Differential Geometry and Quantum Mechanics

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SUMMARY

The discussion centers on the intersection of Differential Geometry and Quantum Mechanics, specifically referencing Geroch's notes on the subject. Participants seek additional literature that emphasizes the geometrical aspects of Quantum Mechanics. A notable recommendation includes von Neumann's "The Mathematical Foundations of Quantum Mechanics," recognized as a foundational text in non-commutative geometry. Both texts are essential for understanding the geometrical formulation of Quantum Mechanics.

PREREQUISITES
  • Understanding of Differential Geometry principles
  • Familiarity with Quantum Mechanics concepts
  • Knowledge of non-commutative geometry
  • Basic mathematical proof techniques
NEXT STEPS
  • Read Geroch's notes on Quantum Mechanics at this link
  • Study von Neumann's "The Mathematical Foundations of Quantum Mechanics"
  • Explore the principles of non-commutative geometry
  • Investigate other texts that integrate geometry with Quantum Mechanics
USEFUL FOR

Physicists, mathematicians, and students interested in the geometrical foundations of Quantum Mechanics and those seeking to deepen their understanding of the mathematical structures underlying quantum theories.

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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