A. Altland and Ben Simons. Condensed Matter Field Theory. This is an advanced book, but one of the best to learn about the modern approach to condensed matter theory, with many-body theory done by functional integral techniques, and a clear and readable presentation of many technical issues.
Ordered phases in optical lattices (superfluid, Mott insulators, ...) Quantum hall states of rapidly rotating BECs Magnetic states of condensed matter (ferromagnets, antiferromagnets, spin glass, ...) Disordered states of matter (Griffiths phases, random field Ising models, localization, ...)
Altland Simons Condensed Matter Field Theory Pdf Free
Lecture Notes and Homework Problems: (see general instruction on homework problems)Sep. 26: note-01hw-01introduction, S-matrix, decay rate, cross section                                          [4.5, [W-I 3.1, 3.2]] Oct. 03: note-02hw-02LSZ formula, spectral representation                                          [4.2--4.4, 4.6--4.8, 7.1, 7.2, [W-I 4.3, 10.7]] Oct. 17: note-03-----Feynman rule, loop expansion // vector field propagator, e+e- to mu+mu-                                          [3.2, 3.3, 3.5, 4.3, 4.4, 4.6--4.8, [W-I 6., 8.], 5.1]                                           [For section 2.4 of the lecture note, see [LB 2.3, 2.5, 3.3], [K 2.1--2.7], [AS 7., 11.] and hw E-2, E-3]Oct. 24: note-04hw-04e+e- to mu+mu-: unpolarized (high energy, threshold), polarized                                          [5.1--5.3] Oct. 31: note-05hw-05crossing symmetry, t-channel 2to2, non-relativistic limit, Mott scattering, LS coupling                                          [5.4] Nov. 07: note-06-----Compton/Thomson scattering // Bethe-Salpeter equation                                           [5.5, [Ni 3.4, 3.5], [LL4 125], [T 10]] Nov. 14: note-07hw-07Bethe-Salpeter equation, fine structure, hyperfine structure, Lamb shift                                          [[LL4 125], [T 10], [LL4 33, 34], [Ni 1.10], [LL4 123], 7.5, Wikipedia] Nov. 21: note-08hw-08atomic transition // partial wave unitarity                                          [??, [W-I 3.6--3.8]] Nov. 28: note-09 -----optical theorem // low-energy effective theory //                                           [7.3] Dec. 05: note-10 -----path integral formulation of quantum mechanics                                           [[FH 3, 8], [Na 2.1], [AS 3.2], 9.1] Dec. 12: note-11hw-11path integral for a 2-state (fermionic) system, and for QFTs                                           [[Na 2.3; 2.2], [AS 4.2], 9.5, 9.2, 9.3, [LB 5.1, 6.1]] Dec. 19: note-12-----free energy, effective action                                           [11.3-5, 16.6, [W-II 16.1-3, 21.6]] Dec. 26: note-13hw-13thermal field theory (imaginary time formalism)                                           [8, 9.2, 9.5, [LB 2.1, 2.6, 3.1]] Jan. 16: note-14hw-14coarse graining, real time (Keldysh) formalism //                                           [[LB, K (see Refs. for the week 3)], [hw E-2]] Jan. 23: note-15-----1-loop computation (anomalous magnetic moment) //                                           [6.2, 6.3] Jan. 30: note-16-----a bonus track: Borel resummation                                           [[W-II 20.7], [AS 5.1], arXiv:1403.1277] Advanced homework problems: D-1, D-2, D-3 and E-1, ..., E-6. Materials that this course did not cover pdf numbers in [     ] are the relevant sections in textbooks and references. When the textbooks or references are not specified, that is [PS] below.
"Introduction to Many-Body Physics", P. Coleman. An amazing treatise on introductory and not so introductory many-body physics applied to condensed matter theory. In addition it provides historical facts and uses plenty of figures to illustrate concepts and experimental results. More updated than others.
Many-body theory courses can often be the first time students are introduced to quantum field theory. As a graduate student in high-energy physics with background in condensed matter/solid state physics, I can say that high-energy versions of QFT courses do not usually focus on applications of QFT outside scattering cross-section calculations, and it is important (even for high-energy theorists in my opinion) to know what to do with QFT as a general tool. There aren't very many books on QFT which do not convert you completely into the high-energy or the cond-mat camp. That's why books like this one are useful in shaping your holistic understanding of QFT.
There are mainly two ways in which path integrals come into play in our discussion. One is in evaluating the probability amplitude of a quantum mechanical process, i.e. a complex number whose squared modulus yields the probability. Suppose we are studying a field ϕ (generally a function of time t and position ) which, in our examples below, is typically an order parameter for some condensed matter (such as a superconductor or a ferromagnet). If we are interested in the probability amplitude associated with the realization of a certain spatial configuration , we can formally write it down as the path integral (for most of the following we will set )
Exam:Wednesday 21 May, 9:00-13:00.You may bring:- an approved calculator- Rottmann: Matematisk formelsamling/Mathematische Formelsammlung- Barnett and Cronin: Mathematical Formulae for Engineering and Science StudentsPre-exam Q&A session:Friday 16 May at 10:15 in E5-103.Curriculum:The curriculum ("pensum") for the exam is based on the material that has been covered in lectures, plus the written solutions to the tutorial problems. For the lecture material one may alternatively use the following notes/sources: - Second quantization- Second quantization representation for the Hamiltonian of an interacting electron gas- Noninteracting electrons. The free electron gas- Tight-binding model for electrons in a crystal- The Hubbard and Heisenberg models, spin-wave theory of ferro- and antiferromagnets, broken symmetry and Goldstone modes- Transformations and symmetries in quantum mechanics- Introduction to Green functions and many-body perturbation theory (except Secs. 4.9 and 4.10)- The Klein-Gordon equation: Sec. 17.1.1 in Hemmer's "Kvantemekanikk".- The Dirac equation: Sec. 17.2 in Hemmer, except Sec. 17.2.4.c about helicity. Note that the following topics which were discussed in lectures (some of them only briefly) are not examinable:- the material on Bloch and Wannier states discussed before the tight-binding model(but note that the material on the tight-binding model is examinable, cf. notes above)- the detailed derivation (using projection operators) of the S=1/2 Heisenberg antiferromagnetic model from the half-filled Hubbard model in the strong-interaction limit- the Mermin-Wagner theorem- aspects of broken symmetry that are not covered in Sec. 6 of the magnetism notes (but, to be clear, the material in that section is examinable)- the Kubo formula for the conductivity (Secs. 4.9 and 4.10 in theGreen function notes)In the tutorials, the following topics are not exam relevant:- Problem 1 in Tutorial 4- Issues related to the projection operators P in problem (e) inTutorial 5.The curriculum this year is very similar to that for the2013 version of the course. A brief summaryof the minor differences between the notes above and last year'sversions can be found here. Resources:Main resources:- Notes by the lecturer. Notes for the varioussections will be identical or similar to those used in the 2013 version of the course.- Ch. 17 on relativistic wave equations in "Kvantemekanikk" by P. C. Hemmer (Tapir, 2005). Supporting resources:There is no single textbook that covers all the material that will be discussed in the course. Much of the material on non-relativistic quantum many-particle systems is covered in "Many-body quantum theory in condensed matter physics" by Bruus and Flensberg (Oxford, 2004), which is the main recommended textbook for this part of the course. Another recent textbook in the same area that may be useful is "Condensed matter field theory" by Altland and Simons (2nd ed., Cambridge, 2010). An old classic is "Quantum theory of many-particle systems" by Fetter and Walecka from 1971 which is available in a non-expensive paperback version (Dover, 2003). The main reference on the quantum magnetism material is "Interacting electrons and quantum magnetism" by Auerbach (Springer, 1994). Other references may be provided later.Tutorial sets: Tutorial Date Presenter Problems Solution 1 17 Jan Toni Müller pdf pdf 2 24 Jan Vigdis Toresen pdf pdf 3 31 Jan Jonas Kjellstadli pdf pdf 4 7 Feb Kilian Mitterweger pdf pdf 5 14 Feb Noemie Jourdain pdf pdf 6 21 Feb Tristan Müller pdf pdf 7 28 Feb Sverre Gulbrandsen pdf pdf 8 7 Mar Camilla Espedal pdf pdf 9 14 Mar Ane Nordlie Johansen pdf pdf 10 21 Mar --- pdf pdf 11 28 Mar Laura Friedeheim Daniel Wennberg pdf pdf 12 4 Apr --- pdf pdf 13 11 Apr Lynn Vera Meissner pdf pdf
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