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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| منشور في: |
2024
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| الملخص: | <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> |
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