Symmetry, Broken Symmetry, and Topology in Modern Physics
Mike Guidry
guidry@utk.edu (Office: 308 South College)
Fall, 2026
Class Homepage: http://eagle.phys.utk.edu/guidry/phys494/
Class Meeting Times
12:55-2:10 pm, TR
Classroom:: TBA
Course Description
Undergraduate physics majors today take classes and participate in research
experiences that expose them increasingly to more advanced mathematical topics
that they will encounter in many research fields if they continue on to graduate
school. However, there is one set of topics and associated mathematics of increasing
importance for various research disciplines that undergraduates are seldom exposed
to in any systematic
fashion. These topics may be organized loosely under the rubric of applying
group theory, Lie algebras, advanced geometry, and topological concepts to physical
systems. In fact, one could argue that in the landscape of undergraduate
mathematical preparation for research at the next level these topics are the
most important omission in the mathematical and conceptual preparation for many
of our students. This course and the book it is based on are an attempt to remedy
that situation.
Textbook
Symmetry, Broken Symmetry, and Topology in Modern Physics, Mike Guidry and Yang Sun, Cambridge University Press (2022)
Course Content
In Physics 494 I propose to cover basic group theory, the Bloch theorem and
Brillouin
zone, Dirac, Weyl, and Majorana equations, Lorentz and Poincaré symmetry, gauge
symmetry,
Berry phases, and spontaneous symmetry breaking as background for an
introduction to topology and topological matter. This will involve major parts
of Chs. 2-5, 13-16, and 24-29 in the book.
Expected Preparation
The course necessarily uses the language of quantum mechanics. Ideally students
will have had a senior-level
quantum physics course. However, I will begin with a brief introduction to the
required quantum theory so students who haven't had
that level of exposure to quantum can still succeed if they are willing to learn
some quantum mechanics as we proceed.
Grade
Homework 30% (graded for completeness, not correctness,
but solutions will be provided). 100% for homework turned in on time and
complete.
Minus 25% per day for late or incomplete. Here is the homework
assignment schedule. Here
are solution sheets for previous homework.
(If you are late with your homework, do not consult the solutions before
turning in your work.)
Midterm Test (probably takehome) 35%
Final Test (probably takehome) 35%
Generative AI Policy
I strongly encourage the creative use of generative AI (genAI), since it is
a powerful tool that physics students need to learn to use ethically and efficiently.
I only require that if you use genAI in doing homework or tests, you add to
your solution sheet a brief description of what AI you used, how you employed
it,
what measures you took to ensure that the AI results made sense, and considerations
you used to be certain you understand the result and how
it was obtained. Also report any unusual (positive or negative) experience,
like a serious AI hallucination. (If you are unfamiliar with AI hallucinations,
see this
link.)
Optional Extra Credit
Up to 5 points added to final average for a presentation relevant to the subject
matter of the class in a recognized seminar at UT or ORNL. Topic can be
journal-club
or research in nature. You must notify me of your intentions beforehand, so
that I can approve the topic and schedule to attend.
Students with Disabilities
Any student who feels that they may need an accommodation based on the impact
of a disability should contact Student Disability Services (http://sds.utk.edu;
phone: 865-974-6087;
email: sda@utk.edu) to coordinate reasonable academic accommodations.
You are also welcome to discuss such issues with me, if you wish.