Heisenberg picture manifests Lorentz invariance?

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SUMMARY

The discussion clarifies that Lorentz invariance is manifest in the Heisenberg picture of quantum mechanics (QM) due to the treatment of operators and states. In this framework, operators are functions of both space and time, while states are independent of these variables, aligning with the principles of Lorentz invariance. Conversely, in the Schrödinger picture, operators depend on space and states depend on time, leading to a lack of manifest Lorentz invariance. This distinction is crucial for understanding the implications of different formulations of quantum theory.

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  • Understanding of quantum mechanics principles
  • Familiarity with the Heisenberg and Schrödinger pictures
  • Knowledge of Lorentz invariance in physics
  • Basic concepts of quantum field theory (QFT)
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Physicists, students of quantum mechanics, and researchers in quantum field theory who seek to deepen their understanding of Lorentz invariance and its manifestation in different quantum frameworks.

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In several textbooks of QM I have read that Lorentz invariance is manifest in Heisnberg picture. How can we deduce that?
 
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In QFT in the Heisenberg picture, we have operators which are functions of space and time, and states which are functions of neither space nor time. This is good, because space and time should be on equal footing in a Lorentz invariant theory. But in the Schrödinger picture, we have operators which are functions of space and states which are functions of time. Here the Lorentz invariance of the theory is not manifest, since we are treating space and time differently.
 
I think I got it... Thank's.
 

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