Mathematics – Dynamical Systems
Scientific paper
Sep 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrvd..38.1773k&link_type=abstract
Physical Review D (Particles and Fields), Volume 38, Issue 6, 15 September 1988, pp.1773-1779
Mathematics
Dynamical Systems
14
Theory Of Quantized Fields, Other Topics In Statistical Physics, Thermodynamics, And Nonlinear Dynamical Systems
Scientific paper
This paper focuses on the particle content of some scalar field as defined with respect to two sets of modes connected via a well-behaved (and unitarily implementable) Bogoliubov transformation. The principal conclusion impacts on the special role of ``random phase'' states, for which the relative phases associated with the projection of the quantum state into two different numbers eigenstates are treated as ``random'' and averaged over in a density matrix. Specifically, it is demonstrated that if, with respect to one set of modes, the field is in a ``random phase'' state, then any other mode decomposition related via a nontrivial Bogoliubov transformation will yield a larger expectation value for the total particle number. This special role of ``random phase'' states is also related to a recently discussed measure of entropy SN which assesses the ``spread'' or ``uncertainty'' in particle number. One specific example of all this is the relative particle content in Minkowski space as defined with respect to the modes natural for inertial and uniformly accelerated observers. Another is the initial and final particle numbers detected by two observers in a ``statically bounded'' universe of the form examined by Parker and Zel'dovich.
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