So this is something that's been bothering me for awhile and I seem to be getting no closer to understanding it on my own. I want to quote two things here; one, an Aaron Bergman post about String Theory at Uncertain Principles; two, Rovelli's LQG textbook, "Quantum Gravity". http://scienceblogs.com/principles/2007/08/what_is_string_theory.php In short, Bergman is saying something that I've seen said elsewhere as well: String theory is really just peturbation theory with 2-D worldsheets instead of 1-D worldlines. In fact as I understand things, if you use worldsheets, you're automatically doing string theory-- if you start with the idea of 2-D worldsheets you can derive string theory backward from the worldsheets. Meanwhile, this is Rovelli on LQG, page 26: So, assuming I understand these two quotes correctly, I can summarize them as: String theory can be peturbatively described by taking the worldline formalism and generalizing it to the next dimension up; in this case the worldsheets form a two-dimensional surface, and the classical action is described by the surface area of the sheet. LQG can be peturbatively described by taking the Feynman Diagram formalism and generalizing it to the next dimension up; in this case the diagram graphs form a web of two-dimensional graph faces, and the graph faces give quantum amplitudes. This seems deeply weird to me. Looking at what are as far as I'm aware two essentially conceptually opposite approaches to quantum gravity based on two very different underlying mathematical objects (strings and spinnets), they both seem to be doing something extremely similar if not identical when it comes down to their strategy for peturbative calculations: they seem, from the descriptions I see, to be taking the Feynman path integral technique and generalizing the mathematical structures by one dimension. However what I'm not sure about is whether these two things really are all that similar, or if they just seem similar to me because I am not informed enough about quantum theory to understand the differences between them. What do I make of this? i feel like I must be misunderstanding something somewhere. I'm wondering if anyone who's more familiar with these issues could help me understand: - Do I correctly understand what string theory and lqg are doing with their respective "peturbative theory + 1 dimension" things? - I'm assuming that generalizing the worldline and generalizing on Feynman diagrams are analagous operations. Although I can find in many places vague assertions the worldline and Feynman diagram are somehow mathematically connected to one another, and I know both are used in calculating path integrals, I don't actually understand what the connection between these two things is. Are these indeed related structures? - I'm assuming that producing the classical action is somehow relatable to producing the quantum amplitudes. But I don't in fact really understand how (or even whether) these two things are related, or in what form the classical action survives when you move to a quantum theory. I have some idea that in a classical theory you have an action which is minimized, and the quantum path integral ultimately assigns the greatest amplitudes to the paths where the classical action is minimized, but I'm not sure what that says about how action and amplitude are connected. - Assuming I understand correct that when you calculate path integrals in normal quantum theory, worldlines have Feynman diagrams associated with them and vice versa (and it's not just that I'm falsely assuming these structures to be related because both have Feynman's name associated with them...). What would the worldlines or worldline analogues associated with a "2D Feynman diagram" look like? What would the Feynman diagrams or analogues associated with a "2D worldsheet" look like? Is it possible to directly compare the String Theory worldsheets Bergman describes and the LQG spinfoams Rovelli describes in this manner as mathematical structures, if that makes sense, despite their fairly different purposes? - Assuming the answer to all above questions is "yes, the thing LQG is doing with 2D Feynman diagrams and the thing string theory is doing with 2d worldsheets are similar"-- does this even mean anything? Please excuse me if I have garbled any of the concepts above.