Extended Hamiltonian Formalism of the Pure Space-Like Axial Gauge Schwinger Model. II(Particles and Fields)

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概要

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• Canonical methods are not sufficient to properly quantize space-like axial gauges. In this paper, we obtain guiding principles that allow for the construction of an extended Hamiltonian formalism for pure space-like axial gauge fields. To do so, we clarify the general role that residual gauge fields play in the space-like axial gauge Schwinger model. In all the calculations, we fix the gauge using the rule n・A = 0, where n is a space-like constant vector, and we refer to its direction as x_. Then, to begin with, we construct a formulation in which the quantization surface is space-like but not parallel to the direction of n. The quantization surface has a parameter that allows us to rotate it, but when we do so, we keep the gauge fixing direction fixed. In that formulation, we can use canonical methods. We bosonize the model to simplify the investigation. We find that the inverse differentiation, (∂_)^<-1>, is ill-defined whatever quantization coordinates we use, as long as the direction of n is space-like. We find that the physical part of the dipole ghost field includes infrared divergences. However, we also find that if we introduce residual gauge fields in such a way that the dipole ghost field satisfies the canonical commutation relations, then the residual gauge fields are determined so as to regularize the infrared divergences contained in the physical part. The propagators then take the form prescribed by Mandelstam and Leibbrandt. We make use of these properties to develop guiding principles that allow us to construct consistent operator solutions in the pure space-like case, in which the quantization surface is parallel to the direction of n, and canonical methods do not suffice.

• 理論物理学刊行会の論文
• 2004-06-25

著者

• Mccartor G

  Department Of Physics Southern Methodist University

• NAKAWAKI Yuji

  Division of Physics and Mathematics, Faculty of Engineering Setsunan University

• MCCARTOR Gary

  Department of Physics, Southern Methodist University

• Mccartor Gary

  Department Of Physics Southern Methodist University

• Nakawaki Y

  Setsunan Univ. Osaka Jpn

• Nakawaki Yuji

  Division Of Physics And Mathematics Faculty Of Engineering Setsunan University

• Nakawaki Yuji

  Division Of Mathematics And Physics Department Of Engineering Setsunan University

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