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Advanced Effective Field Theories

Module PH2123

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

PH2123 is a semester module in 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 40 h 5 CP

Responsible coordinator of the module PH2123 is Antonio Vairo.

Content, Learning Outcome and Preconditions



  • Basics principles of EFTs and renormalization techniques
  • Chiral perturbation theory for mesons
    • Light meson and baryon spectrum
    • The symmetries of massless QCD
    • Isospin
    • U(1) axial anomaly
    • Spontaneous symmetry breaking of SU(Nf) axial
    • Goldstone theorem
    • The scalar quark condensate
    • Non-linear realization of SU(Nf) x SU(Nf)
    • The chiral Lagrangian at order p²
    • Gell-Mann Oakes Renner relations, Gell-Mann Okubo relation, light quark masses
    • The chiral Lagrangian at order p² with external fields
    • Example: the coupling to electromagnetism and the quark masses
    • Equations of motion
    • Power counting
    • Example: π → μ ν and fπ
    • Example: π π → π π
    • The chiral Lagrangian at order (p²)²
    • Chiral perturbation theory at order (p²)²: one loop diagrams
    • The chiral anomaly: the Wess-Zumino-Witten action
    • Example: π° → γ γ
    • Low energy constants
    • Example: Goldstone boson masses at order (p²)²
    • Example: the pion electromagnetic form factor and the electromagnetic radius
  • Chiral perturbation theory for baryons
    • Non-linear realization of the baryon fields
    • Lowest-order effective Lagrangian
    • Power counting
    • Goldberger-Treiman relation and axial-vector current matrix elements
    • Example: π N → π N
    • Example: 1-loop correction to the nucleon mass
    • The heavy-baryon effective theory (HBChPT)
    • The 1/M° Lagrangian
    • Example: π N → π N in HBChPT
    • The 1/M¹ Lagrangian and the order p² Lagrangian
    • Example: 1-loop correction to the nucleon mass in HBChPT
    • A note on chiral perturbation theory and heavy mesons
    • Example: D* → D π
  • Superconductivity from an EFT perspective: a short note
  • Gravity from an EFT perspective: a short note

Learning Outcome

After attending the course, the attendant has become familiar with modern renormalization techniques and effective field theories. This aim is achieved by looking at how the degrees of freedom of ordinary matter (hadrons, nuclei, atoms, molecules) emerge in a systematic fashion from the elementary degrees of freedom of the Standard Model (lepton, quarks, gauge fields).


Quantum Field Theory courses I and II

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

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

Learning and Teaching Methods

preparation and presentation of a lecture, beamer presentation, board work, discussion


complementary literature


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

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

EFTs Lectures at Physics Schools:

School in Applications of Effective Field Theories, U. Milano (2003)

School on Flavor Physics, Centro de Ciencias de Benasque (2008)

H. Georgi, Weak Interactions and Modern Particle Theory, Benjamin/Cummings Publishing Company 1984

J.F. Donoghue, E. Golowich, B.R. Holstein Dynamics of the Standard Model, Benjamin/Cummings Publishing Company 1984

H. Leutwyler, Chiral effective Lagrangians, Schladming 1991, Internationale Universitätswochen für Kern- und Teilchenphysik and TASI 1991, published in Boulder TASI 91:0097-138

H. Leutwyler, Effective field theories, Annals Phys.235:165-203,1994, e-Print: hep-ph/9311274

G. Ecker, Chiral Symmetry, Schladming 1998, Internationale Universitätswochen für Kern- und Teilchenphysik, e-Print: hep-ph/9805500

J. Goity, Chiral Perturbation Theory: brief introduction, Prague 2001, 13th Indian Summer School: Understanding the Structure of Hadrons, Czech. J. Phys.51:B35,2004

S. Scherer, Introduction to Chiral Perturbation Theory, Adv. Nucl. Phys. 7:277,2003, e-Print: hep-ph/0210398

Founding papers:

S. Weinberg, Phenomenological Lagrangians, Physica A96:327,1979

J. Gasser, H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys.158:142,1984

S. Weinberg, The Quantum Theory of Fields Vol. II, Cambridge University Press 1996, Chapter 21

J. Polchinski, Effective Field Theory and Fermi Surface, TASI 1992, published in Boulder TASI 92:0235-276, e-Print: hep-ph/9210046

S. Weinberg, Effective Action and Renormalization Group Flow of Anisotropic Superconductors, Nucl.Phys.B413:567-578,1994 , e-Print: cond-mat/9306055

D. Espriu, D. Puigdomenech, Gravity as an Effective Theory, e-Print: arXiv:0910.4110

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

The exam may be repeated at the end of the semester. There is a possibility to take the exam in the following semester.

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