2020Durham e-Theses (Durham University)Open access

Commentaries on instantons

Calum Joshua Robson

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Abstract

I examine the dynamics of noncommutative instantons of instanton number 2 and commutative instantons of instanton number 3 in 5d Yang Mills theory. I begin by detailing the construction of the instanton solutions, their moduli space, and the moduli space potential using an explicit parametrisation of the moduli space coordinates in terms of the biquaternions. I then go on to numerically analyse the dynamics on the moduli spaces I have constructed.

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I examine the dynamics of noncommutative instantons of instanton number 2 and commutative instantons of instanton number 3 in 5d Yang Mills theory. I begin by detailing the construction of the instanton solutions, their moduli space, and the moduli space potential using an explicit parametrisation of the moduli space coordinates in terms of the biquaternions. I then go on to numerically analyse the dynamics on the moduli spaces I have constructed.

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Available abstract

I examine the dynamics of noncommutative instantons of instanton number 2 and commutative instantons of instanton number 3 in 5d Yang Mills theory. I begin by detailing the construction of the instanton solutions, their moduli space, and the moduli space potential using an explicit parametrisation of the moduli space coordinates in terms of the biquaternions. I then go on to numerically analyse the dynamics on the moduli spaces I have constructed.

Key concepts: Instanton, Moduli space, Noncommutative geometry, Modular equation, Moduli, Moduli of algebraic curves, Commutative property, Space (punctuation)

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