The request by Classical and Quantum Gravity to review the third edition of Claus Kiefer's 'Quantum. Gravity' puts me in a slightly awkward position. This is a. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared. From: Claus Kiefer [view email]. The Semiclassical approximation to quantum gravity - Kiefer, Claus Lect. T C P, Quantum Gravity, the Cosmological Constant and All That - Banks, Tom Nucl.
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The obstacles are of formal and of conceptual nature.
Here, I address the main conceptual problems, discuss their present status, and outline further directions of research. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared.
According to our current knowledge, the fundamental interactions of nature are the strong, the electromagnetic, the weak, and quantum gravity kiefer gravitational interactions.
The first three are successfully described by the Standard Model of particle physics, in which a partial unification of the electromagnetic and the weak interactions has been achieved.
Except for the nonvanishing neutrino masses, there exists at present no empirical fact that is clearly at variance with the Standard Model. quantum gravity kiefer
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From a pure empirical point of view, we thus have no reason to search for new physical laws. From a theoretical mathematical and conceptual point of view, however, the situation is not satisfactory. Whereas quantum gravity kiefer Standard Model is a quantum field theory describing an incomplete unification of interactions, GR is a classical theory.
It can be defined by the Einstein-Hilbert action where is the determinant of the metric, is the Ricci scalar, and is the cosmological constant.
In addition to the two main terms, which consist of integrals over a spacetime regionthere is a term that is defined on the boundary here assumed to be space quantum gravity kiefer of this region.
General Relativity and Quantum Cosmology
This term is needed for a consistent variational principle; here, is the determinant of the three-dimensional metric, and is the trace of the second fundamental form. As one recognizes from 2these equations can no longer have exactly the same form if the quantum nature of quantum gravity kiefer fields in is taken into account.
For then we have operators in Hilbert space on the right-hand side and classical functions on the left-hand quantum gravity kiefer. They spoil the linearity of quantum theory and even seem to be in conflict with a performed experiment [ 4 ].
 Conceptual Problems in Quantum Gravity and Quantum Cosmology
Chapter 9 gives an introduction to string theory by focusing on its quantum gravitational aspects. Chapter 10 contains a discussion of interpretational issues: It also contains a brief review of quantum-gravity phenomenology.
The third edition also contains quantum gravity kiefer extensions throughout the text.
This book will be of interest to researchers and students working in quantum gravity kiefer and gravitation, cosmology, quantum field theory and related topics.
The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered.
Conceptual Problems in Quantum Gravity and Quantum Cosmology
Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all quantum gravity kiefer interactions.
I will highlight a recent proposal how quantum gravity could generate the difference between the top mass and the bottom mass through an asymptotically safe quantum gravity kiefer point. In the past, this was done in the framework of Euclidean quantum gravity, where time was taken to be imaginary.