# Symmetry, Symmetry Breaking and Topology

## Abstract

**:**

## 1. Introduction

#### Landau Theory: Topological and Group Theoretical Ideas

**Theorem**

**A**

**Theorem**

**B**

## 2. Symmetry Breaking Patterns and Selection Rules in a Crystal

#### Thomson Problem

## 3. Symmetry Breaking Selection Rules: Continuous Group

- P($\varphi $) is invariant under the action of G
- P($\varphi $) has a local maximum at $\varphi =0$
- P($\varphi $) is bounded below and $P\left(\varphi \right)\to \infty $ as $(\varphi ,\varphi )\to \infty $
- P($\varphi $) is of maximum degree four
- $P\left(\varphi \right)=P(-\varphi )$

**Theorem**

## 4. Topological Phase Transitions: Graphene

## 5. Conclusions

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**MDPI and ACS Style**

Sen, S.
Symmetry, Symmetry Breaking and Topology. *Symmetry* **2010**, *2*, 1401-1422.
https://doi.org/10.3390/sym2031401

**AMA Style**

Sen S.
Symmetry, Symmetry Breaking and Topology. *Symmetry*. 2010; 2(3):1401-1422.
https://doi.org/10.3390/sym2031401

**Chicago/Turabian Style**

Sen, Siddhartha.
2010. "Symmetry, Symmetry Breaking and Topology" *Symmetry* 2, no. 3: 1401-1422.
https://doi.org/10.3390/sym2031401