Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Consistent discretization and loop quantum geometry.

Rodolfo Gambini1, Jorge Pullin

  • 1Instituto de Física, Facultad de Ciencias, Universidad de la República Iguaá esq. Mataojo, CP 11400 Montevideo, Uruguay.

Physical Review Letters
|March 24, 2005
PubMed
Summary

This study introduces a consistent discretization for general relativity, simplifying constraints and solving the problem of time in quantum geometry. The approach yields a theory with diffeomorphism-invariant spin networks as its physical space.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Potential Gravitational Wave Signatures of Quantum Gravity.

Physical review letters·2021
Same author

The Montevideo Interpretation of Quantum Mechanics: A Short Review.

Entropy (Basel, Switzerland)·2020
Same author

Critical Collapse of a Scalar Field in Semiclassical Loop Quantum Gravity.

Physical review letters·2020
Same author

Milestones of general relativity.

Reports on progress in physics. Physical Society (Great Britain)·2016
Same author

Loop quantization of the Schwarzschild black hole.

Physical review letters·2013
Same author

Local Hamiltonian for spherically symmetric gravity coupled to a scalar field.

Physical review letters·2012

Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • General Relativity

Background:

  • The Hamiltonian and diffeomorphism constraints in general relativity pose significant challenges in canonical quantization.
  • Loop quantum gravity utilizes spin networks to describe quantum states of geometry, but incorporating dynamics remains complex.

Purpose of the Study:

  • To develop a novel approach to quantizing general relativity by applying consistent discretization.
  • To resolve the constraint problem and the problem of time in quantum gravity.
  • To reformulate the physical space of general relativity in terms of diffeomorphism-invariant spin networks.

Main Methods:

  • Applying the "consistent discretization" method to general relativity with continuous spatial slices.
  • Analyzing the resulting theory, which is initially free of constraints.

Related Experiment Videos

  • Imposing the diffeomorphism constraint to reduce the solution space while ensuring its preservation under discrete evolution.
  • Implementing dynamics as a unitary transformation.

    • Main Results:

    • The theory becomes free of the diffeomorphism and Hamiltonian constraints.
    • The diffeomorphism constraint is preserved exactly under discrete evolution.
    • The physical space of the theory corresponds to the kinematical space of loop quantum geometry (diffeomorphism-invariant spin networks).
    • The problem of time is explicitly addressed or reduced to a numerical problem.
    • The technique is demonstrated in (2+1)-dimensional gravity.

    Conclusions:

    • Consistent discretization offers a viable path to quantizing general relativity.
    • This approach naturally incorporates diffeomorphism invariance and addresses fundamental challenges in quantum gravity.
    • The framework provides a new perspective on the structure of spacetime at the quantum level.