Home Mathematics Some comments on infinities on quantum field theory: A functional integral approach
Article
Licensed
Unlicensed Requires Authentication

Some comments on infinities on quantum field theory: A functional integral approach

  • Luiz C. L. Botelho EMAIL logo
Published/Copyright: May 5, 2016

Abstract

We analyze on the formalism of probabilities measures-functional integrals on function space the problem of infinities on Euclidean field theories. We also clarify and generalize our previous published studies on the subject.

We would like to thank to Professor D. Pickrell of Mathematics Department of University of Arizona for discussions on P(φ)2 field theories on Riemann surfaces [12].

References

1 L. C. L. Botelho, A simple renormalization scheme in random surface theory, Modern Phys. Lett. B 13 (1999), 6–7, 203–207. 10.1142/S0217984999000270Search in Google Scholar

2 L. C. L. Botelho, Lecture Notes in Applied Differential Equations of Mathematical Physics, World Scientific, Singapore, 2008. 10.1142/6856Search in Google Scholar

3 L. C. L. Botelho, A method of integration for wave equation and some applications to wave physics, Random Oper. Stoch. Equ. 18 (2010), 4, 301–325. 10.1515/rose.2010.017Search in Google Scholar

4 L. C. L. Botelho, Semi-linear diffusion in ℝD and in Hilbert spaces, a Feynman–Wiener path integral study, Random Oper. Stoch. Equ. 19 (2011), 4, 361–386. 10.1515/ROSE.2011.020Search in Google Scholar

5 L. C. L. Botelho, Some comments on rigorous finite-volume Euclidean quantum field path integrals in the analytical regularization scheme, Adv. Math. Phys. 2011 (2011), Article ID 257916. 10.1142/9789813143470_0008Search in Google Scholar

6 L. C. L. Botelho, A note an Feynman Kac path integral representations for scalar wave motions, Random Oper. Stoch. Equ. 21 (2013), 271–292. 10.1142/9789813143470_0010Search in Google Scholar

7 L. C. L. Botelho, Non-linear diffusion and wave damped propagation: Weak solutions and statistical turbulence behavior, J. Adv. Math. Appl. 3 (2014), 1–11. 10.1166/jama.2014.1047Search in Google Scholar

8 L. C. L. Botelho, On the rigorous ergodic theorem for a class of non-linear Klein Gordon wave propagations, Random Oper. Stoch. Equ. 23 (2015), 1, 53–77. 10.1142/9789813143470_0009Search in Google Scholar

9 J. Glimm and A. Jaffe, Quantum Physics, 2nd ed., Springer, New York, 1987. 10.1007/978-1-4612-4728-9Search in Google Scholar

10 M. R. Green, J. L. Schwarz and E. Witten, Superstring Theory, Cambridge Monogr. Math. Phys. 182, Cambridge University Press, Cambridge, 1996. Search in Google Scholar

11 B. Klaiber, Quantum theory and statistical theory, Lectures in Theoretical Physics, Gordon and Breach, New York (1960), 141–176. Search in Google Scholar

12 D. Pickrell, P(φ)2 quantum field theories and Segal's axioms, Commun. Math. Phys. 280 (2008), 403–425. 10.1007/s00220-008-0467-8Search in Google Scholar

13 B. Simon, The P(φ)2 Euclidean (Quantum) Field Theory, Princeton University Press, Princeton, 1974. Search in Google Scholar

Received: 2015-5-6
Accepted: 2015-11-20
Published Online: 2016-5-5
Published in Print: 2016-6-1

© 2016 by De Gruyter

Downloaded on 5.2.2026 from https://www.degruyterbrill.com/document/doi/10.1515/rose-2016-0006/pdf
Scroll to top button