Suggested readings, incl. original papers (Ref. numbers with dots indicate further reading):
I. Quantum effects in finite volume
[1] K. A. Milton,
The Casimir Effect: Physical Manifestations of Zero-Point Energy (World Scientific, Singapore, 2001); e-Print arXiv:hep-th/9901011.
[2] M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko,
Advances in the Casimir Effect (Oxford Science Publications, Oxford, 2009).
[3] K. A. Milton, L. L. DeRaad, Jr., and J. Schwinger,
Casimir Self-Stress on a Perfectly Conducting Spherical Shell, Ann. Phys.
115, 388 (1978).
[4] M. Bordag, G. Petrov, and D. Robaschik,
Calculation of the Casimir
effect for a scalar field with the simplest non-stationary boundary conditions, Sov. J. Nucl. Phys.
39, 828 (available in Russian as Yad. Fiz.
39, 1315 and from the KEK server
http://ccdb5fs.kek.jp/cgi-bin/img_index?8308199).
[5] E. Elizalde,
Ten Physical Applications of Spectral Zeta Functions, Lecture Notes In Physics series, volume
855 (Springer, Berlin, 2012).
[6] S. Hawking,
Zeta Function Regularization of Path Integrals in Curved Spacetime, Commun. Math. Phys.
55, 133 (1977).
[7] S. A. Fulling and P. C. W. Davies,
Radiation from a Moving Mirror in Two Dimensional Space Time: Conformal Anomaly, Proc. Roy. Soc. Lond. A
348, 393 (1976).
[7.1] H. Epstein, V. Glaser, A. Jaffe,
Nonpositivity of the energy density in quantized field theories, Nuovo Cimento
36, 1016 (1965).
[8] R. Rajaraman,
Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory, (Elsevier, Amsterdam, 1982). Available in Russian as
Р. Раджараман, Солитоны и инстантоны в квантовой теории поля (Москва, "Мир", 1985).
[8.1] A. C. Scott, F. Y. F. Chu, and D. W. McLaughlin,
The soliton: A new concept in applied science, IEEE Proc.
61, 1443 (1973).
II. Quantum effects in strong external fields
[1] S. L. Adler,
Photon Splitting and Photon Dispersion in a Strong Magnetic Field, Ann. Phys.
67, 599 (1971).
[1.1] S. L. Adler and C. Schubert,
Photon Splitting in a Strong Magnetic Field: Recalculation and Comparison with Previous Calculations, Phys. Rev. Lett.
77, 1695 (1996).
[1.2] C. Schubert,
QED in the worldline representation, AIP Conf. Proc.
917, 178 (2007).
[2] J. Schwinger,
On Gauge Invariance and Vacuum Polarization, Phys. Rev.
82, 664 (1951).
[3] H. Nunokawa, V. B. Semikoz, A. Yu. Smirnov, and J. W. F. Valle,
Neutrino conversions in polarized medium, Nucl. Phys. B
501, 17 (1997).
[4] S. Esposito and G. Capone,
Neutrino propagation in a medium with a magnetic field, Z. Phys. C
70, 55 (1996).
[4.1] S. J. Hardy and D. B. Melrose,
Ponderomotive force due to neutrinos, Phys. Rev. D
54, 6491 (1996).
[5] A. A. Andrianov and R. Soldati,
Lorentz symmetry breaking in Abelian vector-field models with Wess-Zumino interaction, Phys. Rev. D
51, 5961 (1995).
[5.1] A. A. Andrianov, R. Soldati, and L. Sorbo,
Dynamical Lorentz symmetry breaking from a (3+1)-dimensional axion-Wess-Zumino model, Phys. Rev. D
59, 025002 (1998).
[5.2] A. A. Andrianov, P. Giacconi, and R. Soldati,
Lorentz and CPT violations from Chern-Simons modifications of QED, JHEP
02, 030 (2002).
[5.3] D. Colladay and V. A. Kostelecky,
Lorentz-violating extension of the standard model, Phys. Rev. D
58, 116002 (1998).
[6] M. K. Parikh and F. Wilczek,
Hawking radiation as tunneling, Phys. Rev. Lett.
85, 5042 (2000).
[7.1] Lectures of prof. Scrucca in Advanced quantum field theory (e.g., for the first study of the worldline formalism):
http://itp.epfl.ch/webdav/site/itp/users/181759/public/aqft.pdf
III. There and back again: From QFT to the lattice field theory
[1] W. A. Harrison,
Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Dover, 1989).
[2] E. Fradkin,
Field Theories of Condensed Matter Physics, (2nd ed., CUP, 2013).
[3] P. Hohenberg and W. Kohn,
Inhomogeneous Electron Gas, Phys. Rev.
136, B864 (1964).
[4] W. Kohn and L. J. Sham,
Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev.
140, 1133 (1965).
[5] DFT lecture notes by Roi Baer, including a nice tutorial on the Thomas-Fermi model (chapter II), are available at
https://openscholar.huji.ac.il/sites/default/files/f-h/files/dft-roi.baer.pdf.
[6] A very handy Hubbard model introduction: R. T. Scalettar,
Elementary Introduction to the Hubbard Model, lecture notes, UC Davis,
http://quest.ucdavis.edu/tutorial/hubbard7.pdf
[7] E. H. Lieb and F. Y. Wu,
Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension, Phys. Rev. Lett.
20, 1445 (1968).
IV. There and back again: QFT as a continuum limit of the lattice theory
[1] A. H. Castro-Neto et al.,
The electronic properties of graphene, Rev. Mod. Phys.
81, 109 (2009).
[2] M. A. H. Vozmediano, M. I. Katsnelson, and F. Guinea,
Gauge fields in graphene, Phys. Rept.
496, 109 (2010).
[3] G. Semenoff,
Condensed-Matter Simulation of a Three-Dimensional Anomaly, Phys. Rev. Lett.
53, 2449 (1984).
[3.1] P. R. Wallace,
The Band Theory of Graphite, Phys. Rev.
71, 622 (1947).
[4] K. Wakabayashi
et al.,
Electronic and magnetic properties of nanographite ribbons, Phys. Rev. B
59, 8271 (1999).
[5.1] D. Gunlycke and C. T. White,
Valley and spin polarization from graphene line defect scattering, J. Vac. Sci. Technol. B
30, 03D112 (2012).
[6] O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin,
Gap generation and semimetal-insulator phase transition in graphene, Phys. Rev. B
81, 075429 (2010).
[7] J. Gonzalez, F. Guinea, and M. A. H. Vozmediano,
Non-Fermi liquid behavior of electrons in the half-filled honeycomb lattice (A renormalization group approach), Nucl. Phys. B
424, 595 (1994).
Selected lecture notes & presentations (access granted to students attending the course):
I. Quantum effects in finite volume
Lecture 1,
The Outline & Before Casimir: the van der Waals forces (presentation, pdf)
Lecture 2,
The Casimir effect: different approaches and their equivalence
(presentation, pdf)
Lecture 3,
The Casimir effect: explicit renormalization, zeta function regularization
(presentation, pdf)
Lecture 4,
The Casimir effect: the Green function technique
(presentation, pdf)
Lecture 5,
The Casimir effect: the dyadic Green function technique, spherical Casimir effect
(presentation, pdf)
Lecture 6,
Fundamentals of the Dynamical Casimir effect
(presentation, pdf)
Lecture 7,
The Dynamical Casimir Effect: arbitrarily moving ‘plate’ in D = 1 + 1
(presentation, pdf)
Lecture 8,
Quantization of classical solutions: the kink (or quantized fields in a self-consistent finite volume)
(presentation, pdf)
II. Quantum effects in strong external fields
Lecture 9,
Photon splitting in strong magnetic field: Heisenberg, Euler, and Adler
(presentation, pdf)
Lecture 10,
Neutrino in dense media and fundamentals of collective neutrino oscillations
(presentation, pdf)
Lecture 11,
Radiative Lorentz violation: the Axion-Wess-Zumino model
(presentation, pdf)
III. There and back again: From QFT to the lattice field theory
Lectures 1-2,
Tight-binding model and its origins
(presentation, pdf)
Lectures 3-4,
Many-particle to one-particle: some recipes. Hartree--Fock & DFT
(presentation, pdf)
Lecture 5,
Lattice field theory: ‘free fields’
(presentation, pdf)
Lectures 6-8,
Lattice field theory: ‘interacting fields’. The Hubbard model &
Fermi surface instabilities; BCS superconductivity
(presentation, pdf)
IV. There and back again: QFT as a continuum limit of the lattice theory
Lecture 9,
Graphene: honey from the honeycomb. Gauge fields, strains, EM interaction
(presentation, pdf)
© Кафедра теоретической физики физического факультета МГУ имени М.В. Ломоносова, 2018