Canonical Quantization: Explaining the Covariance Paradox

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SUMMARY

Canonical quantization in Quantum Field Theory (QFT) is fundamentally not relativistically covariant due to the introduction of the Hamiltonian, which selects a specific time direction. This selection inherently breaks Lorentz covariance, despite the initial formulations appearing Lorentz invariant. Understanding this paradox is crucial for grasping the limitations of canonical quantization in QFT.

PREREQUISITES
  • Quantum Field Theory (QFT) fundamentals
  • Understanding of Lorentz invariance
  • Familiarity with Hamiltonian mechanics
  • Knowledge of canonical quantization techniques
NEXT STEPS
  • Explore the implications of Lorentz covariance in Quantum Field Theory
  • Study the differences between canonical quantization and path integral formulation
  • Investigate alternative quantization methods, such as covariant quantization
  • Learn about the role of the Hamiltonian in quantum mechanics and its impact on symmetry
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on Quantum Field Theory and the implications of quantization methods on relativistic invariance.

shereen1
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Hi all
I am studying Quantum Field Theory. I read the following statement :"Canonical quantisation is intrinsically not relativistically covariant. Can anyone explain why?. Although everything we did from the beginning was lorentz invariant!
Thank you .
 
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You are singling out a particular time direction when you introduce the Hamiltonian. This breaks Lorentz covariance.
 
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