Holomorphic Polar Coordinates and Segal-Bargmann Space

Doctoral Dissertation

Abstract

In Real Euclidean Space, polar coordinates allow mathematicians to calculate the norm of higher dimensional SO-invariant functions with relative ease by reducing the problem to a 1-dimensional integral. In this dissertation I look at the Complex Segal-Bargmann Space using the C_t transform. I find there is a “holomorphic” version of polar coordinates that allows us to do the same in the odd dimensional cases. A geometric approach for this was done by Areerak Kaewthep and Wicharn Lewkeeratiyutkul using the B_t transform in [9], but this method is not easily generalized to non-Euclidean Spaces. Motived by the works of Gestur Olafsson and Henrik Schlichtkrull in [10], I use shift operators to find this “holomorphic” version of polar coordinates in C_t version of the Segal-Bargmann transform.

Attributes

Attribute NameValues
Author Brian Mulholland
Contributor Brian C. Hall, Research Director
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name Doctor of Philosophy
Banner Code
  • PHD-MATH

Defense Date
  • 2019-06-17

Submission Date 2019-06-17
Subject
  • Quantum Mechanics

  • Segal-Bargmann Space

  • SO-Invariant Functions

  • Shift Operators

Record Visibility and Access Public
Content License
  • All rights reserved

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