1306.3575 (M. V. Takook)

Entropy of Quantum Fields in de Sitter Space-time    [PDF]

M. V. Takook

The quantum states or Hilbert space for quantum field theory in de Sitter ambient space notation is explicitly constructed. In this formalism the quantum states are independent of the choice of the coordinate system. They are only depend to the topological character of de Sitter space-time {\it i.e.} $\R \times S^3$ and to the homogeneous space where the unitary irreducible representation of de Sitter group, SO(1,4), is constructed on it. There are different realization or homogeneous space for construction of the unitary irreducible representations of de Sitter group and their corresponding Hilbert spaces. There exist a specific realization with a compact homogeneous space. Each points in the homogeneous space present a vector in Hilbert space. The total number of quantum states is the sum (or integral) on the admissible possible value of the points in the homogeneous space and for the compact homogeneous space it is finite. Although one has an infinite dimensional Hilbert space, the total number of quantum state is finite. The total number of quantum states in this Homogeneous space is a continuous function of the Hubble parameter $H$ and the two parameters $ p$ and $ q$, which classify the unitary irreducible representation of de Sitter group. The eigenvalue of the Casimir operators of de Sitter group are written by them. Then the entropy of the quantum fields on this Hilbert space is calculated, which is finite. This entropy must satisfy the entropy bound and holography principle. The Hubble parameter $H$ and the eigenvalue of the Casimir operator of de Sitter group are de Sitter invariant, then the entropy is invariant for every inertial observer in de Sitter hyperboloid.

View original: http://arxiv.org/abs/1306.3575