Abstract
The previous chapter was concerned with a detailed investigation of decoherence through interaction with the environment. While most examples were discussed in the framework of quantum mechanical systems, i.e. systems with finitely many degrees of freedom, it is the purpose of this chapter to extend these discussions to situations where quantum fields play an important role. Moreover, the inclusion of a quantised gravitational field will entail new conceptual issues such as the absence of a fundamental time parameter.
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References
This is a straightforward generalisation of standard path integral techniques, which is especially suited to treat density matrices, see also Chap. 5.
Die Gleichung (4.7) zeigt, daß die Größen φ nm mit der Zeit stets durchschnittlich abnehmen. Der Grund dafür liegt . . . offenbar in der zunehmenden Phasenunbestimmtheit, welche eine Verminderung der Kohärenzfähigkeit der Strahlung herbeiführt.
Physically, this represents the volume where the electric field is non-vanishing, e.g. the volume of an appropriate cavity.
We consider only the case of spatially closed hypersurfaces. In the asymptotically flat case, the total Hamiltonian can be written as a surface integral.
It is known that (4.31) does not give rise to a unitary evolution in a Fock space built over three-dimensional slices.
The chosen factor ordering is given by the Laplace-Beltrami operator in the configuration space spanned by a and φ.
The decoherence factor in the massive bosonic case, (4.66) and (4.67), comes from the adiabatic part of Ωn and is not directly related to particle creation. This is not in conflict with Hu and Matacz (1995), since there the assumption is being made that the state separates between system and environment in the past, which is not the case here.
We ignore here alternative approaches which use a complex Hamiltonian from the very beginning (Kiefer 1993).
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© 2003 Springer-Verlag Berlin Heidelberg
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Kiefer, C. (2003). Decoherence in Quantum Field Theory and Quantum Gravity. In: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05328-7_4
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DOI: https://doi.org/10.1007/978-3-662-05328-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05576-8
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