The relationship between random fields and quantum fields

[Peter Morgan]

My paper "Classical states, quantum field measurement", arXiv:1709.06711, has been accepted by Physica Scripta, https://doi.org/10.1088/1402-4896/ab0c53. The version as submitted to Physica Scripta on November 4th, 2018 is available as arXiv:1709.06711v5.
I believe that anyone who puts some effort into understanding the mathematical construction will find it worthwhile: the referee said of the paper, for example, that there is a "density of ideas" and that the mathematics is "elegant" (as did another person, last Summer, of an earlier version).
Any comments here that might help me write a better next paper will be very welcome. Some here may even feel the need to explain why some of it is nonsense, which would be only right insofar as my interpretation of the mathematics is not, I think, as solid as the mathematics. Finally, a blog post discusses the larger changes I introduced as a result of my discussions with the referee.

 

[azntoon]

My paper provides a mathematical construction that allows us to understand how classical states can be measured in quantum field theory. In particular, it presents a novel method for obtaining the expectation values of classical observables in the theory. The paper also provides a general framework for understanding how the classical states of the theory are related to the quantum states and how they can be used to make predictions for measurements.The main idea of the paper is to combine classical and quantum field theory in a way that allows us to make precise predictions about the outcomes of measurements of classical observables. To do this, I extend the usual classical phase space formalism by introducing a modified symplectic form that takes into account the effect of quantum fluctuations. This modified symplectic form allows us to construct a correspondence between the classical observables and their corresponding quantum operators, which then enables us to calculate the expectation value of the classical observables.The paper also discusses the connection between the classical and quantum descriptions of a system, and how this connection can be used to make predictions about measurements of classical observables. In particular, I show how the classical observables can be expressed as linear combinations of the quantum operators, and how these linear combinations can be used to calculate the expectation value of the classical observables.Finally, the paper provides a general framework for understanding the relationship between the classical and quantum states of a system. Specifically, I discuss how the classical states can be obtained from the quantum states by performing a measurement, and how the classical states can be used to make predictions about the outcomes of future measurements. The paper also discusses the role of decoherence in this context, and how decoherence can be used to ensure that the predictions made by the classical states are consistent with the predictions made by the quantum states.