OSU Physics: Physics 880.05 Nuclear Many-Body Physics

Welcome to the Physics 880.05 Nuclear Many-Body Physics home page!
URL: http://www.physics.ohio-state.edu/physics/ntg/880/manybody.php
The course information is available here plus lots of supplementary info. Please check this page regularly.

Recent changes to this page:

Assignments

Readings

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

Problem Sets and Hints [subject to change!]

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

Handouts

PDF Copies of Handouts

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

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

Class Notes

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.

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 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.

Send Comments or Questions about Physics 880.05

Send email to Prof. Furnstahl at furnstahl.1@osu.edu

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)	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.

Other Texts