Mathematics – Logic
Scientific paper
Jul 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980gregr..12..511b&link_type=abstract
General Relativity and Gravitation, Volume 12, Issue 7, pp.511-520
Mathematics
Logic
3
Cosmological Models, Universe:Particle Creation
Scientific paper
The time-dependent creation and annihilation operators for a complex scalar field, in a Friedmann space-time, defining particle states with respect to which the Hamiltonian is diagonal, are related by a Bogoliubov transformation to the creation and annihilation operators defined in strict analogy with the procedure carried out in Minkowski space. The Bogoliubov transformation is here written in terms of a unitary operator,U, and an expression for that operator is found via the generating function F=i In U. The properties of the representation obtained by making U act upon the state vector ?Ψ>, to give a new state ?ΨU>, are discussed. It is shown that the particle-number operator remains constant in such a picture so that the evolution of the system with time is clearly seen to depend upon the energy ωk on the one hand, and upon the state vector ?ΨU> on the other. Also, it is pointed out that this new representation permits the “in” and “out” states to be defined unambiguously.
Bonometto Silvio A.
Pollock M. D.
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