  The spectral energy distribution of giant lobes shows one main peak detected
by the Wilkinson Microwave Anisotropy Probe at low energy of $10^{-5}$ eV and a
faint $\gamma$-ray flux imaged by Fermi Large Area Telescope at energy $\geq$
100 MeV. On the other hand, Pierre Auger Observatory associated some
ultra-high-energy cosmic rays with the direction of Centaurus A and IceCube
reported 28 neutrino-induced events in a TeV - PeV energy range, although none
of them related with this direction. In this work we describe the spectra for
each of the lobes, the main peak with synchrotron radiation, and the
high-energy emission with $pp$ interactions. Obtaining a good description of
the main peak, we deduce the magnetic fields, electron densities and the age of
the lobes. Describing successfully the $\gamma$-ray emission by pp interactions
and considering as targets those thermal particles in the lobes with density in
the range $10^{-10}$ to $10^{-4}\, {\rm cm}^{-3}$, we calculate the number of
ultra-high-energy cosmic rays. Although $\gamma$-spectrum is well described
with any density in the range, only when $10^{-4}\, {\rm cm}^{-3}$ is
considered, the expected number of events is very similar to that observed by
Pierre Auger Observatory, otherwise we obtain an excessive luminosity. In
addition, correlating the $\gamma$-ray and neutrino fluxes through pp
interactions we calculate the number of high-energy neutrinos expected in
IceCube. Our analysis indicates that neutrinos above 1 TeV cannot be produced
in the lobes of Centaurus A, which is consistent with the results recently
published by IceCube Collaboration.
