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In 1980, Christ and Lee wrote a paper titled 'Operator ordering and Feynman rules in gauge theories'. In this paper they showed that the Hamiltonian formulation of a non-abelian gauge theory in a general non-covariant gauge is complicated by problems of operator ordering, leading to new nonlocal interactions they call V<SUB>1</SUB> + V<SUB>2</SUB>. In particular this applies to the familiar Coulomb gauge. More recently, Cheng and Tsai have arrived at the same ordering by careful attention to the fact that the Gauss-law constraint is not an operator equation. On the other hand, it is known that the naive Coulomb gauge Feynman rules in non-abelian gauge theory give rise to ambiguous integrals, in addition to the usual ultraviolet divergences. This thesis shows how these ambiguities can be resolved to all orders in perturbation theory. This is done by defining a gauge that interpolates smoothly between the Feynman gauge and the Coulomb gauge, and then using a diagrammatic method to combine the different contributions that arise. The extra terms V<SUB>1</SUB> + V<SUB>2</SUB> of Christ and Lee are then identified with certain two loop ambiguous terms. The only remaining question is whether the method of resolving the ambiguities is compatible with renormalisation. An investigation into the extra complications that renormalisation introduces is carried out.

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Propomos neste trabalho um método de construção de gases clássicos, a partir de uma teoria de gauge pura, no formalismo Hamiltoniano com tempo continuo. O metodo e exemplificado com o modelo de gauge U(l) em v=2 dimensões de espaço-tempo. Neste mesmo modelo, podemos verificar uma estrutra não trivial do vácuo (vácuos- e), como consequência da ambiguidade de quotização. Este resultado e obtido sem a utilização dos métodos semi-clássicos. Também exploramos a relação entre esta estrutura de vácuo com o problema do confinamento. / We describe a method for the construction of classical gases , starting from a pure ga uge theory . The method is apllied to the U(l) gauge theory in v=2 spatial dimensions. For this model we can see the vaccua appearing as a consequence of the quantization ambiguity. The connection between the e vaccua and confinement is discussed.

Propomos neste trabalho um método de construção de gases clássicos, a partir de uma teoria de gauge pura, no formalismo Hamiltoniano com tempo continuo. O metodo e exemplificado com o modelo de gauge U(l) em v=2 dimensões de espaço-tempo. Neste mesmo modelo, podemos verificar uma estrutra não trivial do vácuo (vácuos- e), como consequência da ambiguidade de quotização. Este resultado e obtido sem a utilização dos métodos semi-clássicos. Também exploramos a relação entre esta estrutura de vácuo com o problema do confinamento. / We describe a method for the construction of classical gases , starting from a pure ga uge theory . The method is apllied to the U(l) gauge theory in v=2 spatial dimensions. For this model we can see the vaccua appearing as a consequence of the quantization ambiguity. The connection between the e vaccua and confinement is discussed.

On open access repositories Creative Commons Attribution License CC-BY 4.0 Published source must be acknowledged Publisher's version/PDF may be used / 京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19498号 / 理博第4158号 / 新制||理||1597(附属図書館) / 32534 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 國友 浩, 教授 田中 貴浩, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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