Differential Geometry and Quantum Mechanics

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Discussion Overview

The discussion centers around the exploration of Quantum Mechanics through the lens of Differential Geometry, specifically seeking references and resources that emphasize the geometrical aspects of the subject.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant expresses interest in finding additional books that treat Quantum Mechanics with a focus on its geometrical aspects, referencing Geroch's notes.
  • Another participant requests the specific reference to Geroch's formulation of Quantum Mechanics that was mentioned.
  • A participant provides a link to Geroch's notes as a resource for others interested in this approach.
  • One participant suggests von Neumann's "The Mathematical Foundations of Quantum Mechanics" as a foundational text in non-commutative geometry, noting its thoroughness and lack of prerequisites, while also acknowledging they have not read Geroch's work.

Areas of Agreement / Disagreement

Participants appear to share an interest in the geometrical formulation of Quantum Mechanics, but there is no consensus on which texts are superior or more relevant, as different perspectives on the value of Geroch's and von Neumann's works are presented.

Contextual Notes

Some participants may have differing levels of familiarity with the texts mentioned, and the discussion does not resolve which approach is more effective or comprehensive.

Who May Find This Useful

Readers interested in the intersection of Quantum Mechanics and Differential Geometry, as well as those seeking foundational texts in non-commutative geometry.

Reedeegi
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After finding and reading Geroch's notes on Quantum Mechanics formulated within Differential Geometry, I was wondering if there are other books that treat Quantum Mechanics in a similar fashion, focusing upon the geometrical aspects of Quantum Mechanics in order to formulate it.
 
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Reedeegi said:
After finding and reading Geroch's notes on Quantum Mechanics formulated within Differential Geometry, I was wondering if there are other books that treat Quantum Mechanics in a similar fashion, focusing upon the geometrical aspects of Quantum Mechanics in order to formulate it.

Could you give the reference to Geroch's formulation of QM that you read?
 
AEM said:
Could you give the reference to Geroch's formulation of QM that you read?

Certainly, a copy can be found http://physics.syr.edu/~salgado/geroch.notes/geroch-gqm.pdf" .
 
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Did you read von Neumann's classic "The Mathematical Foundations of Quantum Mechanics" ?
It is basically the starting point of non-commutative geometry.
I do not claim it's better than Geroch's book, which I have not read (!), but in von Neumann's style, nothing is left unproven. Basically, no prerequisite is necessary.
 

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