Indispensability of Ghost Fields and Extended Hamiltonian Formalism in Axial Gauge Quantization of Gauge Fields
| dc.creator | Nakawaki, Y. | |
| dc.creator | McCartor, G. | |
| dc.date | 2000-04-19 | |
| dc.date.accessioned | 2026-07-07T04:09:47Z | |
| dc.date.available | 2026-07-07T04:09:47Z | |
| dc.description | It is shown that ghost fields are indispensable in deriving well-defined antiderivatives in pure space-like axial gauge quantizations of gauge fields. To avoid inessential complications we confine ourselves to noninteracting abelian fields and incorporate their quantizations as a continuous deformation of those in light-cone gauge. We attain this by constructing an axial gauge formulation in auxiliary coordinates $x^μ= (x^+,x^-,x^1,x^2)$, where $x^+=x^0{\rm sin}θ+x^3{\rm cos}θ, x^-=x^0{\rm cos}θ-x^3{\rm sin}θ$ and $x^+$ and $A_-=A^0{\rm cos} θ+A^3{\rm sin}θ=0$ are taken as the evolution parameter and the gauge fixing condition, respectively. We introduce $x^-$-independent residual gauge fields as ghost fields and accomodate them to the Hamiltonian formalism by applying McCartor and Robertson's method. As a result, we obtain conserved translational generators $P_μ$, which retain ghost degrees of freedom integrated over the hyperplane $x^-=$ constant. They enable us to determine quantization conditions for the ghost fields in such a way that commutation relations with $P_μ$ give rise to the correct Heisenberg equations. We show that regularizing singularities arising from the inversion of a hyperbolic Laplace operator as principal values, enables us to cancel linear divergences resulting from $({\partial}_-)^{-2}$ so that the Mandelstam- Leibbrandt form of gauge field propagator can be derived. It is also shown that the pure space-like axial gauge formulation in ordinary coordinates can be derived in the limit $θ\to\fracπ{2}-0$ and that the light-cone axial gauge formulation turns out to be the case of $θ=\fracπ{4}$. | |
| dc.description | 17 pages and uses seceq, psfig and ptptex | |
| dc.identifier | https://arxiv.org/abs/hep-th/0004140 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0004140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/49985 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Indispensability of Ghost Fields and Extended Hamiltonian Formalism in Axial Gauge Quantization of Gauge Fields | |
| dc.type | text |