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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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 |
| id | Manara2_5e285660cb3d0875a73643e50b09c5cf |
| identifier_str_mv | 10.1016/j.aop.2024.169786 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/30024055 |
| publishDate | 2024 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| 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 |