Constraints on anomalous quartic gauge boson couplings from $v$ $\bar{v}$ $\gamma$ $\gamma$ and $q$ $\bar{q}$ gamma gamma events at LEP-2

Anomalous quartic couplings between the electroweak gauge bosons may contribute to the vv gamma gamma and qq gamma gamma final states produced in e+e- collisions. This analysis uses the LEP2 OPAL data sample at centre-of-mass energies up to 209 GeV. Event selections identify vv gamma gamma and qq gamma gamma events in which the two photons are reconstructed within the detector acceptance. The cross-section for the process e+e- -> qq gamma gamma is measured. Averaging over all energies, the ratio of the observed e+e- -> qq gamma gamma cross-section to the Standard Model expectation is R(data/SM) = 0.92 +- 0.07 +- 0.04 where the errors represent the statistical and systematic uncertainties respectively. The vv gamma gamma and qq gamma gamma data are used to constrain possible anomalous W+W- gamma gamma and ZZ gamma gamma couplings. Combining with previous OPAL results from the W+W- gamma final state, the 95% confidence level limits on the anomalous coupling parameters aoz, acz, aow and acw are found to be: -0.007 GeV^-2 < aoz/Lambda^2 < 0.023 GeV^-2 -0.029 GeV^-2 < acz/Lambda^2 < 0.029 GeV^-2 -0.020 GeV^-2 < aow/Lambda^2 < 0.020 GeV^-2 -0.052 GeV^-2 < acw/Lambda^2 < 0.037 GeV^-2 where Lamdba is the energy scale of the new physics. Limits found when allowing two or more parameters to vary are also presented.