  Totally symmetric arbitrary spin conformal fields in (A)dS space of even
dimension greater than or equal to four are studied. Ordinary-derivative and
gauge invariant Lagrangian formulation for such fields is obtained. Gauge
symmetries are realized by using auxiliary fields and Stueckelberg fields. We
demonstrate that Lagrangian of conformal field is decomposed into a sum of
gauge invariant Lagrangians for massless, partial-massless, and massive fields.
We obtain a mass spectrum of the partial-massless and massive fields and
confirm the conjecture about the mass spectrum made in the earlier literature.
In contrast to conformal fields in flat space, the kinetic terms of conformal
fields in (A)dS space turn out to be diagonal with respect to fields entering
the Lagrangian. Explicit form of conformal transformation which maps conformal
field in flat space to conformal field in (A)dS space is obtained. Covariant
Lorentz-like and de-Donder like gauge conditions leading to simple gauge-fixed
Lagrangian of conformal fields are proposed. Using such gauge-fixed Lagrangian,
which is invariant under global BRST transformations, we explain how the
partition function of conformal field is obtained in the framework of our
approach.
