This book gives a description of state-sum quantum gravity models which are based on triangulations of a smooth spacetime manifold. It contains detailed descriptions of Regge quantum gravity, spin-foam models and spin-cube models. Some other similar models, like the dynamical triangulations models, are only briefly described, since the sum over the spacetime triangulations is outside the scope of this book. The book also contains a detailed description of the approach where the piecewise linear (PL) manifold corresponding to a smooth manifold triangulation is considered as the basic structure of the spacetime. Hence the PL structure is not an auxiliary tool used to define the gravitational path integral for a smooth spacetime, but it is taken as a physical property of the spacetime. Consequently, it is straightforward to construct a finite gravitational path integral. Another consequence is that the problems of determination of the classical limit and how to calculate the quantum corrections can be solved by using the effective action method. The smooth manifold limit problem is then replaced by the problem of a smooth manifold approximation for the effective action, which can be obtained by using the standard quantum field theory with a physical cutoff. Some physical effects of a PL spacetime quantum gravity theory are also described, one of which is that the cosmological constant spectrum contains the observed value. A short exposition of higher gauge theory is also given, which is a promising way to generalize a gauge symmetry by using the concept of a 2-group. A 2-group is a categorical generalization of a group, and by using this approach one can construct the spin-cube models of quantum gravity.

Acerca del autor

Aleksandar Miković is a full professor in the Department of Informatics Engineering and Information Systems at Lus�fona University in Lisbon, where he lectures undergraduate and graduate courses in mathematics and physics. He is also a member of the Mathematical Physics Group of the University of Lisbon, which is a research center funded by the Portuguese science foundation. He has written 88 papers on string theory, quantum gravity and related mathematical physics. AM completed his PhD in string theory at the University of Maryland in 1990 under the guidance of Professor Warren Siegel and was a postdoc at Queen Mary College in London in the group of Professor Michael Green until 1992. From 1992 until 1994, he was a postdoc at Imperial College in London, working in the groups of Professor Kelly Stelle and Professor Christopher Isham. From 1994 until 2001, he was a research professor at the Institute of Physics in Belgrade and from 2001 works as a professor at Lus�fona University in Lisbon.

Marko Vojinović is an associate research professor in the Group for Gravitation, Particles and Fields at the Institue of Physics, University of Belgrade, where he does research and supervises young PhD students in quantum gravity. He is also a former member of the Mathematical Physics Group of the University of Lisbon. He has written 33 papers on quantum gravity, general relativity and foundations of quantum mechanics. MV completed his PhD in general relativity at the University of Belgrade in 2008 under the guidance of Professor Milovan Vasilić, and held two postdoc positions at the University of Lisbon in the Group of Mathematical Physics, collaborating with Aleksandar Miković, from 2009 to 2012 and from 2013 to 2016. Since 2016, he works as an associate research professor at the Institute of Physics Belgrade.

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