Physics 880.05 Nuclear Many-Body Physics
Winter/Spring, 2003

Welcome to the Physics 880.05 Nuclear Many-Body Physics home page!
The course information is available here plus lots of supplementary info. Please check this page regularly.

Recent changes to this page:




ReadingTopicReading Due
excerpts from F&W chapter one Proof of second quantization formulas; Coulomb interaction example 01/13/03
excerpts from F&W chapter two Statistical mechanics review and application to non-interacting Fermi and Bose gases in second quantization 01/15/03
excerpts from Negele/Orland text Coherent states and Gaussian integrals 02/03/03
excerpts from Negele/Orland text Function integral formulation; basics of perturbation theory with path integrals 02/05/03
excerpts from Negele/Orland text Hugenholtz diagrams and Feynman rules 02/12/03
excerpts from Negele/Orland text Irreducible diagrams and integral equations 02/19/03
excerpts from Negele/Orland text Lehmann representation and quasiparticle pole 02/24/03
Introduction to Mattuck text Basic idea of quasiparticles (with pictures) 02/26/03
excerpts from Negele/Orland text Landau Theory of Fermi Liquids 03/03/03
excerpts from Negele/Orland text Stationary-phase approximation and loop expansion 03/10/03
excerpts from Negele/Orland text Physical response functions and Green's functions 05/27/03
excerpts from Negele/Orland text Linear response 05/27/03

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Problem Sets and Hints [subject to change!]

Click on the problem set number to get a pdf copy of the assignment.

Due DateAssignmentCommentsSolutions
01/22/03 #1 hints, suggestions, etc. solutions
02/25/03 #2 hints, suggestions, etc. solutions
03/19/03 #3 hints, suggestions, etc. solutions
04/14/03 #4 hints, suggestions, etc. solutions
05/12/03 #5 hints, suggestions, etc. solutions

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PDF Copies of Handouts

Some of the handouts are available in either postscript (ps) or PDF format.

Date OutHandoutComments
06-Jan-2003 Phenomenological potentials (pdf) Graphs of phenomenological central nucleon-nucleon potential and potential between He-3 atoms.

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Xeroxed Handouts

This is a list of excerpts from texts or review articles handed out in class (extras are available from Prof. Furnstahl). In most cases, they can't be scanned because of copyright issues, but there will be some that have links to downloadable versions (e.g., from the arXiv).

Date OutHandoutComments
06-Jan-2003 Furnstahl plenary talk "Recent Developments in the Nuclear Many-Body Problem" (2001).

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Class Notes

The notes are in PDF format only.

Class DateNotesComments
06-Jan-2003 lecture 1 Course logistics and references, overview
08-Jan-2003 lectures 2, 3a Second quantization; delta-function interaction example
13-Jan-2003 lectures 3b, 4a Thermodynamics/statistical mechanics review; grand partition function
15-Jan-2003 lecture 4b Supplement to previous discussion (page 27a); finish of thermodynamics/statistical mechanics review; path integrals for single-particle quantum mechanics
22-Jan-2003 lecture 4b continue path integrals for single-particle quantum mechanics; present formulas for many-body generalization; study a model partition function (Feynman rules!)
27-Jan-2003 lecture 5 Continue the model partition function: linked cluster expansion, Feynman rules (symmetry factors), infinite summations
29-Jan-2003 lecture 6 Loose ends on the model partition function, path integral for bosonic field partition function, lead-in to fermion path integrals
03-Feb-2003 lecture 7 Fermion and boson path integrals, Grassmann numbers.
05-Feb-2003 lecture 8 Perturbation theory for the log of the partition function and for the Green's function from the fermion path integral.
10-Feb-2003 lecture 9 Feynman rules and diagrams at T=0 in coordinate and momentum space.
12-Feb-2003 lecture 10 Deriving the T=0 limit, Dyson's equation, calculating observables using the Green's function.
17-Feb-2003 lecture 11 Review of contour integration, effective field theory.
19-Feb-2003 lecture 12 Cutoff and dimensional regularization and renormalization of the beachball diagram.
24-Feb-2003 lecture 13 Green's function and Lehmann (spectral) representation.
26-Feb-2003 lecture 14 Physical interpretation of Green's function: the quasiparticle concept, model for quasiparticle spectral function, experimental verification of quasiparticle pict.ure in heavy nuclei.
03-Mar-2003 lecture 15 Landau Fermi liquid theory I: phenomenological approach.
05-Mar-2003 lecture 16 Observable properties of a normal Fermi liquid.
10-Mar-2003 lecture 17 Quasiparticle recap, Bose limit of dilute Fermi system, saddlepoint expansion example, Legendre transformation in spin system.
12-Mar-2003 lecture 18 Effective action and large g expansion for dilute Fermi system, Bose limit.
31-Mar-2003 lecture 19 Numerical example of saddlepoint expansion vs. perturbative expansion. Recap of effective action, large g expansion, and Bose limit. Start one-dimensional bound states and pairing.
02-Apr-2003 lecture 20 Bounds states for the 1-d delta function in free space and in the medium.
07-Apr-2003 lecture 21 BCS variational calculation for the 1-d delta function problem (with g=2).
09-Apr-2003 lecture 22 Bogolyubov transformation, excitation spectrum, connection to nuclear physics, exact solution to 1-d delta function.
14-Apr-2003 lecture 23 Recap of nuclear phenomenology from theory, Mathematica notebook for solving the 1D equations, first part of effective action approach to pairing.
16-Apr-2003 lecture 24 Follow-ups to effective action and pairing. Preview of finite systems and density functional theory.
21-Apr-2003 lecture 25 Phenomenology for nuclear finite systems: Skyrme energy functionals.
23-Apr-2003 lecture 26 Loose ends on Skyrme energy functional calculations; introduction to density functional theory (DFT).
28-Apr-2003 lecture 27 Density functional theory and effective field theory with effective actions.
30-Apr-2003 lecture 28 Basics of the nucleon-nucleon force and scattering (phase shifts).
05-May-2003 lecture 29 Symmetries of the NN force.
07-May-2003 lecture 30 Generating a low-momentum, model-independent potential from henomenological NN potentials by applying renormalization group methods.
12-May-2003 lecture 31 Derivation of the renormalization group equation.
14-May-2003 lecture 32 Scattering in the many-body system.
19-May-2003 lecture 33 Particle-hole effects.
28-May-2003 lecture 34 Linear response and correlation functions.
30-May-2003 lecture 35 Supplementary notes on linear response and quasi-elastic scattering.
02-Jun-2003 lecture 36 Loose ends on linear response.

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Mathematica Notebooks

If you use Internet Explorer on a Windows machine, selecting a Mathematica notebook link should automatically open Mathematica with that notebook. On Macs or linux machines or using other browsers, you can set this behavior in the preferences.

Date OutNotebookComments
01/23/03 Model Partition Function Mathematica notebook that calculates and outputs the relative error for the asymptotic expansion of the model partition function considered in class is available. Also, a gnuplot plot file is available.
02/09/03 DeltaSimplify Mathematica package defining DeltaSimplify to simplify spin sums.
02/09/03 Spin Sums I Mathematica notebook with examples of evaluating spin sums using the simplification package (deltasimplify.m).
02/26/03 Quasiparticles Mathematica notebook with a model for a quasiparticle spectral function.

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*Send Comments or Questions about Physics 880.05

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*Nuclear Many-Body Physics References

Course Reserves

The call number is linked to the OSCAR entry. In some cases, this entry includes the table of contents of the book.

Author(s)TitleCall no.Comments
A.L. Fetter and J.D. Walecka Quantum Theory of Many-Particle Systems QC174.5.F43 1971 Classic text, but pre-path integrals. Now available in an inexpensive (about $20) Dover reprint. Get it!
J.W. Negele and H. Orland Quantum Many-Particle Systems QC174.17.P7 N44 1988 Detailed and careful use of path integrals. Full of good physics but most of the examples are in the problems, so it can be difficult to learn from.
N. Nagaosa Quantum Field Theory in Condensed Matter Physics QC174.45.N27 1999 Recent text, covers path integral methods and symmetry breaking.
A.M. Tsvelik Quantum Field Theory in Condensed Matter Physics QC174.45.T79 1995 [02/12/03: Now available!]
M. Stone The Physics of Quantum Fields QC174.45.S79 2000 A combined introduction to quantum field theory as applied to particle physics problems and to nonrelativistic many-body problems. Some very nice explanations.
R.D. Mattuck A Guide to Feynman Diagrams in the Many-Body Problems QC174.5.M34 1967 This is a nice, intuitive guide to the meaning and use of Feynman diagrams. The second edition is from 1976, but the library may only have the older edition. A paperback version is available from Amazon (and probably elsewere) for under $11.
N. Goldenfeld Lectures on Phase Transitions and the Renormalization Group QC175.16.P5 G65 1992 The discussion of scaling, dimensional analysis, and phase transitions is wonderful.
G.D. Mahan Many-Particle Physics QC176.M24 2000 Standard, encyclopedic reference.
P. Ring and P. Schuck The Nuclear Many-Body Problem QC174.17.P7 R56 1980 Somewhat out of date, but still a good, encyclopedic guide to the nuclear many-body problem. Doesn't discuss Green's function methods much and no path integrals.
K. Huang Statistical Mechanics QC174.8.H83 1987 Excellent choice for general treatment of statistical mechanics, with good sections on many-body physics.

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Other Texts

The call number is linked to the OSCAR entry. In some cases, this entry includes the table of contents of the book.

Author(s)TitleCall no.Comments
P. Nozieres Theory of Interacting Fermi Systems QC174.5 .N651 1964 Outdated in many ways, but great physics explanations. (Three copies are available.)
J.F. Donoghue, E. Golowich, B.R. Holstein Dynamics of the Standard Model QC794.6.S75 D66 1991 Good introduction to low-energy, standard model physics.
P.J. Siemens and A.S. Jensen Elements of Nuclei: Many-Body Physics with the Strong Interaction QC793.3.S8 S54 1987 Good survey of nuclear phenomenology and basic methods.

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Related Review and Journal Articles

  1. R.J. Furnstahl, "Recent Developments in the Nuclear Many-Body Problem" (2001).
  2. P. Lepage, "How to Renormalize the Schrodinger Equation" (1997).
  3. S. Beane et al., "From Hadrons to Nuclei: Crossing the Border" (2000).
  4. H.-W. Hammer and R.J. Furnstahl, "Effective Field Theory for Dilute Fermi Systems", Nucl. Phys. A678 (2000) 277.
  5. R.J. Furnstahl and H.-W. Hammer, "Effective Field Theory for Fermi Systems in a Large N Expansion", Ann. Phys. (NY) 302 (2002) 206.
  6. S.J. Puglia, A. Bhattacharyya and R.J. Furnstahl, "Density Functional Theory for a Confined Fermi System with Short-Range Interaction", Nucl. Phys. A 723 (2003) 145.
  7. R.J. Furnstahl, "Three-Body Interactions in Many-Body Effective Field Theory", invited talk at 17th International IUPAP Conference on Few-Body Problems in Physics (FB 17), Durham, North Carolina, 5-10 Jun 2003.
  8. R.J. Furnstahl, "Next Generation Relativistic Models", Lecture Notes in Physics 641 (2004) 1.

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OSU Physics: Physics 880.05 Nuclear Many-Body Physics.
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