### A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory

Gubinelli M, Hofmanová M (2021)
Communications in Mathematical Physics 384(1): 1-75.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Gubinelli, Massimiliano; Hofmanová, MartinaUniBi
Einrichtung
Abstract / Bemerkung
We present a new construction of the Euclidean Phi(4) quantum field theory on R-3 based on PDE arguments. More precisely, we consider an approximation of the stochastic quantization equation on R-3 defined on a periodic lattice of mesh size epsilon and side length M. We introduce a new renormalized energy method in weighted spaces and prove tightness of the corresponding Gibbs measures as epsilon -> 0, M -> infinity. Every limit point is non-Gaussian and satisfies reflection positivity, translation invariance and stretched exponential integrability. These properties allow to verify the Osterwalder-Schrader axioms for a Euclidean QFT apart from rotation invariance and clustering. Our argument applies to arbitrary positive coupling constant, to multicomponent models with O(N) symmetry and to some long-range variants. Moreover, we establish an integration by parts formula leading to the hierarchy of Dyson-Schwinger equations for the Euclidean correlation functions. To this end, we identify the renormalized cubic term as a distribution on the space of Euclidean fields.
Erscheinungsjahr
2021
Zeitschriftentitel
Communications in Mathematical Physics
Band
384
Ausgabe
1
Seite(n)
1-75
ISSN
0010-3616
eISSN
1432-0916
Page URI
https://pub.uni-bielefeld.de/record/2955117

### Zitieren

Gubinelli M, Hofmanová M. A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory. Communications in Mathematical Physics. 2021;384(1):1-75.
Gubinelli, M., & Hofmanová, M. (2021). A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory. Communications in Mathematical Physics, 384(1), 1-75. https://doi.org/10.1007/s00220-021-04022-0
Gubinelli, M., and Hofmanová, M. (2021). A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory. Communications in Mathematical Physics 384, 1-75.
Gubinelli, M., & Hofmanová, M., 2021. A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory. Communications in Mathematical Physics, 384(1), p 1-75.
M. Gubinelli and M. Hofmanová, “A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory”, Communications in Mathematical Physics, vol. 384, 2021, pp. 1-75.
Gubinelli, M., Hofmanová, M.: A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory. Communications in Mathematical Physics. 384, 1-75 (2021).
Gubinelli, Massimiliano, and Hofmanová, Martina. “A PDE Construction of the Euclidean Phi(4)(3) Quantum Field Theory”. Communications in Mathematical Physics 384.1 (2021): 1-75.

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