Fubini vacua as a classical de Sitter vacua

The Fubini's idea to introduce a fundamental scale of hadron phenomena by means of dilatation non-invariant vacuum state in the frame work of a scale invariant Lagrangian field theory is recalled. The Fubini vacua is invariant under the de Sitter subgroup of the full conformal group. We obtain a finite entropy for the quantum state corresponding to the classical Fubini vacua in Euclidean space-time resembeling the entropy of the de Sitter vacua. In Minkowski space-time it is shown that the Fubini vacua is mainly a bath of radiation with Rayleigh-Jeans distribution for the low energy radiation. In four dimensions, the critical scalar theory is shown to be equivalent to the Einstein field equation in the ansatz of conformally flat metrics and to the SU(2) Yang-Mills theory in the 't Hooft ansatz. In D-dimensions, the Hitchin formula for the information geometry metric of the moduli space of instantons is used to obtain the information geometry of the free-parameter space of the Fubini vacua which is shown to be a (D+1)-dimensional AdS space. Considering the Fubini vacua as a de Sitter vacua, the corresponding cosmological constant is shown to be given by the coupling constant of the critical scalar theory. In Minkowski spacetime it is shown that the Fubini vacua is equivalent to an open FRW universe.Comment: 15 pages, revtex4, to appear in Mod.Phys.Lett.

Massive Spinors and dS/CFT Correspondence

Using the map between free massless spinors on d+1 dimensional Minkowski spacetime and free massive spinors on $dS_{d+1}$, we obtain the boundary term that should be added to the standard Dirac action for spinors in the dS/CFT correspondence. It is shown that this map can be extended only to theories with vertex ({\bar\p}\p)^2 but arbitrary $d\ge1$. In the case of scalar field theories such an extension can be made only for $d=2,3,5$ with vertices $\phi^6$, $\phi^4$ and $\phi^3$ respectively

Classification of constraints using chain by chain method

We introduce "chain by chain" method for constructing the constraint structure of a system possessing both first and second class constraints. We show that the whole constraints can be classified into completely irreducible first or second class chains. We found appropriate redefinition of second class constraints to obtain a symplectic algebra among them.Comment: 23 pages, to appear in Int. J. Mod. Phys.