Measurement in QFT: Mapping Fields to Theory's Math Formalism

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SUMMARY

The discussion focuses on the mapping of experimental measurements of quantum fields to the mathematical formalism of Quantum Field Theory (QFT). Participants explore the implications of measurements performed in particle accelerators like the LHC, questioning the eigenstates of fields post-measurement and the relationship between position and momentum operators. Key insights include the interpretation of particle tracks as a series of coarse position measurements that do not violate the Heisenberg Uncertainty Principle (HUP) and the distinction between QFT and non-relativistic Quantum Mechanics (QM). The conversation also highlights the complexity of representing quantum field states as entangled networks throughout spacetime.

PREREQUISITES
  • Quantum Field Theory (QFT) fundamentals
  • Heisenberg Uncertainty Principle (HUP)
  • Particle scattering theory and S-matrix formalism
  • Feynman diagrams and perturbation theory
NEXT STEPS
  • Study the mathematical framework of Quantum Field Theory, focusing on eigenstates and operators
  • Explore the implications of the Heisenberg Uncertainty Principle in experimental measurements
  • Investigate the role of entanglement in quantum field states and their representation
  • Review literature on coarse measurements and their impact on quantum states
USEFUL FOR

Physicists, quantum mechanics researchers, and students of Quantum Field Theory seeking to understand the relationship between experimental measurements and theoretical frameworks in particle physics.

  • #31
vanhees71 said:
But in your reference I don't see a concrete description of a TPC with the POVM formalism.
This would be a separate paper on its own. I just describe how track measurements actually performed with a TCP (no matter how it is built) can be interpreted as a POVM measurement of position and momentum.
vanhees71 said:
I doubt that my experimental colleagues actually building such instruments use the POVM formalism at all ;-)).
Neither did the spectroscopists before 1925 use the modern quantum formalism.

None of your statements mean that one cannot get correct descriptions in terms of POVMs respective energy levels.
 
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  • #32
I don't doubt the POVM formalism in any way. Of course spectroscopists before 1925 didn't use modern quantum formalism. To the contrary before at least 1913 with Bohr's "old quantum mechanics" it was an enigma how to explain the discrete spectra observed by Fraunhofer as well as Kirchhoff and Bunsen in the 19th century. It's only with modern QM that a complete understanding, including intensities, from a generally valid theory has been achieved.
 

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