Spacetime Foliation In Quantum Gravity Springer Theses Yuki Sato by Yuki Sato instant download after payment.

It has been one of the outstanding problems in theoretical physics to formulate a quantum theory of gravity. A naive quantization had been made of Einstein's theory of gravity, which is well established as a classical theory of gravity with space-time regarded as a dynamical object. However, this procedure turns out to lead to mathematical inconsistency, because the Einstein' s theory is not renormalizable.
This may imply that for a proper formulation of quantum gravity, we need a new ingredient that is missing in our current understanding of the physical laws. As an example, it is often argued that string theory is one of the most
promising candidates of a quantum gravity. In string theory, the most fundamental degree of freedom in nature is regarded as a string rather than a point-particle.
Furthermore, a lattice quantum gravity has been studied intensively so far. In this framework, a continuous space-time is approximated with a discretized manifold that is composed of a number of simplices. Dynamical triangulation (DT) is formulated by replacing a path integral over continuous space-times with a sum over
all the way of the discretizations. It is found that DT succeeds in defining quantum gravity in lower dimensions but results in pathologies in realistic four-dimensional quantum gravity. In order to resolve this problem, causal dynamical triangulation (CDT) proposes to incorporate space-time causality into DT. The configurations to be summed over in CDT are restricted by requiring them to be consistent with causality. It is then expected to obtain a consistent quantum gravity in fourdimensional space-time.