Group consists of a set and an operation

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Discussion Overview

The discussion revolves around the concept of groups in the context of elementary particles, specifically focusing on the operations and sets involved in group theory as applied to physics. Participants explore the nature of these groups, their representations, and the implications for understanding particle physics and field theories.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions what specific operations and sets are involved when physicists refer to elementary particles forming a group.
  • Another participant identifies matrix multiplication as the operation for SU(n) and inquires about the types of matrices and their representations.
  • A different participant challenges the notion that elementary particles form a group, suggesting instead that they are irreducible representations of continuous groups, emphasizing the need for understanding group theory and its representations.
  • There is a suggestion that continuous groups contain all necessary information, with specific groups like SU(2) representing only parts of the broader structure.
  • One participant references their journal entry on string theory, indicating that it discusses how field theories are constructed using global and local symmetries, and mentions the emergence of gauge particles from local symmetries.

Areas of Agreement / Disagreement

Participants express differing views on whether elementary particles form a group or are merely representations of continuous groups. There is no consensus on the nature of the operations and sets involved, nor on the implications for particle physics.

Contextual Notes

The discussion includes assumptions about the understanding of group theory and its applications in physics, which may not be universally shared among participants. The specific definitions of groups and operations are not fully resolved.

greatscott
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When physicists say "elementary particles form a group," what kind of operations and sets are in question? (I presume, a group consists of a set and an operation)
 
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Ok, the operation for SU(n) is always matrix multiplication.
Now my next question is, what kind of matrices are concerned? What do the elements of the matrices represent?
 
Nope,u missunderstood.They do not form a group,they are irreductible representations of continuous groups...To fully understand it,u must know group theory and their representations...

Daniel.
 
So the continuous group has all the information and things like spin (SU(2)) are just "parts" of it?
 
I have written all this in my journal. Just look for the "introduction to string theory"-entry, part one. There is a paragraphe especially dedicated to how field theories are constructed using global and local symmetries...When imposing such local symmetries, gauge-particles arise...Check it out, it is all in there

regards
marlon
 

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