What if ϕ4 theory in 4 dimensions is non-trivial in the continuum?
Traditionally, scalar ϕ4 theory in four dimensions is thought to be quantum trivial in the continuum. This tradition is apparently well grounded both in physics arguments and mathematical proofs. Digging into the proofs one finds that they do not actually cover all physically meaningful situations,...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269323006044 |
| _version_ | 1797454342425411584 |
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| author | Paul Romatschke |
| author_facet | Paul Romatschke |
| author_sort | Paul Romatschke |
| collection | DOAJ |
| description | Traditionally, scalar ϕ4 theory in four dimensions is thought to be quantum trivial in the continuum. This tradition is apparently well grounded both in physics arguments and mathematical proofs. Digging into the proofs one finds that they do not actually cover all physically meaningful situations, in particular the case of multi-component fields and non-polynomial action. In this work, I study multi-component scalar field theories in four dimensions in the continuum and show that they do evade the apparently foregone conclusion of triviality. Instead, one finds a non-trivial interacting theory that has two phases, bound states and non-trivial scattering amplitudes in the limit of many components. This has potentially broad implications, both for the foundations of quantum field theory as well as for the experimentally accessible Higgs sector of the Standard Model. |
| first_indexed | 2024-03-09T15:35:54Z |
| format | Article |
| id | doaj.art-4999f8368aaa49f8914708af58d083c4 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-03-09T15:35:54Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-4999f8368aaa49f8914708af58d083c42023-11-26T05:11:22ZengElsevierPhysics Letters B0370-26932023-12-01847138270What if ϕ4 theory in 4 dimensions is non-trivial in the continuum?Paul Romatschke0Department of Physics, University of Colorado, Boulder, CO 80309, USA; Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA; Correspondence to: Department of Physics, University of Colorado, Boulder, CO 80309, USA.Traditionally, scalar ϕ4 theory in four dimensions is thought to be quantum trivial in the continuum. This tradition is apparently well grounded both in physics arguments and mathematical proofs. Digging into the proofs one finds that they do not actually cover all physically meaningful situations, in particular the case of multi-component fields and non-polynomial action. In this work, I study multi-component scalar field theories in four dimensions in the continuum and show that they do evade the apparently foregone conclusion of triviality. Instead, one finds a non-trivial interacting theory that has two phases, bound states and non-trivial scattering amplitudes in the limit of many components. This has potentially broad implications, both for the foundations of quantum field theory as well as for the experimentally accessible Higgs sector of the Standard Model.http://www.sciencedirect.com/science/article/pii/S0370269323006044 |
| spellingShingle | Paul Romatschke What if ϕ4 theory in 4 dimensions is non-trivial in the continuum? Physics Letters B |
| title | What if ϕ4 theory in 4 dimensions is non-trivial in the continuum? |
| title_full | What if ϕ4 theory in 4 dimensions is non-trivial in the continuum? |
| title_fullStr | What if ϕ4 theory in 4 dimensions is non-trivial in the continuum? |
| title_full_unstemmed | What if ϕ4 theory in 4 dimensions is non-trivial in the continuum? |
| title_short | What if ϕ4 theory in 4 dimensions is non-trivial in the continuum? |
| title_sort | what if ϕ4 theory in 4 dimensions is non trivial in the continuum |
| url | http://www.sciencedirect.com/science/article/pii/S0370269323006044 |
| work_keys_str_mv | AT paulromatschke whatifph4theoryin4dimensionsisnontrivialinthecontinuum |