Classical Optics and Special Relativity (361-0-1)

Instructors

Carl Eric Dahl

Meeting Info

Technological Institute L160: Mon, Wed, Fri 9:00AM - 9:50AM

Overview of class

Special relativity is at the heart of our most foundational understanding of the universe. The very nature of what particles can exist are entirely constrained by quantum mechanics and the representations of the Lorentz group. How can special relativity which allows space and time to rotate into each other be consistent with the quantum mechanics of Bohr, Planck, Heisenberg, and Schrodinger which as we learn treats time on a very special footing? Our path to the answer of relativistic quantum field theory begins by understanding our first relativistic classical effective field theory: Classical Electrodynamics. This course will introduce us to the modern language of Lorentz invariant field theory, highlighting universal principles.

Part 1a: Foundations and Review (Special Relativity). Symmetry groups (2-D rotations, 3-D rotations, Lorentz transformations). Special relativity and relativistic notation. Energy and momentum of a point particle.

Part 1b: Foundations and Review (E&M): Electromagnetism in one frame of reference. Maxwell's equations, conservation laws and the Poynting vector, Scalar and vector potentials and their E&M gauge transformations.

Part 2: Relativistic electrodynamics. 4-vector current and potentials, the electromagnetic field tensor, Maxwell equations in relativistic form. Lorentz transformations and invariants of the current and fields.
The stress-energy tensor. The relativistic point particle.

Part 3: Action principles. The electromagnetic field interacting with a point particle. Conservation laws from symmetry via Noether.

Part 4: Solving the wave equations using Green's functions. The Green's function in relativistic form. Relativistic particle moving in an arbitrary manner. The Lienard-Wiechert potentials.

Part 6: Linear acceleration and synchrotron radiation. Multipole expansion of radiation fields.

Part 7: Advanced classical optics, Fraunhofer and Fresnel diffraction, non-linear media.

Teaching Method

The course will be lecture driven with weekly homework and take-home final.

Class Materials (Required)

We will reference the following texts, available online at no charge to Northwestern students:

Griffiths, "Introduction to Electrodynamics", 5th Edition.
https://www.cambridge.org/highereducation/books/introduction-to-electrodynamics/FD23E188E2BDCDB40199CFE3386EC08F#contents

Blandford and Thorne, "Applications of Classical Physics", http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/