#### Physics from Finance

*Omid Zarifi, Physics and Math Undergraduate Student, Sharif University of Technology*

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**

##### Lecture 1

*Finance: Intuitively and Mathematically (1)*

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!

##### Lecture 2

*Finance: Intuitively and Mathematically (2)*

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*

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*

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.