# Undergraduate Program

## The Kapitza Society

In 2016 the “Kapitza Society” was created by Jean Weill in honor of the “Kapitza Club” founded by Peter Kapitza in the 1920s in Cambridge. Our goal is simple: to bring together a small team of elite students with an insatiable thirst for knowledge in order to explore theoretical physics outside of our classes. Each session revolves around a lecture by a society member. We meet once a week – thirty minutes for practice problems, then one hour and thirty minutes for theory. We have studied a variety of topics, all at the graduate level: differential geometry, particle physics, Lie algebras, quantum field theory, and quantum information theory.

### Mentors:

- Prof. S. G. Rajeev (Mathematics and Physics): s.g.rajeev@rochester.edu
- Prof. Alex Iosevich (Mathematics): iosevich@math.rochester.edu

### Current Members (Spring 2021):

- Kelly Aspinwall (Physics): kaspinw2@u.rochester.edu
- Jeremy Atkins, President (Physics & Astronomy, Mathematics): jatkins5@u.rochester.edu
- Soren Helhoski (Physics & Astronomy): shelhosk@u.rochester.edu
- Jose M. Torres Lopez (Physics, Mathematics): jtorre10@u.rochester.edu
- Benjamin Ostergaard (Physics): bosterga@u.rochester.edu
- Kai Reed (Physics, Mathematics): kreed8@u.rochester.edu

### Topics Covered:

**Quantum Field Theory (Fall 2020):**

Resources Used:

- "Quantum Field Theory in a Nutshell" by A. Zee

Projects:

- Kelly Aspinwall: "Field Theory in Curved Spacetime and the Stress-Energy Tensor"
- Jeremy Atkins: "Modeling Particle Interactions with Feynman Diagrams"
- Soren Helhoski: "Canonical Quantization & the Path Integral Formulation: A Brief Comparison"
- Benjamin Ostergaard: "Free Field Theory and Propagators"
- Jose M. Torres Lopez: "Introduction to Feynman Diagrams"

**Group Theory and Particle Physics II (Spring 2020):**

Resources Used:

- "Group Theory in a Nutshell for Physicists" by A. Zee

Projects:

- Jeremy Atkins: "Three Derivations of the Dirac Equation"
- Soren Helhoski: "Double Covers and Some Applications to Spinor Representations"
- David Mayrhofer: "The Spin Representations of SO(2n)"
- Benjamin Ostergaard: "The Weyl Equation"
- Fatima Zaidouni: "The Lorentz Group and Relativistic Physics"

**Group Theory and Particle Physics II (Spring 2020):**

Resources Used:

- "Group Theory in a Nutshell for Physicists" by A. Zee

Projects:

- Jeremy Atkins: "Three Derivations of the Dirac Equation"
- Soren Helhoski: "Double Covers and Some Applications to Spinor Representations"
- David Mayrhofer: "The Spin Representations of SO(2n)"
- Benjamin Ostergaard: "The Weyl Equation"
- Fatima Zaidouni: "The Lorentz Group and Relativistic Physics"

**Group Theory and Particle Physics I (Fall 2020):**

Resources Used:

- "Group Theory in a Nutshell for Physicists" by A. Zee

Projects:

- Jeremy Atkins: "SU(2)'s Double-Covering of SO(3)"
- David Mayrhofer: "Characterization of SU(N)"
- Byron Osterweil: "Angular Momentum and the Clebsh-Gordon Decomposition"
- Tyler Perlman: "Representations of the Rotation Groups SO(N)"
- Kyhl Webber: "Tools and Concepts Involved in the Representation of Rotation Groups in Physics"
- Fatima Zaidouni: "Lie Algebra of SO(3) and Ladder Operators"

**Cosmology (Spring 2019):**

Resources Used:

- "Modern Cosmology" by Scott Dodelson

Projects:

- Tri Nguyen: "The Fundamentals of Cosmology"
- Jeremy Atkins: "The Boltzmann Equation for Photons and Dark Matter"
- David Mayrhofer: "The Basic Tools and Questions of Cosmology"
- Fatima Zaidouni: "The Source of Curvature"

- Byron Osterweil: "Non-Equilibrium Universal Evolution"
- Tyler Perlman: "Boltzmann Equation for Photons"
- Kyhl Weber: "Introduction to and Simple Applications of the Boltzmann Equation"

**Black Hole Physics (Fall 2018):**

Resources Used:

- “Gravity: An Introduction to Einstein's General Relativity” by James B. Hartle

Projects:

- Tri Nguyen: "From Gravitational Collapse to Black Holes"
- Jeremy Atkins: "Solving the Geodesic Equation"
- David Mayrhofer: "First Order Approximations in General Relativity"
- Fatima Zaidouni: "Gravitational Lensing"
- Byron Osterweil: "The Schwartzchild Geometry"
- Tyler Perlman: "Gravitational Waves"
- Kyhl Weber: "Kerr Geometry and Rotating Black Holes"

** ****Quantum Field Theory II (Spring 2018): **

Resources Used:

- “Lectures on Quantum Field Theory” by Ashok Das

Projects:

- Jeremy Atkins: "The Free Klein Gordon Field Theory"
- David Mayrhofer: "Complex Solutions to the Klein-Gordon Equation"
- Logan Meredith: "Helicity, chirality, and the Dirac equation in the non-relativistic limit"
- Tri Nguyen: "Field Interactions"
- Ben Saltzman:"Second Quantization of the Klein-Gordon Equation"
- Jean Weill: "The Dirac Equation"

**Quantum Information Theory I (Fall 2017):**

Resources Used:

- “Quantum Information Theory” by Mark M. Wilde (2nd edition)

Projects:

- Logan Meredith: "The CHSH game as a Bell test thought experiment"
- Ben Saltzman: "Noisy Quantum Measurement"
- Jean Weill: "Statistical and Quantum Mechanics"

**Quantum Field Theory (Spring 2017):**

Resources Used:

- “Quantum Field Theory” by Franz Mandl and Graham Shaw (2nd edition)

Projects:

- Sanha Cheong:“Example of Lowest-Order Processes in QED”
- Adam Lott: "Introduction to Lagrangian Field Theory"
- Logan Meredith: “Calculating Transition Amplitudes from Feynman Diagrams”
- Jean Weill: “Lagrangian Field Theory”
- Emily Windes: “From Harmonic Oscillators to Fields”

**Mathematics and Particle Physics (Fall 2016):**

Resources Used:

- “Symmetry and the Standard Model” by Matthew Robinson (1st edition)
- “Introduction to Elementary Particles” by David Griffiths (2nd edition)
- “Lie Groups, Lie Algebras, and Representations” by Brian C. Hall (2nd edition).

Projects:

- Jean Weill: "Introduction to Special Relativity”

**Differential Geometry (Spring 2016):**

Resources Used:

- “Elementary Differential Geometry” by Barrett O’ Neil (2nd edition)
- Lecture notes for Differential Geometry made by James S. Cook for a class he taught at the Liberty University, which can be found on this site: http://www.supermath.info/DifferentialGeometry.html

Projects:

- Jean Weill:
*“Calculus on Euclidean Space”*

### Previous Members:

- Sanha Cheong (Physics PhD, Stanford): sanha@standford.edu
- Noah Chrein (Mathematics PhD, U Maryland): nchrein@terpmail.umd.edu
- Adam Lott (Mathematics PhD, UCLA): adamlott99@math.ucla.edu
- Logan Meredith (Theoretical Physics PhD, U Illinois Urbana-Champaign): logantm2@illinois.edu
- David Mayrhofer (Physics PhD, U Minnesota): mayrh005@umn.edu
- Tri Nguyen, President (Physics & Astronomy): tnguy@mit.edu
- Byron Osterweil (Mathematics PhD, UC Irvine): osterweb@uci.edu
- Tyler Perlman (Physics, Mathematics): tperlman@u.rochester.edu
- Ben Saltzman (Physics PhD, UC Berkeley): ben.saltzman@berkeley.edu
- Kyhl Webber (Physics): kweber8@u.rochester.edu
- Jean Weill, Founder (Theoretical Physics PhD, Northwestern): jeanweill@u.northwestern.edu
- Emily Windes (Mathematics PhD, U of R): ewindes@u.rochester.edu
- Fatima Zaidouni (Astrophysics Masters, Cambridge; Astro PhD, MIT)