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In the thread "Difference between field and wavefunction" is explained very well what are they from formal mathematical point of view and how trough second quantization one gets QF from WF. But there is not treated the issue of transition from epistemology (WF especially in Copenhagen interpretation) to ontology (QF-quantum fields) I can not see how the second quantization (a mathematical procedure) raises wavefunction (an epistemological construct) in QM which is loosly speaking square root of probability (very strongly stated in standard QM) to an ontological object a real existing thing e.g. QF underlying everything. I can not find such Statement in QFT books which start with QM wavefunction but this Statement is widely popularized by some physisists. May it that the WF is an emerging phenomenon due to reality of the QF? Than WF should not be considered very strange?

Mercury
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    What do you mean by 'real matter'? It seems you're asking about how second quantisation works, but surely that is explained near the start of every QFT book. – jacob1729 Nov 13 '19 at 13:37
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    Near duplicate? – Cosmas Zachos Nov 13 '19 at 13:47
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    Possible duplicate of Difference between field and wavefunction –  Nov 13 '19 at 14:45
  • @jacob1729 by real matter I mean that QF are discussed as the building blocks of universe. What could be more real than this? But WF is just probability nothing real (barring de Broglie Bohm). Second Quantization is mathematical mapping (almost clear to me) - so it is astonishing it will lead to real matter. – Mercury Nov 13 '19 at 15:44
  • What is not explicitly written in the linked answer is that also in QFT the system is essentially described by a wavefunction. The problem is that if your configuration space is say the real line the Hilbert space is not separable and a description via wavefunction is not suitable. One rather characterizes the system by a sufficiently large number of expectation values (for example Wightman functions). But this is somehow just a mathematical complications. The name second quantization is very misleading in that there is nothing more quantum to it. – lcv Nov 13 '19 at 16:52

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