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Nonperturbative lorentzian path integral for gravity

Ambjorn1, Jurkiewicz, Loll

  • 1The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark.

Physical Review Letters
|September 16, 2000
PubMed
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We developed a regularized path integral for Lorentzian quantum gravity using dynamically triangulated causal spacetimes. This approach avoids degenerate geometric phases found in Euclidean gravity, offering a robust framework for quantum gravity research.

Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Cosmology

Background:

  • Path integrals are crucial for quantum mechanics and quantum field theory.
  • Lorentzian quantum gravity presents challenges due to its complex spacetime structure.
  • Dynamical triangulations offer a non-perturbative approach to quantizing spacetime.

Purpose of the Study:

  • To construct a well-defined regularized path integral for Lorentzian quantum gravity.
  • To investigate the properties of spacetime histories in this framework.
  • To compare the results with dynamically triangulated Euclidean gravity.

Main Methods:

  • Utilizing dynamically triangulated causal spacetimes.
  • Defining a unique Wick rotation to the Euclidean sector for each spacetime geometry.

Related Experiment Videos

  • Analyzing the properties of the transfer matrix for finite lattice volumes.

    • Main Results:

    • A well-defined regularized path integral for Lorentzian quantum gravity was successfully constructed.
    • All spacetime histories exhibit a discrete proper time.
    • The transfer matrix is self-adjoint, bounded, and strictly positive for finite volumes.
    • Degenerate geometric phases, problematic in Euclidean gravity, are absent.

    Conclusions:

    • The proposed method provides a robust framework for Lorentzian quantum gravity.
    • The discrete proper time and positive transfer matrix suggest a well-behaved quantum spacetime.
    • This approach overcomes limitations of previous Euclidean gravity models.