Stochastic quantization associated with the exp(Φ)₂-quantum field model driven by space-time white noise on the torus in the full L¹-regime

1. Albeverio, S., De Vecchi, F.C., Gubinelli, M.: The elliptic stochastic quantization of some two dimen- sional Euclidean QFTs. Ann. Inst. H. Poincaré Probab. Stat. 57, 2372–2414 (2021)

2. Albeverio, S., Høegh-Krohn, R.: Uniqueness of the physical vacuum and the Wightman functions in the infinite volume limit for some non-polynomial interactions. Commun. Math. Phys. 30, 171–200 (1973)

3. Albeverio, S., Høegh-Krohn, R.: The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time. J. Funct. Anal. 16, 39–82 (1974)

4. Albeverio, S., Høegh-Krohn, R.: Uniqueness of the global Markov property for Euclidean fields. The case of trigonometric interactions. Commun. Math. Phys. 68, 95–128 (1979)

5. Albeverio, S., Kawabi, H., Mihalache, S.-R., Röckner, M.: Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) (to appear). https://doi.org/10.2422/2036-2145. 202105_106. Original version: arXiv:2004.12383

6. Albeverio, S., Kusuoka, S.: The invariant measure and the flow associated to the Ф4-quantum field model. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 20, 1359–1427 (2020)

7. Albeverio, S., Ma, Z.-M., Röckner, M.: Quasi regular Dirichlet forms and the stochastic quantization problem. In: Festschrift Masatoshi Fukushima, Interdiscip. Math. Sci. World Scientific Publishing, Hackensack, vol. 17, pp. 27–58 (2015)

8. Albeverio, S., Röckner, M.: Classical Dirichlet forms on topological vector spaces—closability and a Cameron-Martin formula. J. Funct. Anal. 88, 395–436 (1990)

9. Albeverio, S., Röckner, M.: Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms. Probab. Theory Relat. Fields 89, 347–386 (1991)

10. Bahouri, H., Chemin, J.-Y., Danchin, R.: Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 343. Springer, Heidelberg (2011)

11. Benfatto, G., Gallavotti, G., Nicoló, F.: On the massive sine-Gordon equation in the first few regions of collapse. Commun. Math. Phys. 83, 387–410 (1982)

12. Berestycki, N.: An elementary approach to Gaussian multiplicative chaos. Electron. Commun. Probab. 22(27), 1–12 (2017)

13. Berestycki, N., Powell, E.: Gaussian free field, Liouville quantum gravity and Gaussian multiplica- tive chaos, Lecture Note (2021). Available at the author’s webpage (https://homepage.univie.ac.at/ nathanael.berestycki/Articles/master.pdf)

14. Biskup, M.: Extrema of the two-dimensional discrete Gaussian free field. In: Random Graphs, Phase Transitions, and the Gaussian Free Field. Springer Proc. Math. Stat. Springer, vol. 304, pp. 163–407 (2020)

15. Chandra, A., Hairer, M., Shen, H.: The dynamical sine-Gordon model in the full subcritical regime. Preprint (2018). arXiv:1808.02594

16. Chen, Z.-Q., Fukushima, M.: Symmetric Markov Processes, Time change, and Boundary Theory, London Mathematical Society Monographs Series, vol. 35. Princeton University Press, Princeton (2012)

17. Da Prato, G., Debussche, A.: Strong solutions to the stochastic quantization equations. Ann. Probab. 31, 1900–1916 (2003)

18. Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (1992)

19. Da Prato, G., Zabczyk, J.: Ergodicity for infinite-dimensional systems, London Mathematical Society Lecture Note Series, vol. 229. Cambridge University Press, Cambridge (1996)

20. Dimock, J., Hurd, T.R.: Construction of the two-dimensional sine-Gordon model for β<8π . Commun. Math. Phys. 156, 547–580 (1993)

21. Dubédat, J., Shen, H.: Stochastic Ricci flow on compact surfaces. Int. Math. Res. Not. (to appear). https://doi.org/10.1093/imrn/rnab015. Original version: arXiv:1904.10909

22. Duplantier, B., Sheffield, S.: Liouville quantum gravity and KPZ. Invent. Math. 185, 333–393 (2011)

23. Fröhlich, J.: Classical and quantum statistical mechanics in one and two dimensions: two-component Yukawa- and Coulomb systems. Commun. Math. Phys. 47, 233–268 (1976)

24. Fröhlich, J., Park, Y.M.: Remarks on exponential interactions and the quantum sine-Gordon equation in two space–time dimensions. Helv. Phys. Acta 50, 315–329 (1977)

25. Fröhlich, J., Seiler, E.: The massive Thirring–Schwinger model (QED2): convergence of perturbation theory and particle structure. Helv. Phys. Acta 49, 889–924 (1976)

26. Garban, C.: Dynamical Liouville. J. Funct. Anal. 278(108351), 1–54 (2020)

27. Glimm, J., Jaffe, A.: Quantum Physics: A Functional Integral Point of View. Springer, Berlin (1986)

28. Gubinelli, M., Imkeller, P., Perkowski, N.: Paracontrolled distributions and singular PDEs. Forum Math. Pi 3(e6), 1–75 (2015)

29. Hairer, M.: A theory of regularity structures. Invent. Math. 198, 269–504 (2014)

30. Hairer, M., Labbé, C.: The reconstruction theorem in Besov spaces. J. Funct. Anal. 273, 2578–2618 (2017)

31. Hairer, M., Shen, H.: The dynamical Sine-Gordon model. Commun. Math. Phys. 341, 933–989 (2016)

32. Høegh-Krohn, R.: A general class of quantum fields without cut-offs in two space-time dimensions. Commun. Math. Phys. 21, 244–255 (1971)

33. Hoshino, M., Kawabi, H., Kusuoka, S.: Stochastic quantization associated with the exp(Ф)2-quantum field model driven by space-time white noise on the torus. J. Evol. Equ. 21, 339–375 (2021)

34. Junnila, J., Saksman, E.: Uniqueness of critical Gaussian chaos. Electron. J. Probab. 22(11), 1–31 (2017)

35. Kahane, J.-P.: Sur le chaos multiplicatif. Ann. Sci. Math. Québec 9, 105–150 (1985)

36. Kechris, A.-S.: Classical Descriptive Set Theory, Graduate Texts in Mathematics, vol. 156. Springer, New York (1995)

37. Kozono, H., Ogawa, T., Taniuchi, Y.: Navier–Stokes equations in the Besov space near L∞ and BM O. Kyushu J. Math. 57, 303–324 (2003)

38. Kusuoka, S.: Høegh-Krohn’s model of quantum fields and the absolute continuity of measures. In: Ideas and Methods in Quantum and Statistical Physics (Oslo. 1988). Cambridge University Press, Cambridge, pp. 405–424 (1992)

39. Lieb, E.H., Loss, M.: Analysis, Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence, vol. 14 (2001)

40. Ma, Z.-M., Röckner, M.: Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Springer, Berlin, Heidelberg (1992)

41. Mourrat, J.-C., Weber, H.: Global well-posedness of the dynamic Ф4 model in the plane. Ann. Probab. 45, 2398–2476 (2017)

42. Oh, T., Robert, T., Tzvetkov, N., Wang, Y.: Stochastic quantization of Liouville conformal field theory (2020). arXiv:2004.04194

43. Oh, T., Robert, T., Wang, Y.: On the parabolic and hyperbolic Liouville equations. Commun. Math. Phys. 387, 1281–1351 (2021)

44. Ondreját, M.: Uniqueness for stochastic evolution equations in Banach spaces. Dissertaiones Math. (Rozprawy Mat.) 426, 63pp (2004)

45. Rhodes, R., Vargas, V.: Gaussian multiplicative chaos and applications: a review. Probab. Surv. 11, 315–392 (2014)

46. Robert, R., Vargas, V.: Gaussian multiplicative chaos revisited. Ann. Probab. 38, 605–631 (2010)

47. Simon, B.: The P(ф)2 Euclidean (Quantum) Field Theory, Princeton Series in Physics. Princeton University Press, Princeton (1974)

48. Simon, J.: Compact sets in the space L p(0, T B). Ann. Mat. Pura Appl. (4) 146, 65–96 (1987)

49. Triebel, H.: Characterizations of Besov–Hardy–Sobolev spaces: a unified approach. J. Approx. Theory 52, 162–203 (1988)