Wahlpflichtvorlesung für Wi.Se. 2012/2013:

“Decays in Quantum Field Theory”

von Dr. Francesco Giacosa


Zeit (Time) (2 Std)                Fr, 14:00 (c.t.)-16:00, wöchentlich. Erster Termin: 19/10/2012.

Raum (Room):                   2.114 (Aquarium-Raum)

Web-page:                      http://th.physik.uni-frankfurt.de/~giacosa/decays.html

Email:                                          giacosa@th.physik.uni-frankfurt.de

Link zur Uni-Seite:             hier

Achtung: am Fr. 11/1/2013 gibt es die Vorlesung; am Fr. 18/1/2013 fällt sie aus.




  • Rabi oscillations in Quantum Mechanics (QM): basic equations and quantum-Zeno effect.
  • Detailed discussion of the experiment of Itano et al, Phys.Rev. A41 (1990) 2295-2300.
  • Decay of an unstable state in QM within the Lee Hamiltonian formalism. Non-exponential decay law.
  • Discussion of the experiments of Raizen et al. Nature 387 (1997) and Phys. Rev. Lett, Vol. 87, nr 4 (2001).
  • Quantitative description of measurement in QM.
  • Decays in Quantum Field Theory (QFT): basic recall of the main properties with a Lagrangian involving scalar fields.
  • Spectral functions and non-exponential decay law in QFT. The role of the loops.
  • Decays involving fermions. New interesting phenomena. Example: the decay of the Higgs.
  • Chiral models and evaluation of decays of hadrons. Discussion of past, present and future hadron experiments.
  • Three-body (Dalitz) decays.
  • Higher-order processes.


Moreover, it will be necessary to recall and introduce new elements of complex analysis (complex functions, Riemann sheets, …).


Handsouts and useful links

  • Presentation of the course: here (19/10/2012).
  • Rabi-oscillations: here (19/10/2012).
  • Rabi-osicllations (part 2) and the quantum-Zeno-effect: here (26/10/2012).

Discussion of the article Itano et al, Phys.Rev. A41 (1990) 2295-2300. http://tf.nist.gov/general/pdf/858.pdf

Experiment by Balzer et al, Optics Communications Vol. 211, 235-241 (2002)


For a theoretical deepening, see also “Quantum Zeno and inverse quantum Zeno effects” by P. Facchi and S. Pascazio: http://www.ba.infn.it/~pascazio/publications/zenoreview.pdf

  • Comments on Itano et al: here (2/11/2012). (N+1) energy levels, periodicity, Poincare time, and Mathematica file: here. (2/11/2012).
  • General properties of an unstable system for short times: here. (2/11/2012).
  • Lee Hamiltonian (part 1): here. (2/11/2012).

Lee Hamiltonian (part 2), propagator and spectral function in QM: here. (9/11/2012). Recall and Ersak’s argument: here (23/11/2012).

Discussion of the articles: Experimental Evidence for Non-Exponential Decay in Quantum Tunneling, by Wilkinson et al, published in Nature 387, pgs. 575-577 (1997): http://george.ph.utexas.edu/~quantopt/papers/exp_evidence.pdf

Observation of the Quantum Zeno and Anti-Zeno Effects in an Unstable System, by Fischer et al, published in  Phys. Rev. Lett. 87, 040402 (2001)


Summary paper on the non-exponential decay law in quantum mechanics:

Decay theory of unstable quantum systems, by Fonda, Ghirardi and Rimini, published in

Rept.Prog.Phys. 41 (1978) 587-631 

http://iopscience.iop.org/0034-4885/41/4/003/ (download from the Uni is possible)

Summary paper on the Zeno effect an the measurement theory

Quantum Zeno effect by general measurements, by Kosnino and Shimizu,

published in Phys.Rept. 412 (2005) 191-275 


  • Example of an unstable state within a Lee Hamiltonian (by Thomas Wolkanowski, 30/11/2012): here.
  • Quantum Field Theory with scalar fields: decays, spectral functions, survival probability (7/12/2012): here.

F. Giacosa and G. Pagliara, On the spectral functions of scalar mesons, published in Phys. Rev. C76 (2007) 065204: http://arxiv.org/pdf/0707.3594.pdf.

            F. Giacosa and G. Pagliara, Deviation from the exponential decay law in relativistic quantum field theory: the example of strongly 
            decaying particles, published in Mod.    
            Phys. Lett. A 26 (2011) 224: http://arxiv.org/pdf/1005.4817.pdf    

            F. Giacosa, Deviation from the exponential decay law in relativistic quantum field theory: the example of strongly decaying    particles, published in Found.Phys. 42 (2012)   

          1262-1299: http://arxiv.org/pdf/1110.5923.pdf

            P. T. Matthews and A. Salam, Relativistic field theory of unstable particles, published ins Phys. Rev. 112 (1958) 283 and Relativistic theory of unstable particles. 2,     
          published in Phys. Rev. 115 (1959) 1079.
  • Decays in QFT involving vector fields: the example of the rho meson into two pions (14/12/2012): here.
  • Decays in QFT involving fermion fields: the decay of the Higgs into fermions (21/12/2013): here.
  • Three-body decays in QFT (11/1/2013): here

      Useful link from PDG: http://pdg.lbl.gov/2012/reviews/rpp2012-rev-kinematics.pdf 

  • Three-body decays in QFT, part II (25/1/2013): here
  • Chiral symmetry and decays (1/2/2013): here.
  • Determination of the free parameters of a theory and their errors (1/2/2013): pdf.
  • Summary of the course and discussion of the latest experiment involving decays of hadrons (15/2/2013): here.

How do we see light? The exp. Setup of the group of Haroche in 2 min: http://www.youtube.com/watch?v=2dRr-fnPCwM










Tutorials and exercises (1 hour per week): Friday 16:00-17:00. Room 2.114.


Sheet 1 (26/10/2012): pdf.

Sheet 2 (2/11/2012): pdf.

Sheet 3 (9/11/2012): pdf.

Sheet 4 (23/11/2012): pdf.

Sheet 5 (30/11/2012): pdf.

Sheet 6 (7/12/2012): pdf.

Sheet 7 (14/12/2012): pdf.

Sheet 8 (21/12/2012): pdf. (Hints to ex. 3: hint1 and hint2)

Sheet 9 (11/1/2013): pdf.

Sheet 10 (25/1/2013): pdf.

Sheet 11 (1/2/2013): pdf.







Number of credit points: 4.


Criteria for the credit points: 2 presentations of the results. 60% of the points. At most 2 times missing.



Solutions: pdf.



Contact: giacosa@th.physik.uni-frankfurt.de