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- W2276299675 abstract "This is the first of two papers which study the semiclassical limit of a loop quantum gravity (LQG) canonical quantization of unidirectional plane gravity waves. Initially I formulate an exact LQG in which each triad, E^x_X for example, grasps only one of the x holonomies present at the vertex. Field strengths are non-local, constructed from holonomies which connect two neighboring vertices of the spin network. The equations are simplified using a semiclassical approximation, meaning eigenvalues of the volume operator are assumed to be large enough that the [volume, holonomy] commutators may be replaced by their quantum field theory limits. Additionally, SU(2) holonomies are expanded in sines and cosines, sines are assumed small, and terms quadratic in sines are dropped. In the semiclassical limit many non-local features disappear. However, differences replace derivatives with respect to z, the propagation direction; and semiclassical triads grasp both holonomies present at each vertex. Gauge-fixing constraints, as well as the constraint that the wave is traveling only in one direction, are formulated in a language appropriate to LQG. A subsequent paper constructs a sinusoidal solution using a Hilbert space of coherent states tailored to the symmetry of the plane wave case." @default.
- W2276299675 created "2016-06-24" @default.
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- W2276299675 date "2013-05-12" @default.
- W2276299675 modified "2023-09-27" @default.
- W2276299675 title "A semiclassical Hamiltonian for plane waves in loop quantum gravity" @default.
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