Who introduced group theory into quantum field theory?

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Discussion Overview

The discussion revolves around the historical introduction of group theory into quantum field theory (QFT), exploring the contributions of various key figures in the field. Participants are examining the roles of Wigner and Weyl in this context.

Discussion Character

  • Historical, Debate/contested

Main Points Raised

  • One participant suggests that Wigner was the first to introduce group theory into QFT, referencing a classic paper from 1939.
  • Another participant agrees with the attribution to Wigner, indicating a consensus on his significant role.
  • Some participants propose that while Wigner was crucial for applications of group theory in quantum mechanics and QFT, Weyl also played a vital role by introducing group methods related to the foundations of quantum mechanics.
  • It is noted that Weyl contributed to modern differential geometry and group technology in classical mechanics, with a specific mention of his coining the term "symplectic."

Areas of Agreement / Disagreement

There is some agreement on Wigner's contributions, but the discussion also highlights differing views regarding Weyl's role and the specifics of their contributions, indicating that multiple competing views remain.

Contextual Notes

Participants have not fully resolved the timeline or the specific contributions of Wigner and Weyl, and there may be missing assumptions regarding the definitions of "introduction" and "applications" of group theory.

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I am trying to search for the first person who introduced group theory into quantum field theory.
 
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Wigner?
 
genneth said:
Wigner?

That would be my guess too.
In a classic paper published in 1939.
 
I would say, Wigner was mainly responsible for all applications of group theory in QM (and then QFT), whereas Weyl (from von Neumann's Hilbert spaces) introduced group methods to study the fundations of quantum mechanics.
 
humanino said:
I would say, Wigner was mainly responsible for all applications of group theory in QM (and then QFT), whereas Weyl (from von Neumann's Hilbert spaces) introduced group methods to study the fundations of quantum mechanics.

Indeed --- any Weyl also introduced much of the modern differential geometry and group technology to the study of classical mechanics. The term "symplectic" was in fact coined by him </trivia>
 

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