Stueckelberg and Higgs Mechanisms: Frames and Scales
We consider Yang–Mills theory with a compact gauge group <i>G</i> on Minkowski space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi>...
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MDPI AG
2022-06-01
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| Online Access: | https://www.mdpi.com/2218-1997/8/7/361 |
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| author | Alexander D. Popov |
| author_facet | Alexander D. Popov |
| author_sort | Alexander D. Popov |
| collection | DOAJ |
| description | We consider Yang–Mills theory with a compact gauge group <i>G</i> on Minkowski space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> and compare the introduction of masses of gauge bosons using the Stueckelberg and Higgs mechanisms. The Stueckelberg field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> is identified with a <i>G</i>-frame on the gauge vector bundle <i>E</i> and the kinetic term for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> leads to the mass of the gauge bosons. The Stueckelberg mechanism is extended to the Higgs mechanism by adding to the game a scalar field describing rescaling of metric on fibres of <i>E</i>. Thus, we associate Higgs fields as well as running coupling parameters with conformal geometry on fibres of gauge bundles. In particular, a running coupling tending to zero or to infinity is equivalent to an unbounded expansion of <i>G</i>-fibres or its contraction to a point. We also discuss scale connection, space-time dependent Higgs vacua and compactly supported gauge and quark fields as an attribute of confinement. |
| first_indexed | 2024-03-09T05:45:10Z |
| format | Article |
| id | doaj.art-825185d1360c49b6b7d69a25110fd5f8 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T05:45:10Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-825185d1360c49b6b7d69a25110fd5f82023-12-03T12:21:46ZengMDPI AGUniverse2218-19972022-06-018736110.3390/universe8070361Stueckelberg and Higgs Mechanisms: Frames and ScalesAlexander D. Popov0Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, GermanyWe consider Yang–Mills theory with a compact gauge group <i>G</i> on Minkowski space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> and compare the introduction of masses of gauge bosons using the Stueckelberg and Higgs mechanisms. The Stueckelberg field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> is identified with a <i>G</i>-frame on the gauge vector bundle <i>E</i> and the kinetic term for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> leads to the mass of the gauge bosons. The Stueckelberg mechanism is extended to the Higgs mechanism by adding to the game a scalar field describing rescaling of metric on fibres of <i>E</i>. Thus, we associate Higgs fields as well as running coupling parameters with conformal geometry on fibres of gauge bundles. In particular, a running coupling tending to zero or to infinity is equivalent to an unbounded expansion of <i>G</i>-fibres or its contraction to a point. We also discuss scale connection, space-time dependent Higgs vacua and compactly supported gauge and quark fields as an attribute of confinement.https://www.mdpi.com/2218-1997/8/7/361gauge theoriesHiggs mechanismStandard Modelconfinement |
| spellingShingle | Alexander D. Popov Stueckelberg and Higgs Mechanisms: Frames and Scales Universe gauge theories Higgs mechanism Standard Model confinement |
| title | Stueckelberg and Higgs Mechanisms: Frames and Scales |
| title_full | Stueckelberg and Higgs Mechanisms: Frames and Scales |
| title_fullStr | Stueckelberg and Higgs Mechanisms: Frames and Scales |
| title_full_unstemmed | Stueckelberg and Higgs Mechanisms: Frames and Scales |
| title_short | Stueckelberg and Higgs Mechanisms: Frames and Scales |
| title_sort | stueckelberg and higgs mechanisms frames and scales |
| topic | gauge theories Higgs mechanism Standard Model confinement |
| url | https://www.mdpi.com/2218-1997/8/7/361 |
| work_keys_str_mv | AT alexanderdpopov stueckelbergandhiggsmechanismsframesandscales |