Path integrals and the quantum Routhian

In this thesis, we consider the use of the Routhian in quantum mechanics, which is an object halfway between a Lagrangian and a Hamiltonian expressing the dynamics of a system in terms of conserved momentum and non-cyclic coordinates. Starting from the phase space path integral, we derive an expression for the quantum mechanical propagator of a system written in terms of its Routhian. We then go on to show how this formalism can provide calculational simplifications in simple situations such as a free particle on a line or a circle, and we demonstrate that for a particle in a constant magnetic field, by using conserved momentum it is possible to obtain a positive definite measure after Wick rotating to imaginary time. By doing this, we are able to obtain the quantum corrections to the partition function. Finally, we attempt to develop a general method for approximating the partition function for a particle on a sphere if there is a conserved azimuthal momentum, and consider in detail the free particle on a sphere. We reduce the problem to having to solve a complicated differential equation, obtaining an answer very close to the exact result in the simplest approximation.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Poland, David, 1982-

Advisor dc:contributor.advisor

• Frank Wilczek.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/32755

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/32755