1. ---- Functional Integrals in ---- ---- Affine Quantum Gravity ----
John R. Klauder
University of Florida
Dresden, September, 2007

2. Affine Quantum Gravity
Kinematical variables
Metric positivity
Initial representation
Without constraints
Quantum constraints
Projection operator method
Imposition of constraints
Functional integral representation

3. Kinematical variables
Affine commutation relations

4. Initial representation
Affine coherent states

5. Quantum constraints
Enforcing the constraints

6. Quantum constraints (2)
Non-standard constraints
REDUCIBLE , IRREGULAR , MIXED REGULAR AND IRREGULAR

7. Quantum constraints (3)
Observables

8. Imposition of Constraints
Path integral

9. Initial representation
Affine coherent states

10. Imposition of Constraints (2)
Functional integral
The Heart of the Matter

11. Further Issues Nonrenormalizability? Appearance of Time?
Hard-core interpretation
Appearance of Time?
Soluble examples
Removal of Cutoffs?
Choose proper representation
Reduce as necessary
notes

12. Hard-core interaction
Free and pseudo-free theories
Theory
DISCONTINUOUS PF F
CONTINUOUS
Coupling constant

13. Hard-core interaction (2)
Idealized functional integral 16

14. Hard-core interaction (3)
Unconventional model analysis

15. Summary: AQG Preserve metric positivity Gravitational anomaly
Affine kinematical variables
Gravitational anomaly
Projection operator method
Functional integral formalism
Continuous-time regularization
Nonrenormalizable theory
Hard-core interaction

16. Thank you !