Renormalization group and effective potential: a simple non-perturbative approach
We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self...
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| Format: | Article |
| Language: | English |
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SciPost
2022-09-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.5.3.044 |
| _version_ | 1818017283847487488 |
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| author | Jose Gaite |
| author_facet | Jose Gaite |
| author_sort | Jose Gaite |
| collection | DOAJ |
| description | We develop a simple non-perturbative approach to the calculation of a field
theory effective potential that is based on the Wilson or exact renormalization
group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)]
of converting the exact renormalization group into a self-consistent
renormalization method. It yields a simple second order differential equation
for the effective potential. The equation can be solved and its solution is
compared with other non-perturbative results and with results of perturbation
theory. In three dimensions, we are led to study the sextic field theory
($\lambda\phi^4+g\phi^6$). We work out this theory at two-loop perturbative
order and find the non-perturbative approach to be superior. |
| first_indexed | 2024-04-14T07:24:10Z |
| format | Article |
| id | doaj.art-0cca93deac104c5abb3abdde51277cc4 |
| institution | Directory Open Access Journal |
| issn | 2666-9366 |
| language | English |
| last_indexed | 2024-04-14T07:24:10Z |
| publishDate | 2022-09-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj.art-0cca93deac104c5abb3abdde51277cc42022-12-22T02:06:03ZengSciPostSciPost Physics Core2666-93662022-09-015304410.21468/SciPostPhysCore.5.3.044Renormalization group and effective potential: a simple non-perturbative approachJose GaiteWe develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple second order differential equation for the effective potential. The equation can be solved and its solution is compared with other non-perturbative results and with results of perturbation theory. In three dimensions, we are led to study the sextic field theory ($\lambda\phi^4+g\phi^6$). We work out this theory at two-loop perturbative order and find the non-perturbative approach to be superior.https://scipost.org/SciPostPhysCore.5.3.044 |
| spellingShingle | Jose Gaite Renormalization group and effective potential: a simple non-perturbative approach SciPost Physics Core |
| title | Renormalization group and effective potential: a simple non-perturbative approach |
| title_full | Renormalization group and effective potential: a simple non-perturbative approach |
| title_fullStr | Renormalization group and effective potential: a simple non-perturbative approach |
| title_full_unstemmed | Renormalization group and effective potential: a simple non-perturbative approach |
| title_short | Renormalization group and effective potential: a simple non-perturbative approach |
| title_sort | renormalization group and effective potential a simple non perturbative approach |
| url | https://scipost.org/SciPostPhysCore.5.3.044 |
| work_keys_str_mv | AT josegaite renormalizationgroupandeffectivepotentialasimplenonperturbativeapproach |