Methods of Theoretical Physics

Physics 231, Fall 2018
Prof. Flip Tanedo; office hours by appt.
TA. Ian Chaffey; office hours Tue 1-3pm (Physics 3004S)

Syllabus

Please see the schedule of meetings below.

Note that there will be no meeting on the following days:

• Monday, Oct 22: no meeting
• Friday, Oct 26: no meeting
• Monday, Nov 12: no meeting
• Friday, Nov 16: no meeting
• Monday, Nov 19: no meeting
• Friday, Nov 23: no meeting

Course Description

This is a crash course in (a) mathematical methods for physics and (b) necessary science communication for your Ph.D. The topics are selected to be useful in your graduate coursework and research. This is not a mathematics course, it is boot camp for physicists.

Textbook

There is no required textbook, though I particularly like Mathematics for Physics & Physicists by Appel (ISBN: 9780691131023).

I strongly recommended that you have access to at least one general “math methods for physicists” reference. If you have a favorite one from undergrad, you may use that (e.g. Arfken & Weber or Boas). The book by Byron and Fuller is a solid choice and is inexpensive as a Dover edition. You can also find many free digital references through the UCR library.

• Mathematics of Classical and Quantum Physics, Byron and Fuller

• Mathematical Methods in the Physical Sciences, Mary Boas

• Mathematical Physics: a Modern Introduction to its Foundations, Sadri Hassani; digital version free from UCR Library.

• Mathematics of Classical and Quantum Physics, Byron and Fuller

• Mathematical Methods of Physics, Mathews and Walker

• Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, Barlow; if we do statistics.

If you find references that you really like, please feel free to e-mail me to share them. (Bonus: make a GitHub pull request to add it to the list.)

It may be useful to refer to last year’s course notes. The 2016 version if this course was more [differential] geometric, though also more prone to have errors.

Homework

1. Short Homework due Wed, Oct 3: dimensional analysis
   Long homework due Mon, Oct 15: linear algebra

2. Short Homework due Wed, Oct 17: Green’s Function Primer
   Long homework due Mon, Oct 29: What’s a Green’s Function

3. Short Homework due Wed, Oct 31: Analytic Functions are Too Nice
   Long homework due Mon, Nov 12: Complex Analysis

Talk Schedule

Topics to be assigned and discussed in our meetings. The order was determined using random.org and then the undergrads were rearranged to talk first. Suggested topics are listed.

• Wed, Oct 10:
  Kyle Perez: HW1b, extra credit 2(f).
  Sergio Garcia: My summer research.
  Thomas Waddleton: HW1b, Problem 1.
  Christopher Cain: Interpreting HW1b, Problem 3.
  John Lee: Explain HW1b eq (2.1), discuss boundary conditions.

• Wed, Oct 17: Michael Worcester: What is the NSF GRFP?
  Shirash Regmi: What to expect from TA’ing a lab
  Medhanie Estiphanos: Research talk Mehmet Kilinc: What kind of outreach can a grad student do?
  Cameron Racz: What resources does GradSuccess have for phys/astro students?

• Wed, Oct 24:
  Ao Shi: unavailable
  Ian Cadenhead: Research talk
  Linke Xie: Homework 2B: Research talk
  Elizabeth Finney: Impostor’s Syndrome
  Ming-Feng Ho: Homework 2B, Problem 1.3

• Wed, Oct 31:
  The talks for this session are now on Dec 7 due to concerns that the 5 minute talk preparation is an undue burden during midterm exams.

• Wed, Nov 7:
  Meng Hou,
  Yongda Zhu,
  Jackson Kishbaugh-Maish,
  Robert Dawson,
  Adam Green: E&M homework

• Wed, Nov 14:
  Xilin Liang: Monte Carlo in HEP,
  Michael Gordon,
  Chen Wang: superconductivity,
  William Baker: red dwarfs

• Wed, Nov 21:
  Nakul Gangolli: units in astronomy,
  Shixiong Wang: separation of variables,
  Cameron Chevalier: quantizing gravity,
  Jonathan Turner: sandwich, spaghetti, meatballs

• Wed, Nov 28:
  Varrick Suezaki: paper mache the Earth,
  Yifan Liu: quantum random walk,
  Erik Loyd: inverse functions,
  Zahra Sattari: EFT for cosmology

• Wed, Dec 5:
  Mehrdad Phoroutan Mehr: expansion vs. inflation,
  Alexander Mercaldi: entropy vs. gravity,
  Brian Lee: terrible integrals,
  Mahdi Qezlou: cosmology,
  Mingda Guo: Int. Young Physicists’ Tournament

Evaluation

Five homework assignments (two parts each) will be assigned every other Monday. These will consist of a short homework (5 points, due the following Wednesday) and a long homework (20+ points, due in 2 weeks).

In addition, each students will give one five minute talk (25 points) over the course of the quarter. Periodic in-class assessments in the form of index cards (1 point) will help me tailor the course trajectory as we go. There will be no exams.

I strongly encourage you to work together. Please abide by the UCR Academic Integrity Policies.

“Lecture” Notes

These notes are provided as is and may have errors. They also do not include the questions and discussions from class. The most meaningful parts of this class (like grad school as a whole) will be unscripted.

• Meeting 01: Welcome, dimensional Analysis. Index Card: (1) What should I know about you? (2) How do you learn?

• Meeting 02-03: Scaling, error analysis with dimensional analysis. Discretized functions as vector spaces, derivatives as linear operators. Suggested reading: Linear Algebra Done Right, Axler. First few chapters as needed. You can access the book through the library when you’re on the UCR network. If you’re off-campus, you can use the UCR VPN.

• Meeting 04: HW1b question and answer session. Discretized functions review. Index Card: How will you be evaluated after your PhD? Suggested reading: The books by Byron and Fuller, Mathews and Walker cover this type of materials. You will also find problems similar to our model of a molecule in Howard Georgi’s waves lecture notes. This line of thought led to ideas like dimensional deconstruction.

• Meeting 05: Row vectors as linear transformations on vectors. Bases. Bra-ket notation.

• Meeting 06: Green’s functions in linear algebra… taking the inverse.

• Meeting 07: Green’s functions in linear algebra: a trivial example. Sample pop talk: focusing on your audience. Life pro tips for surviving graduate school.

• Meeting 08: Q & A and Pop Talks. Index Card: observations of good traits and pitfalls in today’s pop talks.

• Meeting 09: Inner products on function space. Self-adjoitness, Hermiticity, all that.

• Meeting 10-11 (Additional): Constructing Green’s functions of self-adjoint differential operators using (1) completeness, (2) patching.

• Meeting 12: Q & A and Pop Talks, Notes

• Meeting 13: Introduction to complex analysis. Analyticity, Cauchy-Riemann equations.

• Meeting 14: Q & A and Pop Talks

• Meeting 15 - 18: Cauchy integral theorem, complex analysis, analyticity, causality. Spotty notes: 17, 18, (Notes from 2017 class: 11, 12, 13, 14, 14, 15, 16, 17)

• Meeting 19: Dispersion relations

• Meetings 20, 21: Q & A and Pop Talks

• Meeting 22: Solving for Green’s Functions (notes from 2017)

• Meeting 23, 24: Q & A and Pop Talks

• Meeting 25 - 26: Damped Harmonic Oscillator (HW notes)

• Meeting 27: Q & A and Pop Talks

• Meeting 28: Green’s functions in 3D

• Meeting 29: Some notes on statistics

• Meeting 30: No meeting.

• Meeting 31: Last Pop Talks

• Meeting 32: So long and thanks for all the fish (review, slideshow)