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Title: | Properties of the O(N) Vector Model in Various Dimensions Properties of the O(N) Vector Model in Various Dimensions license.txt |
Authors: | Huang, Richard |
Advisors: | Pufu, Silviu S |
Department: | Physics |
Class Year: | 2020 |
Abstract: | In this thesis, we study the O(N) vector model, which is a quantum field theory of N real scalar fields ϕi with a quartic interaction λ4(ϕiϕi)2. We will study the theory in a range of dimensions using two complementary approximation schemes, epsilon expansion in dimensional continuation and the large N approximation. First, we describe various classical solutions of the O(N) model on the sphere Sd for d=6 and 8. Then by computing the determinant of fluctuations about these classical backgrounds, it is possible to provide an alternative method of computing the beta functions in d=6−ϵ and d=8−2ϵ. Finally, we also consider some of the thermodynamic properties of the critical O(N) model by placing the theory on the thermal cylinder S1×Rd−1. We find that in the range 2<d<4 and 6<d<8, there exists a real solution for the thermal mass. Interestingly, the leading order contribution to the thermal mass in d=6+ϵ and d=8−ϵ is found to have a fractional dependence on ϵ. This is understood by deriving the result diagrammatically and summing over an infinite class of diagrams. |
URI: | http://arks.princeton.edu/ark:/88435/dsp01t435gg93k |
Type of Material: | Princeton University Senior Theses |
Language: | en |
Appears in Collections: | Physics, 1936-2020 |
Files in This Item:
File | Description | Size | Format | |
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HUANG-RICHARD-THESIS.pdf | 894.99 kB | Adobe PDF | Request a copy |
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