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Effective Field Theories

Module PH2245

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2245 is a semester module in German or English language at Master’s level which is offered in winter semester.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 30 h 5 CP

Responsible coordinator of the module PH2245 is Antonio Vairo.

Content, Learning Outcome and Preconditions


The lecture course provides an introduction to effective field theories (EFTs) and renormalization techniques with applications ranging from high energy to atomic physics. The course consists in three parts: (1) basics of EFTs and renormalization group; (2) introduction to the Heavy Quark Effective Theory (HQET); (3) non-relativistic EFTs and applications to atomic physics.

Learning Outcome

The student will learn how to build effective field theories from identifying the relevant degrees of freedom and symmetries to renormalize them.  The basics will be broad and applicable to all effective field theories. Some specific EFTs will be worked out in more detail.


Quantum Mechanics 1 + 2 and some basic knowledge of Quantum Field Theory and the Standard Model.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Effective Field Theories Vairo, A. Thu, 08:30–10:00, PH 3343

Learning and Teaching Methods

Lectures will be delivered on the blackboard. Literaure and further bibliographycal material can be found on the webpage of the course.


Links to the literature and a detailed outline of the course is in


  • 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

Module Exam

Description of exams and course work

In a written exam of 60 minutes the learning outcome is tested using comprehension questions and sample problems.

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

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