What is an interpretation of wave of field?

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SUMMARY

The discussion centers on the interpretation of wave fields in Quantum Field Theory (QFT), specifically addressing whether the trajectory of a wave represents the "classical trajectory" of a particle created by the field. The conversation references Gleason's Theorem and Soler's Theorem as foundational concepts in understanding probability amplitudes and number density amplitudes of particles. The participants suggest that the field's wave propagation is integral to grasping the underlying principles of quantum mechanics, hinting at a potential second quantum revolution in the field.

PREREQUISITES
  • Quantum Field Theory (QFT) fundamentals
  • Gleason's Theorem
  • Soler's Theorem
  • Understanding of probability amplitudes in quantum mechanics
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  • Research the implications of Gleason's Theorem in quantum mechanics
  • Explore Soler's Theorem and its applications in QFT
  • Read the article on the potential second quantum revolution in quantum mechanics
  • Investigate the relationship between wave propagation and particle trajectories in QFT
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Physicists, quantum mechanics students, and researchers interested in Quantum Field Theory and the philosophical implications of wave-particle duality.

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What is an interpretation of wave of field(wave that its medium is field) in QFT?Is it correct that the trajectory that wave propagates is the "classical trajectory" of particle created by the field?
 
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As a beginner I think probability amplitude or number density amplitude of particle propagates as wave. I appreciate your teachings.
 
Well this is starting to get into what the interpretation sub-forum handles. But keeping it to what this section discusses have a look at Gleason's Theorem:
https://en.wikipedia.org/wiki/Gleason's_theorem

And in a related vein we also have the interesting Solers Theorem:
https://en.wikipedia.org/wiki/Solèr's_theorem

The following to some extent brings it together:
https://royalsocietypublishing.org/doi/10.1098/rsta.2016.0393

After many years of thinking about QM I believe in what the article suggests - we may be on the verge of a second quantum revolution on why QM is as it is - but progress is slow. Here is a modern attempt:
https://arxiv.org/pdf/1508.03709.pdf

Beyond that you need to take it up in the interpretations section.

Thanks
Bill
 
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