Wheeler-Dewitt equation and canonical quantum gravity

Click For Summary
SUMMARY

The Wheeler-Dewitt equation is central to canonical quantum gravity, where the Hamiltonian is set to zero due to the invariance under reparametrizations. This condition applies universally to gravitational fields in general relativity and also to relativistic point particles in geodesic motion. The discussion emphasizes the implications of Ricci-flat space-time on the Hamiltonian's value, asserting that it remains zero in such contexts.

PREREQUISITES
  • Understanding of canonical quantum gravity
  • Familiarity with the Wheeler-Dewitt equation
  • Knowledge of general relativity principles
  • Concept of Ricci-flat space-time
NEXT STEPS
  • Research the implications of the Wheeler-Dewitt equation in quantum cosmology
  • Study the role of reparametrization invariance in gravitational theories
  • Explore the relationship between Ricci-flat space-time and quantum gravity
  • Examine examples of geodesic motion in relativistic physics
USEFUL FOR

The discussion is beneficial for theoretical physicists, researchers in quantum gravity, and students studying general relativity and its implications in modern physics.

ylping
Messages
4
Reaction score
0
In the canonical quantum gravity, Hamiltonian equal zero, why? Since the split is space, the time is a constant? or the space-time is Ricci-flat?

In other words, if the space-time is Ricci-flat whether time supersurface, Hamiltonian equal zero?
 
Physics news on Phys.org
The hamiltonian is equal to zero in any system which is invariant under reparametrizations. This is always the case for the gravitational field in general relativity. Another example is a relativistic point particle in geodesic motion.
 

Similar threads

  • · Replies 16 ·
Replies
16
Views
7K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 24 ·
Replies
24
Views
8K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 13 ·
Replies
13
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 20 ·
Replies
20
Views
6K
  • · Replies 15 ·
Replies
15
Views
6K
  • · Replies 26 ·
Replies
26
Views
6K