A PDE construction of the Euclidean Φ43 quantum field theory
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About this item
| Description: |
Hofmanova, M
Thursday 25th October 2018 - 14:00 to 15:00 |
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| Created: | 2018-10-29 10:32 |
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| Collection: | Scaling limits, rough paths, quantum field theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Hofmanova, M |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | We present a self-contained construction of the Euclidean Φ4 quantum field theory on R3 based on PDE arguments. More precisely, we consider an approximation of the stochastic quantization equation on R3 defined on a periodic lattice of mesh size ε and side length M. We introduce an energy method and prove tightness of the corresponding Gibbs measures as ε→0, M→∞. We show that every limit point satisfies reflection positivity, translation invariance and nontriviality (i.e. non-Gaussianity). Our argument applies to arbitrary positive coupling constant and also to multicomponent models with O(N) symmetry. Joint work with Massimiliano Gubinelli. |
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