Commutation Relations: Relativistic Quantum Mechanics

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    Commutation Relations
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Discussion Overview

The discussion revolves around the validity of usual commutation relations, such as those between position and momentum, within the framework of relativistic quantum mechanics (RQM) and quantum field theory (QFT). The scope includes theoretical considerations and conceptual clarifications regarding the treatment of time and position in these contexts.

Discussion Character

  • Debate/contested, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant asserts that the usual commutation relations hold in one-particle relativistic quantum mechanics, specifically referencing the Dirac equation.
  • Another participant suggests that the situation becomes more complex in quantum field theory, implying that the validity of commutation relations may not be straightforward.
  • A different viewpoint is presented, arguing against the existence of a time operator in quantum mechanics, which raises questions about the foundational aspects of the theory.
  • Another participant echoes the sentiment regarding the absence of a time operator in field theory, noting that position is treated as a parameter rather than an operator.

Areas of Agreement / Disagreement

Participants express differing views on the validity of commutation relations in relativistic quantum mechanics and quantum field theory, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

Participants highlight the lack of a time operator in both quantum mechanics and field theory, suggesting that this absence may influence the treatment of commutation relations. However, the implications of this absence are not fully resolved.

Who May Find This Useful

This discussion may be of interest to those studying relativistic quantum mechanics, quantum field theory, or the foundational aspects of quantum mechanics, particularly regarding the treatment of time and position operators.

touqra
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Does the usual commutation relations, e.g. between position and momentum, remains valid in relativistic quantum mechanics?
 
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Yes in one particle RQM like the Dirac equation.
But things get more complicated in QFT.
 
No, because there's no such thing as time operator in quantum mechanics.

Daniel.
 
As far as I'm aware, there's no such thing as a time operator in field theory. My understanding was that, for field theory, they demoted position to a parameter like time, and promoted the wave equation to the status of an operator.
 

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