2026-09-20T11:14:55Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/327552022-01-13T07:54:41Zcom_1721.1_7582com_1721.1_7581col_1721.1_131024
Frank Wilczek.
Poland, David, 1982-
Massachusetts Institute of Technology. Dept. of Physics.
Massachusetts Institute of Technology. Department of Physics
2006-05-15T20:27:41Z
2006-05-15T20:27:41Z
2004
2004
http://hdl.handle.net/1721.1/32755
56748238
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.
Includes bibliographical references (p. 37).
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.
by David Poland.
S.B.
37 p.
1114020 bytes
1113500 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Physics.
Path integrals and the quantum Routhian
Thesis
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<Abstract>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.</Abstract>
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