As shown by Epstein and Glaser, the operator valued distribution (OPVD) formalism permits to obtain a non-standard regularization scheme which leads to a divergences-free quantum field theory. The present formulation gives a tool to calculate finite scattering matrix without adding counter-terms. After a short recall about the OPVD formalism in 3+1-dimensions, Gaussian functions and Harmonic Hermite-Gaussian functions are used as test functions. The field resulting from this approach obeys the Klein-Gordon equation. The vacuum fluctuation calculation then gives a result regularized by the Gaussian factor. The example of scalar quantum electrodynamics theory shows that Gaussian functions may be used as test functions in this approach. The result shows that the scale of the theory is described by a factor arising from Heisenberg uncertainties. The Feynman propagators and a study on loop convergence with the example of the tadpole diagram are given. The formulation is extended to Quantum Electrodynamics. Triangle diagrams anomaly are calculated efficiently. In the same approach, using Lagrange formulae to regularize the singular distribution involved in the scattering amplitude gives a good way to avoid infinities. After applying Lagrange formulae, the test function could be reduced to unity since the amplitude is regular. Ward-Takahashi identity is calculated with this method too and this shows that the symmetries of the theory are unbroken.
Published in | International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 4) |
DOI | 10.11648/j.ijamtp.20180404.12 |
Page(s) | 98-104 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2019. Published by Science Publishing Group |
Quantum Electrodynamics, Triangle Anomaly, Ward-Takahashi Identity, Partition of Unity, Operator Valued Distribution, Gaussian Functions, Tadpole Diagram
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APA Style
Hasimbola Damo Emile Randriamisy, Raoelina Andriambololona, Hanitriarivo Rakotoson, Ravo Tokiniaina Ranaivoson, Roland Raboanary. (2019). Gaussian as Test Functions in Operator Valued Distribution Formulation of QED. International Journal of Applied Mathematics and Theoretical Physics, 4(4), 98-104. https://doi.org/10.11648/j.ijamtp.20180404.12
ACS Style
Hasimbola Damo Emile Randriamisy; Raoelina Andriambololona; Hanitriarivo Rakotoson; Ravo Tokiniaina Ranaivoson; Roland Raboanary. Gaussian as Test Functions in Operator Valued Distribution Formulation of QED. Int. J. Appl. Math. Theor. Phys. 2019, 4(4), 98-104. doi: 10.11648/j.ijamtp.20180404.12
AMA Style
Hasimbola Damo Emile Randriamisy, Raoelina Andriambololona, Hanitriarivo Rakotoson, Ravo Tokiniaina Ranaivoson, Roland Raboanary. Gaussian as Test Functions in Operator Valued Distribution Formulation of QED. Int J Appl Math Theor Phys. 2019;4(4):98-104. doi: 10.11648/j.ijamtp.20180404.12
@article{10.11648/j.ijamtp.20180404.12, author = {Hasimbola Damo Emile Randriamisy and Raoelina Andriambololona and Hanitriarivo Rakotoson and Ravo Tokiniaina Ranaivoson and Roland Raboanary}, title = {Gaussian as Test Functions in Operator Valued Distribution Formulation of QED}, journal = {International Journal of Applied Mathematics and Theoretical Physics}, volume = {4}, number = {4}, pages = {98-104}, doi = {10.11648/j.ijamtp.20180404.12}, url = {https://doi.org/10.11648/j.ijamtp.20180404.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180404.12}, abstract = {As shown by Epstein and Glaser, the operator valued distribution (OPVD) formalism permits to obtain a non-standard regularization scheme which leads to a divergences-free quantum field theory. The present formulation gives a tool to calculate finite scattering matrix without adding counter-terms. After a short recall about the OPVD formalism in 3+1-dimensions, Gaussian functions and Harmonic Hermite-Gaussian functions are used as test functions. The field resulting from this approach obeys the Klein-Gordon equation. The vacuum fluctuation calculation then gives a result regularized by the Gaussian factor. The example of scalar quantum electrodynamics theory shows that Gaussian functions may be used as test functions in this approach. The result shows that the scale of the theory is described by a factor arising from Heisenberg uncertainties. The Feynman propagators and a study on loop convergence with the example of the tadpole diagram are given. The formulation is extended to Quantum Electrodynamics. Triangle diagrams anomaly are calculated efficiently. In the same approach, using Lagrange formulae to regularize the singular distribution involved in the scattering amplitude gives a good way to avoid infinities. After applying Lagrange formulae, the test function could be reduced to unity since the amplitude is regular. Ward-Takahashi identity is calculated with this method too and this shows that the symmetries of the theory are unbroken.}, year = {2019} }
TY - JOUR T1 - Gaussian as Test Functions in Operator Valued Distribution Formulation of QED AU - Hasimbola Damo Emile Randriamisy AU - Raoelina Andriambololona AU - Hanitriarivo Rakotoson AU - Ravo Tokiniaina Ranaivoson AU - Roland Raboanary Y1 - 2019/01/25 PY - 2019 N1 - https://doi.org/10.11648/j.ijamtp.20180404.12 DO - 10.11648/j.ijamtp.20180404.12 T2 - International Journal of Applied Mathematics and Theoretical Physics JF - International Journal of Applied Mathematics and Theoretical Physics JO - International Journal of Applied Mathematics and Theoretical Physics SP - 98 EP - 104 PB - Science Publishing Group SN - 2575-5927 UR - https://doi.org/10.11648/j.ijamtp.20180404.12 AB - As shown by Epstein and Glaser, the operator valued distribution (OPVD) formalism permits to obtain a non-standard regularization scheme which leads to a divergences-free quantum field theory. The present formulation gives a tool to calculate finite scattering matrix without adding counter-terms. After a short recall about the OPVD formalism in 3+1-dimensions, Gaussian functions and Harmonic Hermite-Gaussian functions are used as test functions. The field resulting from this approach obeys the Klein-Gordon equation. The vacuum fluctuation calculation then gives a result regularized by the Gaussian factor. The example of scalar quantum electrodynamics theory shows that Gaussian functions may be used as test functions in this approach. The result shows that the scale of the theory is described by a factor arising from Heisenberg uncertainties. The Feynman propagators and a study on loop convergence with the example of the tadpole diagram are given. The formulation is extended to Quantum Electrodynamics. Triangle diagrams anomaly are calculated efficiently. In the same approach, using Lagrange formulae to regularize the singular distribution involved in the scattering amplitude gives a good way to avoid infinities. After applying Lagrange formulae, the test function could be reduced to unity since the amplitude is regular. Ward-Takahashi identity is calculated with this method too and this shows that the symmetries of the theory are unbroken. VL - 4 IS - 4 ER -