Physics from Finance
💡 Why this Subject?
There’s a deep and beautiful connection between finance and physics. But so far, this connection was used almost exclusively by economists to get a better grip on the financial market. The main idea of this short course, however, is to use the connection between finance and physics to translate in the opposite direction. Specifically, the goal of this course is to use a toy version of the financial market to explain fundamental models of nature that physicists have developed in the past century.
Modern physics often appears like a conglomerate of several seemingly unrelated models (like electrodynamics, quantum mechanics, general relativity, and so on). These models are usually discussed completely independently in different textbooks and academic courses. However, it turns out that the key ideas at the heart of all these models are exactly the same. Therefore, by studying a small number of key ideas, we can understand them all from a common perspective. Although these key ideas are somewhat abstract and hard to appreciate, we can try to understand them intuitively by talking about a toy model of the financial market. And It's exactly our goal in these lectures!
🌠 About the Course
This is a short course, which will be held virtually in "Physics & Math Circles" of Quanta, in Fall 2021. Qunata is a student-organized system for academic discussions, based on the Physics Department of SUT. There are no restrictions for participating in these lectures. If you're eager, you're welcome to join!
Time: Thursdays 19:00 - 20:00
Place: vc.sharif.edu/ch/quanta
📚 Sources & Suggested Readings
The main contents of this short course are based on the book "Physics from Finance: A Gentle Introduction to Gauge Theories, Fundamental Interactions and Fiber Bundles" by Jakob Schwichtenberg. However, I'll suggest some additional sources during the lectures for those who want to go further and deeper. So, this section is updated gradually...
✤ J. Schwichtenberg, Demystifying Gauge Symmetry (2019), physics.hist-ph/1901.10420
✤ J. Maldacena, The Symmetry and Simplicity of the Laws of Physics and the Higgs Boson (2014), physics.pop-ph/1410.6753
✤ A recorded talk based on the above article by Maldacena in IAS in 2012: Link on YouTube or Dideo!
🌟 Prerequisites
There are no special prerequisites for following this course! If you already know what Calculus and Complex Numbers are, feel free to follow these lectures! But if you have no formal physics education yet, undoubtedly, some details will be harder or even impossible to understand. Also if you're a somewhat advanced student of physics, this course allows you to understand many things you probably already know from a completely new perspective!
🎬 Timeline of Lectures
You can find here the video of each lecture along with a short description of the topics that are discussed.
❖ Lecture 1 - Finance: Intuitively & Mathematically (1) - 8 Mehr 1400
In this lecture, after talking about some basic issues about the whole course, we start to build our toy model of the financial market, first intuitively and then mathematically. We get to know the players, their actions, and the arena which we use to describe what is going on in our toy model. Then we find that in writing the equations of motion of our toy model, for describing its dynamics, we can just use some special quantities, called Gauge Invariant Quantities. Why? And what are these gauge invariant quantities? Watch the video of the first lecture!
❖ Lecture 2 - Finance: Intuitively & Mathematically (2) - 15 Mehr 1400
This is the second and the last lecture on the construction of our financial toy model. We investigate the continuum limit and find a good quantity to describe apple current! In the end, we get to know a deep notion: Covariant Derivative!
❖ Lecture 3 - An Interlude: The Arena of Physics - 22 Mehr 1400
As the title shows, this lecture is a short interlude to our journey. We talk about the four known Fundamental Interactions and their general features, the Standard Model of Particle Physics, and two types of transformations classifications in physics: Local vs. Global Transformations, and Passive vs. Active Transformations.
❖ Lecture 4 - Electrodynamics + Gauge Symmetry in Physics - 29 Mehr 1400
In this lecture, we see the exact similarity between our financial toy model and the Covariant Form of Electrodynamics and then talk about why it's possible. After that, we describe Gauge Symmetries in Quantum Mechanics and Electrodynamics. It the end, we define Group Structure and the notion of Group Action for a better understanding of the notion of Symmetry.
❖ Lecture 5 - Fiber Bundles - 6 Aban 1400
If you have any questions about the course or discussed topics, let me know by o.zarifi78[at]gmail.com or the comment section below.
