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Physics
Beyond the Standard Models
Theory of Loop Quantum Gravity
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[QUOTE="atyy, post: 6429949, member: 123698"] In older approaches to try to define LQG, there was a problem with writing down a well-defined theory that satisfies the Hamiltonian constraint. These older approaches are called "canonical" LQG, because "canonical" is a term in physics relating to defining theories by a Hamiltonian. A more recent approach is to try to define LQG using spin foams, which is often called "covariant" LQG. There have been proposal to define a theory, but it has been unclear whether these give rise to general relativity as an approximation in the appropriate regime. General relativity is our best current theory of gravity, so LQG must agree with general relativity in the appropriate regime. One example is the flatness problem. General relativity says that spacetime is curved, but some analyses suggested that the EPRL and FK spin foam proposals produce flat spacetime. Here is some recent work trying to clarify the issue. [URL]https://arxiv.org/abs/2011.14468[/URL] Discrete gravity dynamics from effective spin foams Seth K. Asante, Bianca Dittrich, Hal M. Haggard "Using a simple toy model, we will show that for path integrals with weakly imposed second class constraints, the semiclassical limit - ##\bar{h} \rightarrow 0## does not, in general, reproduce the classical dynamics. The flatness problem in spin foams is just one example of this more general issue. A possible way to resolve this issue is to update the definition of the semiclassical limit." [URL]https://arxiv.org/abs/2005.00988[/URL] Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity Muxin Han, Hongguang Liu "Our result proves that the new path integral formulation has the correct semiclassical limit, and indicates that the reduced phase space quantization in LQG is semiclassically consistent. Based on these results, we compare this path integral formulation and the spin foam formulation, and show that this formulation has several advantages including the finiteness, the relation with canonical LQG, and being free of cosine and flatness problems." [/QUOTE]
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Theory of Loop Quantum Gravity
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