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Vector Fields, Flows and Lie Groups of Diffeomorphisms
\sigma_{c+t} (x) = \sigma_c (\sigma_t (x)) \equiv \sigma_c \circ evolution equation implies at once the Gell-Mann-Low functional equation. The latter appears therefore as a trivial consequence of the existence of a vector field on the action's space of renormalized QFT.
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| Lenguaje: | eng |
| Publicado: |
1999
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| Acceso en línea: | https://dx.doi.org/10.1007/s100520000375 http://cds.cern.ch/record/412222 |
| _version_ | 1780894666726572032 |
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| author | Peterman, A. |
| author_facet | Peterman, A. |
| author_sort | Peterman, A. |
| collection | CERN |
| description | \sigma_{c+t} (x) = \sigma_c (\sigma_t (x)) \equiv \sigma_c \circ evolution equation implies at once the Gell-Mann-Low functional equation. The latter appears therefore as a trivial consequence of the existence of a vector field on the action's space of renormalized QFT. |
| id | cern-412222 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 1999 |
| record_format | invenio |
| spelling | cern-4122222023-03-14T18:01:10Zdoi:10.1007/s100520000375http://cds.cern.ch/record/412222engPeterman, A.Vector Fields, Flows and Lie Groups of DiffeomorphismsParticle Physics - Theory\sigma_{c+t} (x) = \sigma_c (\sigma_t (x)) \equiv \sigma_c \circ evolution equation implies at once the Gell-Mann-Low functional equation. The latter appears therefore as a trivial consequence of the existence of a vector field on the action's space of renormalized QFT.The freedom in choosing finite renormalizations in quantum field theories (QFT) is characterized by a set of parameters $\{c_i \}, i = 1 ..., n >...$, which specify the renormalization prescriptions used for the calculation of physical quantities. For the sake of simplicity, the case of a single $c$ is selected and chosen mass-independent if masslessness is not realized, this with the aim of expressing the effect of an infinitesimal change in $c$ on the computed observables. This change is found to be expressible in terms of an equation involving a vector field $V$ on the action's space $M$ (coordinates x). This equation is often referred to as ``evolution equation'' in physics. This vector field generates a one-parameter (here $c$) group of diffeomorphisms on $M$. Its flow $\sigma_c (x)$ can indeed be shown to satisfy the functional equation $$ \sigma_{c+t} (x) = \sigma_c (\sigma_t (x)) \equiv \sigma_c \circ \sigma_t $$ $$\sigma_0 (x) = x,$$ so that the very appearance of $V$ in the evolution equation implies at once the Gell-Mann-Low functional equation. The latter appears therefore as a trivial consequence of the existence of a vector field on the action's space of renormalized QFT.hep-th/9912131CERN-TH-99-389CERN-TH-99-389oai:cds.cern.ch:4122221999-12-16 |
| spellingShingle | Particle Physics - Theory Peterman, A. Vector Fields, Flows and Lie Groups of Diffeomorphisms |
| title | Vector Fields, Flows and Lie Groups of Diffeomorphisms |
| title_full | Vector Fields, Flows and Lie Groups of Diffeomorphisms |
| title_fullStr | Vector Fields, Flows and Lie Groups of Diffeomorphisms |
| title_full_unstemmed | Vector Fields, Flows and Lie Groups of Diffeomorphisms |
| title_short | Vector Fields, Flows and Lie Groups of Diffeomorphisms |
| title_sort | vector fields, flows and lie groups of diffeomorphisms |
| topic | Particle Physics - Theory |
| url | https://dx.doi.org/10.1007/s100520000375 http://cds.cern.ch/record/412222 |
| work_keys_str_mv | AT petermana vectorfieldsflowsandliegroupsofdiffeomorphisms |