Introduction and comments: Quantum field theory and space-time (Q2724958)

From the comments: If some more-or-less direct generalization of conventional quantum-field-theoretical quantization schemes is going to work, I believe it will be based on the connection approach. On the other hand, I share Bryce's unease with the heavy emphasis on the canonical approach, with its inherent three-plus-one breakup of space-time, which has so far also characterized the Ashtekar approach. One would hope that a more intrinsically four-dimensional variant of that approach could be found, but still based on the connection. I have been more-and-more impressed by the profundity and power of the path integral approach to non-relativistic quantum mechanics, with its inherently space-time viewpoint. I would hope that ultimately some way of extending Ashtekar's emphasis on the three-connection and triad variables to the four-connection and tetrads could be found by combining it with the path integral approach to quantization. Meanwhile, one can only applaud and admire the new insights that those working on the Ashtekar program are bringing to the many problems of quantum gravity.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00052].