Physics With Friends

This Session's Topic
Gravitons, Dilatons, and Kalb-Ramond Fields: Exploring the Spectrum of the Quantized Closed String

Overview
This is a collaborative study group dedicated to understanding the foundations, motivations, and current landscape of quantum gravity research. Our goal is to build a clear conceptual picture of why quantum gravity is challenging, what the major approaches attempt to do, and how they compare.

Developing a coherent understanding of quantum gravity requires engaging with the mathematics. As such, we will work through explicit equations and derivations to understand how gravitational dynamics emerge, how quantum consistency constrains theories, and why certain results are unavoidable rather than assumed.

Participants should have a basic familiarity with the principles of quantum mechanics, quantum field theory, and general relativity, and be comfortable with the Lagrangian formalism of physical theories.

What to expect

• We assign readings, lectures to watch, and curated exercises prior to each meeting, which will be announced below.
• During the meetings, one or more of the volunteers will walk through the assigned materials and moderate the discussion.
• Additional discussion between meetings will take place on our chat server, where we can exchange solutions, notes, interesting and relevant articles, etc. Notes and solutions may also be hosted in our Github repository.

What this group is NOT

• Not a popular science or sci-fi discussion group.
• Not a high-pressure, exercise-heavy bootcamp.
• Not a forum to strongly endorse or air grievances against any one approach to quantum gravity .

For casual physics chat or general discussion, please see our other Meetup groups.

Community & Continuity
We maintain a live chat server for continuing discussions between meetups, and a link can be provided upon request if you’d like to join. This even is part of the broader Physics With Friends community, which hosts multiple collaborative study tracks across physics and mathematics.

Last meeting we developed an intrinsic way to parallel transport tangent vectors across a curved surface. This meeting asks the natural next question: what happens if we carry a vector all the way around a closed loop and bring it back to where it started?

On a curved surface, it may return pointing in a different direction. That net rotation is called holonomy.

In Chapter 24 of Tristan Needham’s Visual Differential Geometry and Forms, we will begin with a striking example on the sphere, then extend the idea to general geodesic triangles. We will see how holonomy connects parallel transport, angular excess, and Gaussian curvature, and why holonomy is additive when a region is subdivided.

This is also an important step in our longer goal: following Needham’s geometric path toward the Einstein Field Equation. The chapters ahead move from holonomy and curvature to geodesic deviation, Riemann curvature, Ricci curvature, and finally Einstein’s description of gravity as curved spacetime.

Background: You should be comfortable with basic calculus and vectors. Familiarity with tangent planes, geodesics, Gaussian curvature, and parallel transport will help. We will briefly review what is needed from Chapter 23. No prior tensor calculus or General Relativity is required.

This event is part of the Physics With Friends community, which hosts collaborative study groups in physics and mathematics.

Join us every other Tuesday for an open-ended casual discussion with our book club for Roger Penrose's The Road to Reality, the magnum opus of one of the greatest theoretical physicists of our time. In a single volume, Penrose takes the reader from basic mathematical and logical arguments through advanced math and then onto modern physics, relativity, quantum theory, and beyond.

Please have access to a copy of the book and have read at least one chapter prior to attending. We normally agree to read one particular chapter in advance and then spend our meeting time discussing that chapter and its problem set, sometimes branching off to other parts of the book. We support each other to go at whatever pace is comfortable and we discuss material that we find interesting or challenging. Those of us who want to work on the problem sets can help one another. Sometimes someone will want to make a mini-presentation on a topic of their liking. We also maintain a private chat room for those who want to stay in touch between meetings.