Abstract
We present the construction of a new family of coherent states for quantum theories of connections obtained following the polymer quantization. The realization of these coherent states is based on the notion of graph change, in particular the one induced by the quantum dynamics in Yang-Mills and gravity quantum theories. Using a Fock-like canonical structure that we introduce, we derive the new coherent states that we call the graph coherent states. These states take the form of an infinite superposition of basis network states with different graphs. We further discuss the properties of such states and certain extensions of the proposed construction.
Highlights
The polymer quantization is a quantization procedure developed in the context of background independent approaches to quantum field theories
We introduced a new family of coherent states on the Hilbert space of a polymer quantum theory of connections with an arbitrary compact gauge group G
Inspired from the quantum dynamics of Yang-Mills and gravity, the notion of a graph change lies at the core of the construction
Summary
The polymer quantization is a quantization procedure developed in the context of background independent approaches to quantum field theories. In the case of gravity and gauge theories, the full kernel of the Hamiltonian operator, which would eventually form the physical Hilbert space, is yet unknown This translates into several obstacles in the investigation and understanding of the quantum dynamics as well as the extraction of physical predictions from the theory. The physical Hamiltonian operator generates evolution with respect to a matter clock, and the question of solving the constraint equation is entirely avoided It remains that any physical prediction in a deparametrized theory relies on the choice of interesting physical states. The subject of this article is the introduction of new coherent states for polymer quantum theories of connections with compact internal gauge group, which include gravity and Yang-Mills fields We call these new states graph coherent states, as they exhibit a certain compatibility with a particular graph change, and they take the form of a superposition of basis states with different graphs.
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