Tomáš Liko and Louis H Kauffman 2006 Class. Quantum Grav. 23 R63 doi:10.1088/0264-9381/23/4/R01
Tomáš Liko1 and Louis H Kauffman2
Show affiliationsWe discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative canonical quantum general relativity (loop quantum gravity). This leads naturally to a discussion of the Kodama wavefunction, a state which is conjectured to be the ground state of the gravitational field with positive cosmological constant. This review can serve as a self-contained introduction to loop quantum gravity and related areas. Our intent is to make the paper accessible to a wider audience that may include topologists, knot theorists, and other persons innocent of the physical background to this approach to quantum gravity.
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
04.60.Ds Canonical quantization
04.20.Fy Canonical formalism, Lagrangians, and variational principles
32S55 Milnor fibration; relations with knot theory (See also 57M25, 57Q45)
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C45 Quantization of the gravitational field
83C47 Methods of quantum field theory (See also 81T20)
57Q45 Knots and links (in high dimensions) (For the low-dimensional case, see 57M25)
Issue 4 (21 February 2006)
Received 6 May 2005, in final form 30 November 2005
Published 31 January 2006
Tomáš Liko and Louis H Kauffman 2006 Class. Quantum Grav. 23 R63
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