Description

Quantum mechanics can be formulated in many ways; apart from the usual approach involving Hilbert space of states and linear operators - it can also be formulated in terms of path integrals (sums of over all 'classical-like' paths). This project will involve the study of this path integral formulation of this formulation and the comparison of the two approaches.

Furthermore, nonrelativistic quantum mechanics deals basically with bosonic quantities. However, in nature fermionic quantities are also very important. The fields that describe them have different properties and in some models in field theory people have spotted a symmetry of many quantities under the interchange of bosons and fermions. This symmetry, called supersymmetry, plays an important role in many currently fashionable models in particle physics (string theory etc...).

Supersymmetry can also be applied to quantum mechanics. The second part of the project will look at various supersymmetric quantum mechanical models and their formulation in terms of path integrals. From then on the project can develop in many directions from generalisations to field theory to the applications in many areas of physics and mathematics.

Prerequisites

Resources