Yuji Nakawaki

Fermion structures of state vectors of the Schwinger model with multi-fermions

On formule un modele de Schwinger en jauge de Coulomb avec plusieurs fermions de facon consistante dans une boite [−L,L] en introduisant des degres de liberte dynamiques vraies des champs electromagnetiques

The Indispensability of Ghost Fields in the Light-Cone Gauge Quantization of Gauge Fields

We continue McCartor and Robertson’s recent demonstration of the indispensability of ghost fields in the light-cone gauge quantization of gauge fields. It is shown that the ghost fields are indispensable in deriving well-defined antiderivatives and in regularizing the most singular component of the gauge field propagator. To this end it is sufficient to confine ourselves to noninteracting abelian fields. Furthermore, to circumvent dealing with constrained systems, we construct the temporal gauge canonical formulation of the free electromagnetic field in auxiliary coordinates x µ =( x − ,x + ,x 1 ,x 2 ), where x − = x 0 cosθ − x 3 sinθ, x + = x 0 sinθ + x 3 cosθ and x − plays the role of time. In so doing we can quantize the fields canonically without any constraints, unambiguously introduce “static ghost fields” as residual gauge degrees of freedom and construct the light-cone gauge solution in the light-cone representation by simply taking the light-cone limit (θ → π ). As a by product we find that, with a suitable choice of vacuum, the Mandelstam-Leibbrandt form of the propagator can be derived in the θ = 0 case (the temporal gauge formulation in the equal-time representation).

An Axial Gauge Formulation for QED2

By choosing background electric field properly, we remedy the surface-modified action formulation of Halpern and Senjanovic and of Pak. It is found that if the proper background electric field satisfies an appropriate commutation relation, Hamiltonian equation can agree with Lagrange equation in a physical space defined by means of charge Q by Qlphys>=O. An operator solution to massless spinor QED, is demonstrated to show that our formulation is consistent in every respect. Two ways to incorporate chiral transformations to the solution are also exhibited.

Perturbative Formulation of Pure Space-Like Axial Gauge QED with Infrared Divergences Regularized by Residual Gauge Fields

We construct a new perturbative formulation of pure space-like axial gauge QED in which the inherent infrared divergences are regularized by residual gauge fields. For this purpose, we carry out our calculations in the coordinates x μ = (x + , x - , x 1 , x 2 ), where x + = x 0 sin θ + x 3 cos θ and x - = x 0 cos θ - x 3 sin θ. Here, A_ = A 0 cos θ + A 3 sin θ = n·A = 0 is taken as the gauge fixing condition. We show in detail that, in perturbation theory, infrared divergences resulting from the residual gauge fields cancel infrared divergences resulting from the physical parts of the gauge field. As a result, we obtain the gauge field propagator proposed by Mandelstam and Leibbrandt. By taking the limit θ→π 4, we are able to construct a light-cone formulation that is free from infrared divergences. With that analysis complete, we next calculate the one-loop electron self-energy, something not previously done in the light-cone quantization and light-cone gauge.

1+1 Gauge theories in the light-cone representation

We present a representation independent solution to the continuum Schwinger model in light-cone (A+=0) gauge. We then discuss the problem of finding that solution using various quantization schemes. In particular we shall consider equal-time quantization and quantization on either characteristic surface, x+=0 or x−=0.

PHYSICAL CHARGED FERMIONS IN THE FERMION - MONOPOLE SYSTEM

Abstract In order to demonstrate existence of physical charged fermions in the system consisting of a doublet of J = 0 massless fermions coupled to the radial electric field in the presence of a point-like SU(2) monopole, it is shown that the system is equivalent to that of a doublet of two-dimensional massless fermions carrying renormalized charges. As a consequence, it follows that charges are quantized if we confine ourselves to Fock space of the free massless fermion fields.