عنوان

A Convergent Continuum Strong Coupling Expansion for Quantum Mechanics & Quantum Field Theory/String Tensions in Deformed Yang-Mills theory

Number

TLpq2322785114

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

A Convergent Continuum Strong Coupling Expansion for Quantum Mechanics & Quantum Field Theory/String Tensions in Deformed Yang-Mills theory

General Material Designation

[Thesis]

First Statement of Responsibility

Shalchian Tabrizi, Mohammad Erfan

Subsequent Statement of Responsibility

Poppitz, Erich

Name of Publisher, Distributor, etc.

University of Toronto (Canada)

Date of Publication, Distribution, etc.

2019

Specific Material Designation and Extent of Item

178

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

University of Toronto (Canada)

Text preceding or following the note

2019

Text of Note

This Thesis is a collection of three different works: "A Convergent Continuum Strong Coupling Expansion For Quantum Mechanics \& Quantum Field Theory": The notion of an asymptotic weak coupling expansion about an exactly solvable model in QM and QFT is generalized to an all positive value coupling convergent expansion. This is done by rescaling the variables available in the theory by free parameters, then adding and subtracting the exactly solvable model. The rest (initial rescaled theory by free parameters + the subtracted exactly solvable model) is expanded about the added exactly solvable model. Evaluating finite orders of this expansion at its extremum points with respect to the free parameter(s) gives a sequence that converges to the result of the previous asymptotic expansion. This method is applied to quantum mechanics and quantum field theory. The electron g-factor calculation is improved at the one loop level using this method. "String Tensions in Deformed Yang-Mills Theory": Yang-Mills theory defined on usd\mathbb{R}^3 \times S^1usd deconfines at high temperatures or small circle sizes usdS^1usd. In order to have a confining theory for arbitrary small spacial circle sizes usdS^1usd that can be studied analytically a deformation of Yang-Mills theory is considered. In this work we calculate the k-string tensions for SU(N) deformed Yang-Mills theory on usd\mathbb{R}^3 \times S^1usd. The k-string tensions usdT_kusd for usd2 \leq N \leq 10usd are calculated in two different ways: by a numerical minimization and a (novel) analytical evaluation of the string tension action. We find that dYM k-string ratios usdT_k/T_1usd do not obey the well-known sine- or Casimir-scaling laws. Instead, we show that the ratios usdT_k/T_1usd are bound above by a square root of Casimir scaling, previously found to hold for stringlike solutions of the MIT Bag Model. Our results also indicate that, at large values of N, k-strings in dYM do not become free. "A Generalization of Picard-Lindelof Theorem/ The Method of Characteristics to Systems of PDE": Picard-Lindelof theorem of ordinary differential equations and the method of characteristics is unified/generalized to the following system of PDE: usdC_{il}(x,y) {\partial y_i / \partial x_l} + {\partial y_i / \partial x_m} = D_i(x,y)usd.

Mathematics

Particle physics

Physics

Poppitz, Erich

Shalchian Tabrizi, Mohammad Erfan

Electronic name

p

[Thesis]

276903

a

Y