What is V-representable and how is it used?

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Discussion Overview

The discussion revolves around the term "V-representable," with participants seeking to clarify its meaning and context. The inquiry touches on both mathematical and physical aspects, as the term appears to have implications in both fields.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses confusion about the term "V-representable" and notes difficulty in finding introductory resources.
  • Another participant suggests that context is necessary to provide a meaningful explanation.
  • A different participant proposes that "V-representable" may refer to a group representation as linear transformations from a vector space to itself, but this is speculative without further context.
  • Another participant references a definition related to particle-density distribution and ground-state density for some potential, indicating a possible connection to physics.
  • One participant concludes that the term seems to relate more to physics than to linear and abstract algebra, suggesting a divergence in understanding its application.

Areas of Agreement / Disagreement

Participants generally agree that the term requires more context for proper interpretation. There are competing views on whether "V-representable" is primarily a mathematical or physical concept, and the discussion remains unresolved.

Contextual Notes

The discussion highlights a lack of clarity regarding the definitions and applications of "V-representable," with participants expressing uncertainty about its mathematical versus physical relevance.

kof9595995
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what's "V-representable"

Just encountered this word, not sure what it means. I tried google and wiki, but didn't find any introductory articles, only some professional articles which mentioned this word.
Can someone introduce a bit?
P.S. I'm not even sure where to post question, for I haven't figured out whether it's more mathematical or physical, so I put it here, randomly.
 
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Perhaps some context would be useful...
 


As rochfor1 says, we really need to know the context.

Until then I would guess that you are saying that group G has a representation as a group of linear transformations from vector space V to itself.
 


HallsofIvy said:
As rochfor1 says, we really need to know the context.

Until then I would guess that you are saying that group G has a representation as a group of linear transformations from vector space V to itself.

I think V refers to potential, I only found a definition(sort of, not quite formal) from an abstract of a article:
http://pra.aps.org/abstract/PRA/v47/i1/p153_1
"A particle-density distribution is said to be v-representable if it is the ground-state density for some potential v(r)"
And I don't understand it.
 


Then this has nothing to do with "Linear and Abstract Algebra"! In fact, it sounds like it is physics rather than mathematics.
 

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