### Abstract

Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasis on the role of degrees of freedom and on differences between Lagrangian and Hamiltonian treatments. A general scheme is then provided which allows one to compute effective equations perturbatively in a Hamiltonian formalism. Here, one can expand effective equations around any quantum state and not just a perturbative vacuum. This is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive. The discussion also demonstrates the number of free parameters expected in effective equations, used to determine the physical situation being approximated, as well as the role of classical symmetries such as Lorentz transformation properties in effective equations. An appendix collects information on effective correction terms expected from loop quantum gravity and string theory.

Original language | English (US) |
---|---|

Pages (from-to) | 25-52 |

Number of pages | 28 |

Journal | International Journal of Geometric Methods in Modern Physics |

Volume | 4 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*International Journal of Geometric Methods in Modern Physics*,

*4*(1), 25-52. https://doi.org/10.1142/S0219887807001941

}

*International Journal of Geometric Methods in Modern Physics*, vol. 4, no. 1, pp. 25-52. https://doi.org/10.1142/S0219887807001941

**Quantum gravity and higher curvature actions.** / Bojowald, Martin; Skirzewski, Aureliano.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum gravity and higher curvature actions

AU - Bojowald, Martin

AU - Skirzewski, Aureliano

PY - 2007/2/1

Y1 - 2007/2/1

N2 - Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasis on the role of degrees of freedom and on differences between Lagrangian and Hamiltonian treatments. A general scheme is then provided which allows one to compute effective equations perturbatively in a Hamiltonian formalism. Here, one can expand effective equations around any quantum state and not just a perturbative vacuum. This is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive. The discussion also demonstrates the number of free parameters expected in effective equations, used to determine the physical situation being approximated, as well as the role of classical symmetries such as Lorentz transformation properties in effective equations. An appendix collects information on effective correction terms expected from loop quantum gravity and string theory.

AB - Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasis on the role of degrees of freedom and on differences between Lagrangian and Hamiltonian treatments. A general scheme is then provided which allows one to compute effective equations perturbatively in a Hamiltonian formalism. Here, one can expand effective equations around any quantum state and not just a perturbative vacuum. This is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive. The discussion also demonstrates the number of free parameters expected in effective equations, used to determine the physical situation being approximated, as well as the role of classical symmetries such as Lorentz transformation properties in effective equations. An appendix collects information on effective correction terms expected from loop quantum gravity and string theory.

UR - http://www.scopus.com/inward/record.url?scp=33847795558&partnerID=8YFLogxK

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U2 - 10.1142/S0219887807001941

DO - 10.1142/S0219887807001941

M3 - Article

AN - SCOPUS:33847795558

VL - 4

SP - 25

EP - 52

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 1

ER -