5 research outputs found
Group theoretical approach to quantum fields in de Sitter space I. The principal series
Using unitary irreducible representations of the de Sitter group, we
construct the Fock space of a massive free scalar field.
In this approach, the vacuum is the unique dS invariant state. The quantum
field is a posteriori defined by an operator subject to covariant
transformations under the dS isometry group. This insures that it obeys
canonical commutation relations, up to an overall factor which should not
vanish as it fixes the value of hbar. However, contrary to what is obtained for
the Poincare group, the covariance condition leaves an arbitrariness in the
definition of the field. This arbitrariness allows to recover the amplitudes
governing spontaneous pair creation processes, as well as the class of alpha
vacua obtained in the usual field theoretical approach. The two approaches can
be formally related by introducing a squeezing operator which acts on the state
in the field theoretical description and on the operator in the present
treatment. The choice of the different dS invariant schemes (different alpha
vacua) is here posed in very simple terms: it is related to a first order
differential equation which is singular on the horizon and whose general
solution is therefore characterized by the amplitude on either side of the
horizon. Our algebraic approach offers a new method to define quantum field
theory on some deformations of dS space.Comment: 35 pages, 2 figures ; Corrected typo, Changed referenc
On the cubic interactions of massive and partially-massless higher spins in (A)dS
Cubic interactions of massive and partially-massless totally-symmetric
higher-spin fields in any constant-curvature background of dimension greater
than three are investigated. Making use of the ambient-space formalism, the
consistency condition for the traceless and transverse parts of the
parity-invariant interactions is recast into a system of partial differential
equations. The latter can be explicitly solved for given s_1-s_2-s_3 couplings
and the 2-2-2 and 3-3-2 examples are provided in detail for general choices of
the masses. On the other hand, the general solutions for the interactions
involving massive and massless fields are expressed in a compact form as
generating functions of all the consistent couplings. The St\"uckelberg
formulation of the cubic interactions as well as their massless limits are also
analyzed.Comment: 42 pages, 2 tables, LaTex. Comments on two-derivative couplings
involving partially-massless spin-2 fields added, typos corrected, references
added. v2: final version to appear in JHEP. v3: formulae (3.4) and (3.9)
correcte