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Towards loop quantum gravity without the time gauge.

Francesco Cianfrani1, Giovanni Montani

  • 1ICRA-International Center for Relativistic Astrophysics, Physics Department (G9), University of Roma Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy. francesco.cianfrani@icra.it

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Summary
This summary is machine-generated.

The Hamiltonian formulation of the Holst action offers a solution for second-class constraints in a generic local Lorentz frame. This enables loop quantum gravity quantization even without a time-gauge condition.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • General Relativity

Background:

  • The Holst action is a key formulation in theoretical physics, particularly in the context of quantum gravity.
  • Hamiltonian formulations are crucial for understanding the dynamics and quantization of physical theories.
  • Second-class constraints pose challenges in the quantization of constrained systems.

Purpose of the Study:

  • To review the Hamiltonian formulation of the Holst action.
  • To find a solution for second-class constraints within a generic local Lorentz frame.
  • To explore the applicability of loop quantum gravity quantization under specific conditions.

Main Methods:

  • Reviewing the established Hamiltonian formulation of the Holst action.
  • Solving second-class constraints associated with a generic local Lorentz frame.
  • Generalizing Ashtekar-Barbero-Immirzi connections to simplify rotation constraints.

Main Results:

  • A solution for second-class constraints in the Hamiltonian formulation of the Holst action was found for a generic local Lorentz frame.
  • The rotation constraints were successfully reduced to a Gauss-like form through a generalized Ashtekar-Barbero-Immirzi connection.
  • The study demonstrates that loop quantum gravity quantization is feasible even when the time-gauge condition is not imposed.

Conclusions:

  • The Hamiltonian formulation of the Holst action provides a viable framework for addressing constraints in gravity.
  • The generalization of Ashtekar-Barbero-Immirzi connections offers a powerful tool for simplifying constraints in quantum gravity.
  • This work broadens the conditions under which loop quantum gravity quantization can be applied, enhancing its potential applicability.