Applying Riemann-Hilbert Space Curvature to Quantum Mechanics

  • Context: Graduate 
  • Thread starter Thread starter Loren Booda
  • Start date Start date
  • Tags Tags
    Space
Click For Summary
SUMMARY

The discussion focuses on the application of Riemann-Hilbert space curvature in quantum mechanics, specifically within the context of quantum field theory in curved spacetime. It highlights the significance of incorporating gauge fields to enhance the generality of these theories. The exploration of infinite-dimensional complex vector fields within Hilbert spaces is emphasized as a crucial aspect of this theoretical framework.

PREREQUISITES
  • Understanding of Riemannian geometry and curvature
  • Familiarity with quantum field theory concepts
  • Knowledge of Hilbert spaces and infinite-dimensional vector fields
  • Basic principles of gauge theory in physics
NEXT STEPS
  • Research the implications of Riemannian geometry in quantum mechanics
  • Study the role of gauge fields in quantum field theory
  • Explore the mathematical foundations of infinite-dimensional Hilbert spaces
  • Investigate applications of curvature in physical theories
USEFUL FOR

The discussion is beneficial for theoretical physicists, mathematicians specializing in geometry, and researchers focused on advanced quantum mechanics and field theory applications.

Loren Booda
Messages
3,115
Reaction score
4
Has a Hilbert space (e. g., containing an infinite-dimensional complex vector field) with curvature been applied to problems in quantum mechanics? Just asking.
 
Physics news on Phys.org
This is quantum field theory in curved space time. Gauge fields make such theories even more general.
 

Similar threads

  • · Replies 61 ·
3
Replies
61
Views
6K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 55 ·
2
Replies
55
Views
6K
  • · Replies 0 ·
Replies
0
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K