Resources, Readings, and References

Resources, Readings, and References#

Textbooks#

The textbooks for this course are:

For details, please see the Syllabus.

Conventions#

Different texts use different conventions. In these notes, we follow the conventions of

  • [Donoghue and Sorbo, 2022]: (Eqs. (3.22), (4.35) and (4.44).)

  • [Zee, 2010]: (p. xxv and §I.3 Eq. (21).)

  • [Langacker, 2017]: (Table 1.2 and Eq. (2.29).)

    \[\begin{gather*} \mat{g} = \diag(1, -1, -1, -1),\\ (\partial_\mu\partial^\mu + m^2)D_F(x) = -\delta^{(4)}(x),\\ \tilde{D}_{F}(p^{\mu}) = \frac{1}{p^2 - m^2 + \I 0^+}. \end{gather*}\]

  • [`t Hooft, 2016]: (C.f. Footnote 1 on Page 6, and Eqs. (2.6), (2.9), and (2.10).)

    \[\begin{gather*} \mat{g} = \diag(-1, 1, 1, 1),\\ (-\partial_\mu\partial^\mu + m^2)D_F(x) = \delta^{(4)}(x),\\ \tilde{D}_{F}(p^{\mu}) = \frac{1}{\vect{p}^2 - (p^0)^2 + m^2 - \I 0^+}. \end{gather*}\]

  • [Lancaster and Blundell, 2014]: (§0.4 Eq. (13) and Eqs. (17.16) and (17.25))

    \[\begin{gather*} \mat{g} = \diag(1, -1, -1, -1),\\ (\partial_\mu\partial^\mu + m^2)D_F(x) = -\I\delta^{(4)}(x),\\ \tilde{D}_{F}(p^{\mu}) = \frac{\I}{p^2 - m^2 + \I 0^+}. \end{gather*}\]

  • [Srednicki, 2007]

  • [Maggiore, 2005]: (p. xii and Eqs. (5.82) and (5.83).)

    \[\begin{gather*} \mat{g} = \diag(1, -1, -1, -1),\\ (\partial_\mu\partial^\mu + m^2)D_F(x) = -\I\delta^{(4)}(x),\\ \tilde{D}_{F}(p^{\mu}) = \frac{\I}{p^2 - m^2 + \I 0^+}. \end{gather*}\]

References#

[tH16] (1,2)

Gerard `t Hooft. The Conceptual Basis of Quantum Field Theory, chapter 7, pages 661–729. Elsevier, 2016. doi:10.1016/B978-044451560-5/50010-5.

[BH86]

Daniel Baye and P-H Heenen. Generalised meshes for quantum mechanical problems. J. Phys. A, 19(11):2041–2059, 1986. doi:10.1088/0305-4470/19/11/013.

[BO99]

Carl M. Bender and Steven A. Orszag. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. Springer, 1999. ISBN 978-0-387-98931-0. doi:10.1007/978-1-4757-3069-2.

[Boy99]

John P. Boyd. The Devil's invention: asymptotic, superasymptotic and hyperasymptotic series. Acta Appl. Math., 56(1):1–98, 1999. doi:10.1023/A:1006145903624.

[Col88]

Sidney Coleman. Aspects of symmetry: Selected Erice Lectures of Sidney Coleman. Cambridge University Press, Cambridge, 1988.

[Cor97]

J. F. Cornwell. Group Theory in Physics: An Introduction. Volume 1 of Techniques of Physics. Academic Press, San Diego, 1997. ISBN 978-0121898007. doi:10.1016/B978-0-12-189800-7.X5000-6.

[CFP92]

R. J. Creswick, H. A. Farach, and C. P. Poole, Jr. Introduction to Renormalization Group Methods in Physics. Wiley, 1 edition, 1992. ISBN 9780471600138.

[DS22] (1,2)

John Donoghue and Lorenzo Sorbo. A Prelude to Quantum Field Theory. Princeton University Press, Princeton, New Jersey, 2022. ISBN 9780691223483.

[DGH14]

John F. Donoghue, Eugene Golowich, and Barry R. Holstein. Dynamics of the Standard Model. Volume 35 of Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology. Cambridge University Press, 2 edition, 2014. ISBN 9781009291002. doi:10.1017/9781009291033.

[Gau00]

Walter Gautschi. Gauss–Radau formulae for Jacobi and Laguerre weight functions. Mathematics and Computers in Simulation, 54(4–5):403–412, December 2000. URL: http://dx.doi.org/10.1016/S0378-4754(00)00179-8, doi:10.1016/s0378-4754(00)00179-8.

[Geo19]

Howard Georgi. Lie Algebras in Particle Physics. Volume 54 of Frontiers in physics. CRC Press, Boca Raton, FL, 2 edition, May 2019. ISBN 978-0-367-09172-9. doi:10.1201/9780429499210.

[Hua13]

Kerson Huang. A critical history of renormaliation. Int. J. Mod. Phys. A, 28(29):1330050, November 2013. arXiv:1310.5533, doi:10.1142/s0217751x13300500.

[LB14]

Tom Lancaster and Stephen J. Blundell. Quantum Field Theory for the Gifted Amateur. Oxford University Press, Oxford, UK, 2014. ISBN 978–0–19–969932–2.

[Lan17] (1,2)

Paul Langacker. The Standard Model and Beyond. Series in high energy physics, cosmology, and gravitation. CRC Press, Boca Raton, FL, 2 edition, 2017. ISBN 9781315170626. doi:10.1201/b22175.

[Lep97]

Peter Lepage. How to renormalize the Schrödinger equation. 1997. URL: http://arxiv.org/abs/nucl-th/9706029, arXiv:nucl-th/9706029.

[LC02]

Robert G. Littlejohn and Matthew Cargo. Bessel discrete variable representation bases. J. Chem. Phys., 117(1):27–36, July 2002. doi:10.1063/1.1481388.

[LCC+02]

Robert G. Littlejohn, Matthew Cargo, Tucker Carrington, Jr., Kevin A. Mitchell, and Bill Poirier. A general framework for discrete variable representation basis sets. J. Chem. Phys., 116(20):8691–8703, 2002. doi:10.1063/1.1473811.

[Mag05]

Michele Maggiore. A Modern Introduction to Quantum Field Theory. Volume 12 of Oxford Master Series in Statistical, Computational, and Theoretical Physics. Oxford University Press, Oxford, UK, 2005. ISBN 0 19 852073 5.

[McG18]

John McGreevy. Physics 217: The renormalization group, Fall 2018. 2018. URL: http://physics.ucsd.edu/~mcgreevy/f18/.

[Mer07]

N. D. Mermin. Quantum Computer Science: An Introduction. Cambridge University Press, 2007. ISBN 978-0-511-33982-0. URL: https://www.cambridge.org/core/books/quantum-computer-science/66462590D10C8010017CF1D7C45708D7, doi:10.1017/CBO9780511813870.

[ML03]

Cleve Moler and Charles Van Loan. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49, 2003. URL: http://dx.doi.org/10.1137/S00361445024180, doi:10.1137/S00361445024180.

[NC10]

Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010. URL: https://doi.org/10.1017%2Fcbo9780511976667, doi:10.1017/cbo9780511976667.

[Nvastase19]

Horaţiu Nǎstase. Classical Field Theory. Cambridge University Press, Cambridge, UK, 2019. ISBN 9781108477017. doi:10.1017/9781108569392.

[SN04]

Barry I. Schneider and Nicolai Nygaard. Discrete variable representation for singular Hamiltonians. Phys. Rev. E, 70:056706, November 2004. URL: https://link.aps.org/doi/10.1103/PhysRevE.70.056706, arXiv:physics/0407076, doi:10.1103/PhysRevE.70.056706.

[Sre07]

Mark Srednicki. Quantum Field Theory. Cambridge University Press, Cambridge; New York, 2007. ISBN 9780521864497.

[Tan05]

Shina Tan. S-wave contact interaction problem: a simple description. 2005. arXiv:cond-mat/0505615, doi:10.48550/arXiv.cond-mat/0505615.

[Zee10]

Anthony Zee. Quantum Field Theory in a Nutshell. In a Nutshell. Princeton University Press, 2 edition, 2010. ISBN 9780691140346.

[Zee23]

Anthony Zee. Quantum Field Theory, As Simply As Possible. Princeton University Press, Princeton, New Jersey, 2023. ISBN 978-0-691-17429-7.

Linear Algebra#