Extended Hamiltonian Formalism of the Pure Space-Like Axial Gauge Schwinger Model

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概要

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• We demonstrate that pure space-like axial gauge quantizations of gauge fields can be constructed in ways that are free from infrared divergences. To do so, we must extend the Hamiltonian formalism to include residual gauge fields. We construct an operator solution and an extended Hamiltonian of the pure space-like axial gauge Schwinger model. We begin by constructing an axial gauge formulation in auxiliary coordinates, x^μ=(x^+, x^-), where x^+=x^0 sinθ+x^1 cosθ, x^-=x^0 cosθ-x^1 sinθ, and we take A_-=A^0 cosθ+A^1 sinθ=0 as the gauge fixing condition. In the region 0≤θ<π/4, we can take x^- as the evolution parameter and construct a traditional canonical formulation of the temporal gauge Schwinger model in which residual gauge fields dependent only on x^+ are static canonical variables. Then we extrapolate the temporal gauge operator solution into the axial region, π/4<θ<π/2, where x^+ is taken as the evolution parameter. In the axial region we find that we have to take the representation of the residual gauge fields realizing the Mandelstam-Leibbrandt prescription in order for the infrared divergences resulting from (∂_-)^<-1> to be canceled by corresponding ones resulting from the inverse of the hyperbolic Laplace operator. We overcome the difficulty of constructing the Hamiltonian for the residual gauge fields by employing McCartor and Robertson's method, which gives us a term integrated over x^-= constant. Finally, by taking the limit θ→π/2-0, we obtain an operator solution and the Hamiltonian of the axial gauge (Coulomb gauge) Schwinger model in ordinary coordinates. That solution includes auxiliary fields, and the representation space is of indefinite metric, providing further evidence that "physical" gauges are no more physical than "unphysical" gauges.

• 理論物理学刊行会の論文
• 2001-07-25

著者

• NAKAWAKI Yuji

  Division of Physics and Mathematics, Faculty of Engineering Setsunan University

• Mccartor Gary

  Department Of Physics Southern Methodist University

• Nakawaki Y

  Setsunan Univ. Osaka Jpn

• Nakawaki Yuji

  Division Of Mathematics And Physics Department Of Engineering Setsunan University

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