1 / 16

John R. Klauder University of Florida

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

rainer
Download Presentation

John R. Klauder University of Florida

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  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? • Hard-core interpretation • Appearance of Time? • Soluble examples • Removal of Cutoffs? • Choose proper representation • Reduce as necessary

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

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

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

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

  16. Thank you !

More Related