Aspects of quantum theory in 1+1 and slightly more dimensions

We consider four problems in (1+1)-dimensional physics. Each of these problems had important connections to the physical behavior of (3+ 1 )-dimensional systems. First, we consider problem of fermions interacting with multiple bosonic solitons. We describe a new approximation scheme for determining the fermion energy spectrum and apply it to (1 + 1 )-dimensional two-component fermions coupled to scalar field solitons. Second, we study (1+1)-dimensional behavior in particles falling toward a Schwarzchild black hole . Using a non-covariant choice for the momentum cutoff, we examine the photon self-energy integral. We find evidence that the photons acquire an effective mass with a nonzero imaginary part, so that the photons may decay. Third, we consider cold fermions trapped in a high aspect ratio potential, which confines the particles to move in only one direction. The purely (1 + 1 )-dimensional aspects of this problem have been extensively studied. We examine the corrections that arise because of the underlying (3+ 1 )-dimensional character of the situation and determine the zero-temperature shifts in the (1+1)-dimensional energy spectrum. Fourth, we present a toy model, which is related, by analogy to the problem of electron-inhabited bubbles in liquid helium. An analysis of the I-dimensional model suggests that the recent suggestion that the electron bubbles may split in two is incorrect.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Altschul, Brett David, 1977-

Advisor dc:contributor.advisor

• Roman W. Jackiw.

• Mathematics.

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/1721.1/29343

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29343