six four-fermion operators and the positronium decay width
    • pNRQED: Lagrangian, power counting, matching
    • Example: the hydrogen atom and the Lamb shift
    • Example: the Rayleigh scattering in pNRQED


After successful completion of the module the students are able to

  1. build effective field theories,
  2. compute Wilson coefficients and renormalize them,
  3. solve renormalization group equations
  4. compute observables in principle at any order in the expansion  parameter(s).

In practice we will work out one loop calculations for non-relativistic effective field theories in QED and QCD.


Keine Vorkenntnisse nötig, die über die Zulassungsvoraussetzungen zum Masterstudium hinausgehen.

Lehrveranstaltungen, Lern- und Lehrmethoden und Literaturhinweise

Lehrveranstaltungen und Termine

VO 4 Effective Field Theories Brambilla, N. Di, 08:00–10:00, PH 3344
Mi, 12:00–14:00, PH 3344
UE 2 Übung zu Effektive Feldtheorien Steinbeißer, S. Vander Griend, P.
Leitung/Koordination: Brambilla, N.
Termine in Gruppen

Lern- und Lehrmethoden

In the thematically structured lecture the learning content is presented. With cross references to many different  fields spanning from high energy physics, physics of beyond the Standard Model, low energy physics and condensed matter many different applications and  a large number of physical examples are presented.

In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In the exercise the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.


Lectures will be given on a blackboard. Slides presentations may also be used. Additional material will be contained on the web page of the lectures and the blog of the lectures with  links to research papers, appropriate chapters of books and further discussion of important questions.

Many physical examples will be presented and worked out in all details. Exercises are suggested and will be discussed as requested. Discussions and feedbacks during the lectures  are strongly encouraged.



  • Principles of EFTs
    • Books:A. Dobado, A. Gomez-Nicola, A.L. Maroto, J.R. Pelaez, Effective Lagrangians for the Standard Model, Springer Verlag 1997
      S. Weinberg, The Quantum Theory of Fields Vol. II, Cambridge University Press 1996, Chapter 19
    • Review papers and lecture notes:A. Pich, Effective field theory, Les Houches 1997, Probing the standard model of particle interactions, Pt. 2* 949-1049, e-Print: hep-ph/9806303
      A.V. Manohar, Effective field theories, Schladming 1996, Perturbative and nonperturbative aspects of quantum field theory* 311-362, e-Print: hep-ph/9606222
      D.B. Kaplan, Effective field theories, 7th Summer School in Nuclear Physics Symmetries, Seattle, e-Print: nucl-th/9506035
      H. Georgi, Effective field theory, Ann.Rev.Nucl.Part.Sci.43:209-252,1993
      B.R. Holstein, Effective effective interactions, Eur.Phys.J.A18:227-230,2003
    • A founding paper:S. Weinberg, Phenomenological Lagrangians, Physica A96:327,1979
    • EFTs courses:School on Flavor Physics, Centro de Ciencias de Benasque (2008)
      Effective field theory course (2013) at MIT by Iain Stewart (with emphasis on SCET)
  • Heavy quark effective theory
  • Books:A.V. Manohar, M.B. Wise, Heavy quark physics, Cambridge University Press 2000
    • Review papers and lecture notes: M. Neubert, Heavy-quark symmetry, Phys.Rept.245:259-396,1994
      B. Grinstein, An introduction to heavy mesons, 6th Mexican School of Particles and Fields, Villahermosa, e-Print: hep-ph/9508227
      T. Mannel, Heavy-quark effective field theory, Rept.Prog.Phys.60:1113-1172,1997
    • Related papers:G.P. Lepage, L. Magnea, C. Nakhleh, U. Magnea, K. Hornbostel, Improved nonrelativistic QCD for heavy quark physics, Phys.Rev.D46:4052-4067,1992, e-Print: hep-lat/9205007
      A.V. Manohar, The HQET/NRQCD Lagrangian to order α/m^3, Phys.Rev.D56:230-237,1997, e-Print: hep-ph/9701294
  • Applications to atomic physics
    • Related papers:W.E. Caswell, G.P. Lepage, Effective Lagrangians for bound state problems in QED, QCD, and other field theories, Phys.Lett.B167:437,1986
      A. Pineda, J. Soto, The Lamb shift in dimensional regularization, Phys.Lett.B420:391-396,1998, e-Print: hep-ph/9711292
      A. Pineda, J. Soto, Potential NRQED: the positronium case, Phys.Rev.D59:016005,1999, e-Print: hep-ph/9805424
      B.R. Holstein, Blue skies and effective interactions, American Journal of Physics 67:422,1999


Beschreibung der Prüfungs- und Studienleistungen

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

In accordance with §12 (8) APSO the exam can be done as an oral exam. In this case the time duration is 25 minutes.

For example an assignment in the exam might be:

  • Typical questions will include: how to construct an EFT, how to match it, how to write an RG equation,
  • how to write an RG equation. Specific physical examples presented during the lecture (HQET,NRQED,pNRQED, etc.) may be also discussed.
  • How to calculate a matching in the effective field theory at tree level and at one loop.
  • How to use the effective field theory to calculate physical observers, masses, decays and scattering processes.
  • How to do a perturbative calculation inside the effective field theory
  • How to use the effective field theory to estimate the scale of new physics.
  • How to use the effective field theory to obtain the parametric dependence of a cross section.

In the exam no learning aids are permitted.

Participation in the tutorials is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of follow the exercises courses and solve 70% of the exercises.


Eine Wiederholungsmöglichkeit wird am Semesterende angeboten.

Aktuell zugeordnete Prüfungstermine

Derzeit sind in TUMonline die folgenden Prüfungstermine angelegt. Bitte beachten Sie neben den oben stehenden allgemeinen Hinweisen auch stets aktuelle Ankündigungen während der Lehrveranstaltungen.

Prüfung zu Effektive Feldtheorien
Mo, 4.2.2019 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin vor So, 24.03.2019. // Dummy date. Contact examiner for individual appointment. Registration for exam date before Sun, 2019-03-24. bis 15.1.2019 (Abmeldung bis 3.2.2019)
Di, 26.3.2019 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin von Mo, 25.03.2019 bis Sa, 27.04.2019. // Dummy date. Contact examiner for individual appointment. Registration for exam date from Mon, 25.03.2019 till Sat, 27.04.2019. bis 25.3.2019
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