Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory

<p dir="ltr">The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even for the simplest case of 1 + 1 dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong coupling parameters to each ot...

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Main Author: Abouzeid M. Shalaby (16810695) (author)
Published: 2024
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author Abouzeid M. Shalaby (16810695)
author_facet Abouzeid M. Shalaby (16810695)
author_role author
dc.creator.none.fl_str_mv Abouzeid M. Shalaby (16810695)
dc.date.none.fl_str_mv 2024-09-12T15:00:00Z
dc.identifier.none.fl_str_mv 10.1016/j.aop.2024.169786
dc.relation.none.fl_str_mv https://figshare.com/articles/journal_contribution/Toward_Exact_Critical_Exponents_from_the_low-order_loop_expansion_of_the_Effective_Potential_in_Quantum_Field_Theory/30024055
dc.rights.none.fl_str_mv CC BY 4.0
info:eu-repo/semantics/openAccess
dc.subject.none.fl_str_mv Mathematical sciences
Mathematical physics
Physical sciences
Quantum physics
Exact critical exponent
Effective potential
Strong-coupling expansion
dc.title.none.fl_str_mv Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
dc.type.none.fl_str_mv Text
Journal contribution
info:eu-repo/semantics/publishedVersion
text
contribution to journal
description <p dir="ltr">The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even for the simplest case of 1 + 1 dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong coupling parameters to each other. He used a variational technique ( back to kleinert and Feynman) to extract accurate values for the strong coupling parameters from which he was able to extract precise critical exponents. In this work, we suggest a simple method of using the effective potential ( low order) to obtain exact values for the strong-coupling parameters for the ϕ<sup>4</sup> scalar field theory in 0 + 1 and 1 + 1 space–time dimensions. For the 0 + 1 case, our results coincide with the well-known exact values already known from literature while for the 1 + 1 case we test the results by obtaining the corresponding exact critical exponent. As the effective potential is a well-established tool in <u>quantum field theory</u>, we expect that the results can be easily extended to the most important three dimensional case and then the dream of getting exact critical exponents is made possible.</p><h2>Other Information</h2><p dir="ltr">Published in: Annals of Physics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.aop.2024.169786" target="_blank">https://dx.doi.org/10.1016/j.aop.2024.169786</a></p>
eu_rights_str_mv openAccess
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identifier_str_mv 10.1016/j.aop.2024.169786
network_acronym_str Manara2
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oai_identifier_str oai:figshare.com:article/30024055
publishDate 2024
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rights_invalid_str_mv CC BY 4.0
spelling Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field TheoryAbouzeid M. Shalaby (16810695)Mathematical sciencesMathematical physicsPhysical sciencesQuantum physicsExact critical exponentEffective potentialStrong-coupling expansion<p dir="ltr">The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even for the simplest case of 1 + 1 dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong coupling parameters to each other. He used a variational technique ( back to kleinert and Feynman) to extract accurate values for the strong coupling parameters from which he was able to extract precise critical exponents. In this work, we suggest a simple method of using the effective potential ( low order) to obtain exact values for the strong-coupling parameters for the ϕ<sup>4</sup> scalar field theory in 0 + 1 and 1 + 1 space–time dimensions. For the 0 + 1 case, our results coincide with the well-known exact values already known from literature while for the 1 + 1 case we test the results by obtaining the corresponding exact critical exponent. As the effective potential is a well-established tool in <u>quantum field theory</u>, we expect that the results can be easily extended to the most important three dimensional case and then the dream of getting exact critical exponents is made possible.</p><h2>Other Information</h2><p dir="ltr">Published in: Annals of Physics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.aop.2024.169786" target="_blank">https://dx.doi.org/10.1016/j.aop.2024.169786</a></p>2024-09-12T15:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1016/j.aop.2024.169786https://figshare.com/articles/journal_contribution/Toward_Exact_Critical_Exponents_from_the_low-order_loop_expansion_of_the_Effective_Potential_in_Quantum_Field_Theory/30024055CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/300240552024-09-12T15:00:00Z
spellingShingle Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
Abouzeid M. Shalaby (16810695)
Mathematical sciences
Mathematical physics
Physical sciences
Quantum physics
Exact critical exponent
Effective potential
Strong-coupling expansion
status_str publishedVersion
title Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
title_full Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
title_fullStr Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
title_full_unstemmed Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
title_short Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
title_sort Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory
topic Mathematical sciences
Mathematical physics
Physical sciences
Quantum physics
Exact critical exponent
Effective potential
Strong-coupling expansion