Quantum field theory of spin networks (Q2752492)

Quantum Field Theory (QFT) is a very rich area, which is much researched during the past few decades. Here the author has studied in detail the various aspects of transition amplitudes in the state-sum models of quantum gravity in \(D=2-4\) spacetime dimensions by using the field theory over the \(G^D\)-formulation, \(G\) being the relevant Lie group.NEWLINENEWLINENEWLINEThe introduction is followed by \(D=2\) model, partition function, transition amplitudes and spin networks, time variables, \(D=3\) model, \(D=4\) model and considerations of the BC-field theory. Simplicial Field Theory for discretized gravity approach is applied all along.NEWLINENEWLINENEWLINEThe paper exhibits a good demonstration of the significant advantage if one completes the Feynman diagram picture of transition amplitudes for the state-sum models of quantum gravity. Suitable Fourier mode operators and the corresponding Fock Space are made use of.NEWLINENEWLINENEWLINEIndeed, to arrive at a complete theory, we need to work further on a simplicial field theory formulation of matter coupled to gravity in full.