Winter/Spring, 2003

Welcome to the Physics 880.05 Nuclear Many-Body Physics home page!

URL: http://www.physics.ohio-state.edu/~ntg/880/manybody.php

The course information is available here plus lots of supplementary
info. Please check this page regularly.

- 08-Sep-2009 --- *** If you are looking for Physics 880.05 for
Autumn 2009 (which is titled
*Many-Body Physics: EFT, RG, and Computation*), please go to http://www.physics.ohio-state.edu/~ntg/880_2009/. - 14-Jun-2004 --- If you are interested in having access to the lecture notes posted here, send email to Dick Furnstahl at furnstahl.1@osu.edu. Warning: typo's in the scanned notes have not been corrected! If there is enough demand (i.e., complaints), I will try to find time to compile errors and post an errata page.

- Course description and info
- Assignments
- General handouts
- Send feedback to the instructors -- anonymous or not
- Resources
- Course Reserves --- available for two hours at the Science and Engineering Library
- Other Texts --- additional references that may be useful (not reserved)
- Review Articles --- useful reviews, summer school lectures, and some journal articles

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

Due Date | Assignment | Comments | Solutions |
---|---|---|---|

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

Date Out | Handout | Comments |
---|---|---|

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

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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 Out | Handout | Comments |
---|---|---|

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

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The notes are in PDF format only.

Class Date | Notes | Comments |
---|---|---|

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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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 Out | Notebook | Comments |
---|---|---|

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

Author(s) | Title | Call 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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The call number is linked to the OSCAR entry. In some cases, this entry includes the table of contents of the book.

Author(s) | Title | Call 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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- R.J. Furnstahl, "Recent Developments in the Nuclear Many-Body Problem" (2001).
- P. Lepage, "How to Renormalize the Schrodinger Equation" (1997).
- S. Beane et al., "From Hadrons to Nuclei: Crossing the Border" (2000).
- H.-W. Hammer and R.J. Furnstahl,
"Effective Field
Theory for Dilute Fermi Systems", Nucl. Phys.
**A678**(2000) 277. - R.J. Furnstahl and H.-W. Hammer,
"Effective Field
Theory for Fermi Systems in a Large N Expansion", Ann. Phys.
(NY)
**302**(2002) 206. - 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. - 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.
- R.J. Furnstahl,
"Next Generation
Relativistic Models",
Lecture Notes in Physics
**641**(2004) 1.

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Your comments and suggestions are appreciated.

[OSU Physics] [Math and Physical Sciences] [Ohio State University]

Last modified: .

furnstahl.1@osu.edu