Other
Scientific paper
Nov 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvd..40.3343r&link_type=abstract
Physical Review D (Particles and Fields), Volume 40, Issue 10, 15 November 1989, pp.3343-3356
Other
9
Scientific paper
To illustrate gravitational effects on the dynamics of a quantized field, the spectrum of excited states available to a linear scalar field in de Sitter space is examined in detail. Explicit Schrödinger-picture wave functionals are obtained for the excitation-number eigenstates of the familiar Fock-space description. The field energies of these states are calculated from expectation values of the appropriate Hamiltonian. The Euclidean vacuum state is seen to be the lowest-energy de Sitter-invariant state, although for any massive or nonconformally coupled field instantaneous Hamiltonian diagonalization, breaking de Sitter invariance, yields states of lower energy. All other de Sitter-invariant vacua are characterized by uniform excitation, relative to the Euclidean vacuum, in all field modes. Associated with any vacuum state is a Fock-space basis of excited states. These have field energies in integral increments above the vacuum; i.e., they represent the quantized excitations of the field's normal modes. The energy increments-the (renormalization-independent) energies of individual ``particles''-differ markedly from the classical normal-mode frequencies of the field. For fields with combined mass and curvature coupling above a certain threshold, ``particle'' energies oscillate at late and early times rather than approach a fixed limit; for fields with strong curvature coupling these energies can even become negative. They show exponential rather than oscillatory time dependence if the combined mass and curvature coupling is below the threshold. Excitation energies of a massless, conformally coupled field have the same time dependence as the energy of a classical relativistic particle, but for other fields with the same mass-curvature-coupling sum, ``particle'' energies have an amplified component, which grows as the radius of the space. The interaction between a field in an excited state and a monopole ``detector'' is also calculated: Each excitation gives, above the vacuum signal, a finite response with a finite width in energy. These effects on ``particle'' energies and interactions are due to modulation of the field normal modes in a time-dependent spacetime metric, so similar effects should occur in general spacetimes.
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