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Abstract |
A rigorous mathematical consideration of quantum field theory in de Sitter
universe is briefly presented in ambient space formalism. This formalism permit us
to solve some physical and mathematical problems in de Sitter space-time. The
concept of mass is defined from the light-cone propagation: massless fields or
particles are propagated on the de Sitter light-cone and the massive cases are
propagated inside the light-cone. In this respect, there appears a big problem of
mass definition for the massless minimally coupled scalar field. This field play
an important role in quantum gravity and mass generation in quantum inflationary
scenario.
The classical field theory consideration is based on group theory and Lie algebra.
From the Casimir operators of the de Sitter group the free field equation is
derived. By using the Lie algebra of de Sitter group one-particle Hilbert state
and unitary irreducible representation can be constructed and then the solution of
the free field equations can be extracted.
In QFT level, the field operator is defined as a map on the Fock space and then is
constructed by the annihilation and creation operators on the Fock space. The free
massive field operator must be transform by the unitary irreducible representation
of the dS group. The act of annihilation operator on the one-particle state
results to the vacuum state which must be fixed by the auxiliary condition. For
the free massless field with s≥1 and massless minimally coupled scalar field
for
obtaining a covariant quantization the field operator must be transform by an
indecomposable representation of dS group. The Hilbert space of the interaction
fields and the time evolution operator are the most challenging problems in de
Sitter universe. |
