Physics 8805 Nuclear Few- and Many-Body Physics
Autumn, 2014

Welcome to the Physics 8805.01 Nuclear Many-Body Physics home page!
The course information is available here plus lots of supplementary info. Please check this page regularly.

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Class meetings

Class DateNotesTopic and supplementary readings Exercises
27-Aug-2014 1. Overview Brief overview of the course  
27-Aug-2014 2. QCD-1 [handwritten] A first look at QCD. Useful lectures on QCD (for us) are by X. Ji (also his chapter 3) and A. Khodjamirian, the Particle Data Group (PDG) has summary articles on the quark model and QCD, and there is a good resource letter on QCD (some background then pointers to detailed references). QCD 1
01-Sep-2014   Labor Day holiday: no class.  
03-Sep-2014 2. QCD-1 (cont.) QCD 1 continued plus discussion of questions. (Lecture by Sebastian; Dick will be in Poland.) The references listed under August 27 may be helpful here.  
08-Sep-2014 3. Scattering-1 [handwritten] Scattering theory 1. An overview of various topics in non-relativistic scattering theory. An AJP article on conventions of scattering theory is very useful. Useful lectures on scattering are by Filomena Nunes and the best introduction to non-relativistic scattering is the book by Taylor (only $20!). There is a Mathematica notebook solving for square-well phase shifts using the Variable Phase Approach. Scattering 1
10-Sep-2014 3. Scattering-1 (cont.) Scattering 1 continued plus a preview of Nuclear Forces 1.  
15-Sep-2014 4. Forces-1 [handwritten] Nuclear Forces 1. Symmetry constraints on NN forces; overview of available interactions; problems with phenomenological potentials. Forces 1
17-Sep-2014 5. Scattering-2 [handwritten] Scattering theory 2. What NN phase shifts tell us about the nucleon-nucleon interaction. Scattering 2
22-Sep-2014 6. Forces-2 Nuclear Forces 2. Nuclear forces at low very energies, which leads us to pionless effective field theory. Forces 2
24-Sep-2014 6. Forces-2 (cont.) Nuclear Forces 2 continued. First look at renormalization and three-body forces for pionless EFT.  
01-Oct-2014 7. Pionless-1 More renormalization and universality in pionless EFT. (see Piazza)
06-Oct-2014 8. MBPT-1 [handwritten] First look at many-body perturbation theory using natural pionless EFT. There are some longer notes on second quantization from a previous course. The Wikipedia article is actually not bad (yea!). (see Piazza)
17-Oct-2014 9. HF-1 [handwritten] Further developments on Hartree-Fock. (see Piazza)
22-Oct-2014 Handwritten sect. 8-9 followups Further details on Feynman rules and power counting applied to pionless EFT for dilute uniform systems, lead in to model partition function to illustrate general Feynman rules, alternatives to perturbation theory, Dyson's equations, etc. There are extensive notes on the model partition function from the 2009 880.05 many-body course. We will do some of this in class and the rest on Piazza. A good set of Gaussian integration formulas in many contexts is in this excerpt from Chapter 1 of Zinn-Justin's classic book on QFT and Critical Phenomena (see also his path integral book for QM). (see Piazza)
27-Oct-2014 Handwritten model partition function Using the model partition function to show how Feynman diagrams (including symmetry factors) arise, how disconnected diagrams cancel out, and how partial infinite resummations can be formulated. (see Piazza "model_Z")
29-Oct-2014 Handwritten notes Transitioning from the model partition function to a real one in path integral form. (see Piazza)
03-Nov-2014 Handwritten notes Non-perturbative expansions in general and self-consistent Hartree-Fock in particular from Dyson's equations. Appendix A notes cover details of the euclidean path integral formalism that will not be covered in class (but some in Piazza). See also the readings from the Negele-Orland many-body book on "Coherent states and Gaussian Integrals", "Function integral formulation; basics of perturbation theory with path integrals", "Hugenholtz diagrams and Feynman rules", and "Irreducible diagrams and integral equations" under Selected Excerpts. (see Piazza)
05-Nov-2014   A mathematician's "easy" example of Feynman integrals in this blog post by David Mumford. In class we looked at slides by Alex Gezerlis on "Strong Paired Fermions" and by Piotr Magierski on the "Path Integral (Auxiliary Field) Monte Carlo approach to ultracold atomic gases". Here are some specific comments on slides in the Magierski talk. We will follow-up on both of these with Piazza questions. (see Piazza)
10-Nov-2014 HF follow-ups [handwritten] We'll use the spectral density slides from Carlo Barbieri and Andrea Cipollones, and the Self-consistent Green’s functions with three-body forces talk from Arianna Carbone. See this Negele-Orland excerpt and this lecture by Barbieri for more on the Lehmann representation and quasiparticles. (see Piazza)
12-Nov-2014 Handwritten RG-1 notes [short overview] Renormalization group (RG) for free space inter-nucleon interactions. We will use a combination of slides from HUGS 2014 lectures by Dick Furnstahl [HUGS-1] [HUGS-2] [HUGS-3] [HUGS-4] [HUGS-5] [HUGS-6]. Today we'll references lectures 1 and 2. (see Piazza)
17-Nov-2014 RG-2 [recap and supplement] More on RG. We'll use slides from HUGS Lecture 2 and Lecture 3 (see Piazza)
24-Nov-2014 RG-3 [recap and supplement] More on RG. We'll use slides from HUGS Lecture 4 (see Piazza)
01-Dec-2014 3NF in PNM and SNM [extra notes on 3NF and tensor force] More on 3-body forces, including their impact on symmetric nuclear matter and pure neutron matter (from HUGS Lecture 4 notes). An early experiment to determine the deuteron quadrupole moment by measuring hyperfine splittings in D2 molecules. (see Piazza)
03-Dec-2014 Chiral EFT [handwritten notes] Selected aspects of chiral effective field theory. Slides with some pictures of resonance saturation and Delta-ful EFT. (see Piazza)
08-Dec-2014 Skyrme EDF and DFT [handwritten notes] A quick introduction to density functionals, building on our Hartree-Fock discussions. Background slides on DFT and Skyrme functionals. Notes on MBPT (revisited). Talk on "The fate of UV physics with renormalization group evolution", which covers many of the recent topics from class. (see Piazza)

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The Piazza home page for 8805 is


Selected Excerpts

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

PDF Copies of Handouts

Date OutHandoutComments

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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).

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Mathematica Notebooks

On some machines clicking the link will start Mathematica directly. If not, "right click" to save the file and then read it into Mathematica separately.

Date OutNotebookComments
09/06/14 Square well energies Notebook that solves the transcendental equation to find bound-state energies for a specified square well potential.
09/06/14 Square well phase shifts Notebook that solves the variable phase approach differential equations to find phase shifts for a specified square well potential.

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IPython Notebooks

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Your comments and suggestions are appreciated.
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