Relativistic Quantum Mechanics & Localized Particles

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Discussion Overview

The discussion revolves around the implications of relativistic quantum mechanics (QM) and quantum field theory (QFT) regarding the localization of particles. Participants explore the challenges of defining particle positions in a relativistic framework, the role of measurements, and the nature of multi-particle states versus single-particle states.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question the lecturer's assertion that localized particles cannot be meaningfully discussed in relativistic QM, seeking clarification on the relationship to Fock-space states.
  • There is a suggestion that QFT allows for calculating probabilities of energy detection at specific locations, but this does not imply knowledge of particle positions.
  • One participant argues that particles must interact with detectors (like calorimeters) to deposit energy, implying that this interaction provides information about particle locations.
  • Another participant distinguishes between predicting trajectories of indistinguishable particles and relying on local measurements to infer their presence near detectors.
  • Some participants assert that QFT can measure exact particle positions without violating the Uncertainty Principle, citing specific theoretical frameworks and literature.
  • There is a contention regarding the validity of applying non-relativistic results to relativistic cases, with some participants arguing that Lorentz-invariance must be respected in these calculations.

Areas of Agreement / Disagreement

Participants express differing views on the ability to localize particles in relativistic QM and QFT, with no consensus reached on whether particle positions can be meaningfully defined or measured in a relativistic context.

Contextual Notes

The discussion highlights limitations in understanding the implications of relativistic effects on particle localization, the dependence on definitions of measurements, and the unresolved nature of certain mathematical steps in the arguments presented.

  • #61
WWCY said:
He said that this was down to the fact that we should be considering multi-particle states in relativistic situation, before introducing Fock-space states.

There have been already a lot of answers, I only want to quote the introduction of "quantum electrodynamics" by Beretetskii-Lifshitz-Pitaevskii
 

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  • #62
A. Neumaier said:
But if you take 4D Fourier transforms then the N-point Green's functions get N times, and can for N>2 no longer be interpreted in terms of inner products of multiparticle states (where there is one time only but multiple space coordinates).
Of course not. The QFT formalism automatically takes care of the Bose/Fermi (anti-)symmetrization.
 
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