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Effective potential describing the evolution of the most complicated anisotropic universe model. In the middle of the figure the universe is isotropic. The contours indicate potential walls which prevent the universe from becoming highly anisotropic close to a classical singularity.

One of the main tools of quantum field theory is that of effective actions. This allows one to compute quantum correction terms to classical equations, thus including quantum effects in a way which makes it easier to find solutions. Moreover, conceptual issues such as the interpretation of a quantum wave function can be circumvented in this way. The usual techniques, based on action principles suitable for low-energy regimes, are not applicable to strong field regimes as they are realized in early cosmology or in black holes. A more general framework has recently been developed, based on the way how deformations of a wave packet back-react on the motion of its peak position, which is now being applied to quantum gravity and cosmology.

Publications

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M. Bojowald, "Loop quantum gravity as an effective theory", in Sixth International School on Field Theory and Gravitation, Ed.: Carlos Pinheiro (AIP, 2012) p.
M. Bojowald and G. M. Paily, "Deformed General Relativity and Effective Actions from Loop Quantum Gravity," Phys. Rev. D 86, 104018 (2012)
M. Bojowald and A. Kempf, "Generalized uncertainty principles and localization in discrete space," Phys. Rev. D 86, 085017 (2012)
M. Bojowald, S. Brahma and E. Nelson, "Higher time derivatives in effective equations of canonical quantum systems," Phys. Rev. D 86, 105004 (2012)
M. Bojowald, "Quantum Cosmology: Effective Theory," Class. Quantum Gravity 29, 213001 (2012)
M. Bojowald and G. M. Paily, "A no-singularity scenario in loop quantum gravity," Class. Quantum Gravity 29, 242002 (2012)
M. Bojowald, "Quantum gravity, space-time structure, and cosmology," J. Phys. Conf. Ser 405, 012001 (2012)
M. Bojowald, "Loop Quantum Gravity and Cosmology: A dynamical introduction", in Foundations of Space and Time - Reflections on Quantum Gravity, Ed.: George Ellis, Jeff Murugan, Amanda Weltman (Cambridge Univ. Press, 2011) p.
M. Bojowald, D. Brizuela, H. H. Hernandez, M. Koop and H. A. Morales-Tecotl, "High-order quantum back-reaction and quantum cosmology with a positive cosmological constant," Phys. Rev. D 84, 043514 (2011) Abstract/Comments
M. Bojowald, P. A. Hoehn and A. Tsobanjan, "Effective approach to the problem of time: General features and examples," Phys. Rev. D 83, 125023 (2011) Abstract/Comments
M. Bojowald, P. A. Hoehn and A. Tsobanjan, "An effective approach to the problem of time," Class. Quantum Gravity 28, 035006 (2011) Abstract/Comments
M. Bojowald, G. M. Paily, J. D. Reyes and R. Tibrewala, "Black-hole horizons in modified space-time structures arising from canonical quantum gravity," Class. Quantum Gravity 28, 185006 (2011) Abstract/Comments
M. Bojowald, D. J. Mulryne, W. Nelson and R. Tavakol, "The high-density regime of kinetic-dominated loop quantum cosmology," Phys. Rev. D 82, 124055 (2010) Abstract/Comments
M. Bojowald and A. Tsobanjan, "Effective constraints and physical coherent states in quantum cosmology: a numerical comparison," Class. Quantum Gravity 27, 145004 (2010) Abstract/Comments
M. Bojowald, "Quantum geometry and quantum dynamics at the Planck scale", in AIP Conf. Proc., (, 2009) 1196, p. 62-71 Abstract/Comments
M. Bojowald, "Quantum gravity effects on space-time", in Proceedings of The Nineteenth Workshop on General Relativity and Gravitation in Japan, (, 2009) p. 1-16 Abstract/Comments
M. Bojowald, J. D. Reyes and R. Tibrewala, "Nonmarginal Lemaitre-Tolman-Bondi-like models with inverse triad corrections from loop quantum gravity," Phys. Rev. D 80, 084002 (2009) Abstract/Comments
M. Bojowald and A. Tsobanjan, "Effective constraints for relativistic quantum systems," Phys. Rev. D 80, 125008 (2009) Abstract/Comments
M. Bojowald, "Consistent Loop Quantum Cosmology," Class. Quantum Gravity 26, 075020 (2009) Abstract/Comments
M. Bojowald, B. Sandhoefer, A. Skirzewski and A. Tsobanjan, "Effective constraints for quantum systems," Rev. Math. Phys. 21, 111 – 154 (2009) Abstract/Comments
M. Bojowald and R. Tavakol, "Recollapsing quantum cosmologies and the question of entropy," Phys. Rev. D 78, 023515 (2008) Abstract/Comments
M. Bojowald and R. Das, "Canonical gravity with fermions," Phys. Rev. D 78, 064009 (2008) Abstract/Comments
M. Bojowald, "Loop Quantum Gravity and Effective Theory," PoS QG-Ph, 10 (2008) Abstract/Comments
M. Bojowald, H. H. Hernandez and A. Skirzewski, "Effective equations for isotropic quantum cosmology including matter," Phys. Rev. D 76, 063511 (2007) Abstract/Comments
M. Bojowald and R. Das, "The radiation equation of state and loop quantum gravity corrections," Phys. Rev. D 75, 123521 (2007) Abstract/Comments
M. Bojowald, H. H. Hernandez, M. Kagan and A. Skirzewski, "Effective constraints of loop quantum gravity," Phys. Rev. D 75, 064022 (2007) Abstract/Comments
M. Bojowald, "Large scale effective theory for cosmological bounces," Phys. Rev. D Rapid Comm. 75, 081301 (2007) Abstract/Comments
M. Bojowald and A. Skirzewski, "Effective Equations of Motion for Quantum Systems," Rev. Math. Phys. 18, 713 – 746 (2006) Abstract/Comments
M. Bojowald, P. Singh and A. Skirzewski, "Coordinate time dependence in Quantum Gravity," Phys. Rev. D 70, 124022 (2004) Abstract/Comments

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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M. Bojowald : Effective equations