Avoiding infinity in Quantum field theory without use of renormalization

Biswaranjan Dikshit¹

Section:Research Paper, Product Type: Isroset-Journal
Vol.7 , Issue.2 , pp.7-11, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrpas/v7i2.711

Online published on Apr 30, 2019

Copyright © Biswaranjan Dikshit . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In quantum field theory (QFT), it is well known that when Feynman diagrams containing loops are evaluated to account for self-interactions, probability amplitude comes out to be infinite which is physically not admissible. So, to make the QFT convergent, various renormalization methods are conventionally followed in which an additional (infinite) counter term is postulated which neutralizes the original infinity generated by diagram. The resulting finite values of amplitudes have agreed with experiments with surprising accuracy. However, proponents of renormalization methods acknowledged that this ad-hoc procedure of subtraction of infinity from infinity to reach at a finite value is not at all satisfactory and there is no physical basis for bringing in the counter term. So, it is desirable to establish a method in QFT which does not generate any infinite term, but which predicts same results as conventional methods do. In this paper, we describe such a technique taking self-interaction quantum electrodynamics diagram representing electron or photon self-energy. In our method, no problem of infinity arises and hence renormalization is not necessary. Still, the dependence of calculated probability amplitude on physical variables in our technique comes out to be same as conventional methods. Using similar procedure, we hope, the problem of non-renormalizability of quantum gravity may be solved in future.

Key-Words / Index Term :
Renormalization, Quantum Field Theory, Electron self energy, Vacuum polarization

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