1. BELARUSIAN STATE UNIVERSITY The Actual Problems of Microworld Physics Gomel, July 27- August 7 Max Planck Institute for Nuclear Physics Regularization of ultraviolet divergence in a model of a particle interacting with a scalar quantum field O. D. Skoromnik, I. D. Feranchuk, D. V. Lu, C. H. Keitel

2. Motivation “I think that the renormalization theory is simply a way to sweep the difficulties of the divergences of electrodynamics under the rug.” (R. P. Feynman) “However, there is no logical justification for it.” (Renormalization) (P. A. M. Dirac)AIP Conf.Series – NY 1981 V.74 P.129

3. Motivation The key questions are the following: 1)Are the infinite renormalization parameters the intrinsic properties of the concrete model of the quantum field theory (QFT) or this is the result of the nonanalytical properties of the QFT characteristics? 2) Does the calculation method exist which allows one to calculate the QFT characteristics without usage of the phenomenological cut-off momentum. In the report we consider the model QFT with divergence when the conventional perturbation theory (PT) is used. We present the non-perturbative method that allows one the following: 1) to analyze the singularity in the system energy considered as a function of a coupling constant 2) to calculate the energy without usage of the phenomenological cut-off momentum.

4. Some definitions

5. QFT model

6. Perturbation theory (1)

7. Perturbation theory (2)

8. Questions 1) Is the “adiabatic switch off of the interaction” necessary? 2)

9. Basics of the operator method (OM)

10. Basics of OM (2)

11. Simple example of OM

12. Uniformly available approximatiom

13. OM applications

14. OM for QFT model

15. Choice of the trial state vector (1)

16. Choice of the trial state vector (2)

17. Zero order approximation

18. Weak coupling limit (1)

19. Weak coupling limit (2)

20. Second order iteration (1)

21. Second order iteration (2)

22. Second order iteration (3)

23. Second order iteration (4)

24. Conclusions http://arxiv.org/abs/1506.07025 The calculation details can be found in:

25. THANK YOU FOR YOUR ATTENTION !