3 ms·
Peter woit recently wrote on this topic in 'The Trouble With Path Integrals': - https://www.math.columbia.edu/~woit/wordpress/?p=13319 https://www.math.columbi
by lukeplato 4y ago
Peter woit recently wrote on this topic in 'The Trouble With Path Integrals':
- https://www.math.columbia.edu/~woit/wordpress/?p=13319 https://www.math.columbia.edu/~woit/wordpress/?p=13319
- https://www.math.columbia.edu/~woit/wordpress/?p=13367 https://www.math.columbia.edu/~woit/wordpress/?p=13367
- wyager 4y agoIt seems like Woit is kind of intending this to serve as a refutation of PIF, but I don't really see why - this sounds more like a description of some problems that are hard in PIF, rather than anything wrong with the underlying theory.
- consilient 4y agoAs an organizational scheme for approximate numerical calculations, the path-integral formulation is fine. But path integrals can't serve as a rigorous foundation for QFTs, because for the most part they don't actually exist. The high-frequency behavior Woit describes is one obstacle; the fact that no infinite-dimensional Lebesgue measure is possible is another. There are others. Presumably there's some mathematical object out there that captures all the data a path integral ought to have without its pathologies, but no one knows what it is yet.