Gauge field theory coherent states (GCS): I. General properties

By T. Thiemann. 2000

234 citations recorded by the source corpus.

In this paper we outline a rather general construction of diffeomorphism covariant coherent states for quantum gauge theories. By this we mean states ψ(A,E), labelled by a point (A,E) in the classical phase space, consisting of canonically conjugate pairs of connections A and electric fields E, respectively, such that: (a) they are eigenstates of a corresponding annihilation operator which is a generalization of A-iE smeared in a suitable way; (b) normal ordered polynomials of generalized annihilation and creation operators have the correct expectation value; (c) they saturate the Heisenberg uncertainty bound for the fluctuations of Â,E; and (d) they do not use any background structure for their definition, that is, they are diffeomorphism covariant. This is the first paper in a series of articles entitled `Gauge field theory coherent states (GCS)' which aims to connect non-perturbative quantum general relativity with the low-energy physics of the standard model. In particular, coherent states enable us for the first time to take into account quantum metrics which are excited everywhere in an asymptotically flat spacetime manifold as is needed for semiclassical considerations. The formalism introduced in this paper is immediately applicable also to lattice gauge theory in the presence of a (Minkowski) background structure on a possibly infinite lattice.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fbdf2895cf3facbd33391c357175c98029ca07e9

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Citations in the corpus

Gauge field theory coherent states (GCS): II. Peakedness properties (2000, background): “…the general form of the above transform guarantees immediately that the gauge-variant Coherent States ψtγ,~g( ~h) := (Ŵtδγµγ ,~h′( ~h))|~h′→~g (4.1) obtained by heat kernel evolution followed by analytic continuation, where ~g = {ge}e∈E(γ) and similarly for ~h, satisfy a number of desired…”
Quantization ambiguities in isotropic quantum geometry (2002, background): “(Another aspect which is not considered here is that semiclassical states should be used which are peaked in both the connection and the triad; see [ 23 , 24, 25] for proposals.”
Gauge field theory coherent states (GCS): III. Ehrenfest theorems (2000, unknown): “To settle this issue we have launched an attack based on coherent states which has culminated in a series of papers called “Gauge Field Theory Coherent States” [ 40 , 41, 42, 43, 44, 45] and this paper is the third one of this collection (to be continued).”
Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation (2002, background): “Pp 0264-9381/06/030909+46$30.00 © 2006 IOP Publishing Ltd Printed in the UK 909 910 H Sahlmann and T Thiemann”
The Spin-Foam Approach to Quantum Gravity (2012, background): “1 Coherent states Coherent states associated to the representation theory of a compact group have been studied by Thiemann and collaborators [351, 349, 335, 349, 354, 355, 356, 352, 46, 47, 171] see also [70].”
Loop quantum gravity and light propagation (2001, background): “It may be possible to come to terms with such difficulties by defining coherent states for diffeomorphism covariant gauge theories [36] or by implementing a genuine statistical geometry [37], for instance.”