Abhay Ashtekar and Jerzy Lewandowski 2004 Class. Quantum Grav. 21 R53 doi:10.1088/0264-9381/21/15/R01
Abhay Ashtekar1,2,3 and Jerzy Lewandowski2,2,3,4
Show affiliationsThe goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
03.65.Sq Semiclassical theories and applications
53B21 Methods of Riemannian geometry
81Txx Quantum field theory; related classical field theories (See also 70Sxx)
Quantum information and quantum mechanics
Issue 15 (7 August 2004)
Received 5 April 2004
Published 9 July 2004
Abhay Ashtekar and Jerzy Lewandowski 2004 Class. Quantum Grav. 21 R53
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