Representations Of De Sitter Group Research Articles

Entropy of massive quantum fields in de Sitter space–time

Using the quantum states or Hilbert spaces for the quantum field theory in de Sitter ambient space formalism the entropy of the massive quantum field theory is calculated. In this formalism, the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group are compact. The unique feature of this homogeneous space is that by imposing certain physical conditions its total number of quantum one-particle states, N1−p, becomes finite although the Hilbert space has infinite dimensions. N1−p is de Sitter invariant and a continuous function of the Hubble constant H and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields is finite and invariant for all inertial observers on de Sitter hyperboloid.

Group theoretical approach to quantum fields in de Sitter space II. The complementary and discrete series

We use an algebraic approach based on representations of de Sitter group to construct covariant quantum fields in arbitrary dimensions. We study the complementary and the discrete series which correspond to light and massless fields and which lead new feature with respect to the massive principal series we previously studied (hep-th/0606119). When considering the complementary series, we make use of a non-trivial scalar product in order to get local expressions in the position representation. Based on these, we construct a family of covariant canonical fields parametrized by SU(1,1)/U(1). Each of these correspond to the dS invariant alpha-vacua. The behavior of the modes at asymptotic times brings another difficulty as it is incompatible with the usual definition of the in and out vacua. We propose a generalized notion of these vacua which reduces to the usual conformal vacuum in the conformally massless limit. When considering the massless discrete series we find that no covariant field obeys the canonical commutation relations. To further analyze this singular case, we consider the massless limit of the complementary scalar fields we previously found. We obtain canonical fields with a deformed representation by zero modes. The zero modes have a dS invariant vacuum with singular norm. We propose a regularization by a compactification of the scalar field and a dS invariant definition of the vertex operators. The resulting two-point functions are dS invariant and have a universal logarithmic infrared divergence.