Symplectic geometry on the Hilbert phase space and foundations of quantum mechanics

2006 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Symplectic Geometry ◽  
Foundations Of Quantum Mechanics

New Foundations of Quantum Mechanics

Physics Today ◽  
1966 ◽  
Vol 19 (9) ◽  
pp. 85-91 ◽  
Author(s):  
Alfred Landé ◽  
Abner Shimony
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics ◽  
New Foundations

scholarly journals Quantum gravity, dynamical phase-space and string theory

2014 ◽  
Vol 23 (12) ◽  
pp. 1442006 ◽  
Author(s):  
Laurent Freidel ◽  
Robert G. Leigh ◽  
Djordje Minic
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
String Theory ◽  
Quantum Gravity ◽  
Momentum Space ◽  
Symplectic Geometry ◽  
Complex Geometry ◽  
Hamiltonian Dynamics ◽  
Natural Extension ◽  
Dynamical Phase

In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).

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