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As I understand, it is postulated that only coherent states in LQG correspond to classical spacetimes. Is the ground state of LQG a coherent state? Otherwise, what principle selects that the universe should be in a coherent state?
Demystifier said:Perhaps one should use an analogy with quantum optics, where coherent states emerge dinamically. It turns out that coherent states are, under certain conditions, stable with respect to decoherence caused by interactions with the environment. In quantum gravity, the role of environment could be played by matter.
The ground state in LQG refers to the lowest energy state of the quantum system, also known as the vacuum state. In Loop Quantum Gravity (LQG), this is a discrete state of the gravitational field, which is described by a network of intersecting loops.
A coherent state in LQG is a quantum state that describes a superposition of many loop states, and is often considered to be a semiclassical state. It is characterized by having a well-defined classical geometry, and is used to describe the gravitational field in LQG.
In LQG, the ground state is considered to be a coherent state, as it represents the lowest energy state of the quantum system. However, it is important to note that the ground state is not a unique coherent state, as there are many different coherent states that can describe the same gravitational field in LQG.
The ground state in LQG is determined through a process called state-sum construction, which involves summing over all possible states of the gravitational field. This includes both loop states and coherent states. The ground state is then identified as the state with the lowest energy in this sum.
The ground state in LQG is significant because it represents the lowest energy state of the gravitational field, and is used as a starting point for calculating other physical quantities in LQG. It also plays a crucial role in understanding the quantum nature of the gravitational field and its relation to classical geometry.