Description

In Classical Mechanics, the exchange of two identical particles is a rather benign operation which is not producing any interesting physics. On the other hand, Quantum Mechanical particles are socially aware and the answer depends on the kind of particles being exchanged. Bosons are defined as particles whose state vector is symmetric while Fermions form states which are anti-symmetric under their exchange. This is the essence of Pauli's exclusion principle.

This crucial minus sign is enough to conclude that two Fermions cannot have the same quantum numbers in a many body system. While bosons can happily coexist in e.g. the lowest energy state, Fermions carefully stack themselves in a way that respects Pauli's exclusion principle. With electrons being a particular kind of Fermion, Pauli's principle is responsible for the vast spectrum of properties across the periodic table.

From a fundamental point of view, the building blocks of relativistic Quantum Field Theories are classified according to their spin. This number is a label indicating how fields transform under the Lorentz transformations. One of the most striking results of Quantum Field Theory the students will explore is the connection between the spin of particles and their Bosonic / Fermionic nature.

The students will have the the opportunity to explore different aspects related to Fermions. There is range of possible topics ranging from fundamental aspects to Condensed Matter theory.

Prerequisites:

• Mathematical Physics II

Co-requisites:

• Quantum Mechanics III

Resources:

• For a brief introduction to the concepts see the Wiki pages
• For a brief description of Pauli's exclusion principle see the Wiki page
• Section 10 of "Principles of Quantum Mechanics" by R. Shankar is an excellent introduction to Quantum many body systems.
• An excellent introduction to field theory is "Quantum Field Theory" by M. Srednicki.
• An good set of notes by D. Tong
• A good introductory book is "A Modern Introduction to Quantum Field Theory" by M. Maggiore.