Noncommutative differential geometry, quantum mechanics and gauge theory

2008 ◽  
pp. 13-24 ◽  
Author(s):  
Michel Dubois-Violette
Keyword(s):  
Differential Geometry ◽  
Quantum Mechanics ◽  
Gauge Theory ◽  
Noncommutative Differential Geometry

Noncommutative differential geometry and new models of gauge theory

1990 ◽  
Vol 31 (2) ◽  
pp. 323-330 ◽  
Author(s):  
Michel Dubois‐Violette ◽  
Richard Kerner ◽  
John Madore
Keyword(s):  
Differential Geometry ◽  
Gauge Theory ◽  
Noncommutative Differential Geometry ◽  
New Models

scholarly journals Non-Commutative Worlds and Relativity

2021 ◽  
Vol 2081 (1) ◽  
pp. 012006
Author(s):  
Louis H Kauffman
Keyword(s):  
Differential Geometry ◽  
Quantum Mechanics ◽  
Gauge Theory ◽  
Hamiltonian Mechanics

Abstract This paper shows how aspects of gauge theory, Hamiltonian mechanics and quantum mechanics arise naturally in the mathematics of a non-commutative framework for calculus and differential geometry.

Chern–Simons gauge theory and symplectic quantum mechanics

2015 ◽  
Vol 93 (9) ◽  
pp. 971-973
Author(s):  
Lisa Jeffrey
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Partition Function ◽  
Partition Functions ◽  
Action Functional ◽  
Symplectic Action ◽  
Chern Simons

We describe the relation between the Chern–Simons gauge theory partition function and the partition function defined using the symplectic action functional as the Lagrangian. We show that the partition functions obtained using these two Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional. We also compute the semiclassical formulas for the partition functions obtained using the two different Lagrangians: the Chern–Simons functional and the symplectic action functional.

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