Transcript Слайд 1 - The Actual Problems of Microworld Physics

BELARUSIAN
STATE
UNIVERSITY
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
The Actual Problems of Microworld Physics
Gomel, July 27- August 7
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
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.
Some definitions
QFT model
Perturbation theory (1)
Perturbation theory (2)
Questions
1) Is
2)
the “adiabatic switch off of the interaction” necessary?
Basics of the operator method (OM)
Basics of OM (2)
Simple example of OM
Uniformly available approximatiom
OM applications
OM for QFT model
Choice of the trial state vector (1)
Choice of the trial state vector (2)
Zero order approximation
Weak coupling limit (1)
Weak coupling limit (2)
Second order iteration (1)
Second order iteration (2)
Second order iteration (3)
Second order iteration (4)
Conclusions
The calculation details can be found in:
http://arxiv.org/abs/1506.07025
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