Test of the Kugo-Ojima confinement criterion in the lattice Landau gauge

We present the first results of numerical test of the Kugo-Ojima confinement criterion in the lattice Landau gauge. The Kugo-Ojima criterion of colour confinement in the BRS formulation of the continuum gauge theory is given by

u_b^a(p^2)=-\delta_b^a

, where

u_b^a

is defined by the two point function of the Faddeev-Popov ghost fields

c, \bar c

and the gauge field

A_\mu

. We measured the lattice version of

u_b^a(0)

in use of

1/(-\partial D(A))

where

D_\mu(A)

is a lattice covariant derivative in the new definition of the gauge fields as

U=e^A

. We obtained that

u_b^a(0)

is consistent with

-c\delta_b^a, c=0.7

in SU(3) quenched simulation data of

\beta=5.5

on

8^4

and

12^4

. We report the

\beta

dependence and finite-size effect of c.

Note:

3 pages Latex, 2 eps figures, Talk given at Lattice99(confine), Pisa, Italy

talk: Pisa 1999/06/29
gauge field theory: SU(3)
lattice field theory
color: confinement
approximation: quenching
Landau gauge
gluon: propagator
ghost: propagator
transformation: Becchi-Rouet-Stora
numerical calculations: Monte Carlo

References(12)

Figures(0)

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