$$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operators
Abstract We demonstrate a model which captures certain attractive features of SU(5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras $$\mathbb {R}$$ R , $$\mathbb {C}$$ C , $$\mathbb {H}$$ H , and $$\mathbb {O}$$...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-05-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-018-5844-7 |
| _version_ | 1818021793560002560 |
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| author | C. Furey |
| author_facet | C. Furey |
| author_sort | C. Furey |
| collection | DOAJ |
| description | Abstract We demonstrate a model which captures certain attractive features of SU(5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras $$\mathbb {R}$$ R , $$\mathbb {C}$$ C , $$\mathbb {H}$$ H , and $$\mathbb {O}$$ O . From the SU(n) symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow’s SU(5) grand unified theory. However, in this case, the transitions leading to proton decay are expected to be blocked, given that they coincide with presumably forbidden transformations which would incorrectly mix distinct algebraic actions. As a result, we find that we are left with $$G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$ Gsm=SU(3)C×SU(2)L×U(1)Y/Z6 . Finally, we point out that if U(n) ladder symmetries are used in place of SU(n), it may then be possible to find this same $$G_{sm}=SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$ Gsm=SU(3)C×SU(2)L×U(1)Y/Z6 , together with an extra $$U(1)_X$$ U(1)X symmetry, related to $$B\!-\!L$$ B-L . |
| first_indexed | 2024-04-14T08:22:41Z |
| format | Article |
| id | doaj.art-fe98db93b42345b19b9570fee9eed668 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-04-14T08:22:41Z |
| publishDate | 2018-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-fe98db93b42345b19b9570fee9eed6682022-12-22T02:04:10ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522018-05-0178511210.1140/epjc/s10052-018-5844-7$$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operatorsC. Furey0Department of Applied Mathematics and Theoretical Physics, University of CambridgeAbstract We demonstrate a model which captures certain attractive features of SU(5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras $$\mathbb {R}$$ R , $$\mathbb {C}$$ C , $$\mathbb {H}$$ H , and $$\mathbb {O}$$ O . From the SU(n) symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow’s SU(5) grand unified theory. However, in this case, the transitions leading to proton decay are expected to be blocked, given that they coincide with presumably forbidden transformations which would incorrectly mix distinct algebraic actions. As a result, we find that we are left with $$G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$ Gsm=SU(3)C×SU(2)L×U(1)Y/Z6 . Finally, we point out that if U(n) ladder symmetries are used in place of SU(n), it may then be possible to find this same $$G_{sm}=SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$ Gsm=SU(3)C×SU(2)L×U(1)Y/Z6 , together with an extra $$U(1)_X$$ U(1)X symmetry, related to $$B\!-\!L$$ B-L .http://link.springer.com/article/10.1140/epjc/s10052-018-5844-7 |
| spellingShingle | C. Furey $$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operators European Physical Journal C: Particles and Fields |
| title | $$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operators |
| title_full | $$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operators |
| title_fullStr | $$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operators |
| title_full_unstemmed | $$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operators |
| title_short | $$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ SU(3)C×SU(2)L×U(1)Y×U(1)X as a symmetry of division algebraic ladder operators |
| title_sort | su 3 c times su 2 l times u 1 y left times u 1 x right su 3 c su 2 l u 1 y u 1 x as a symmetry of division algebraic ladder operators |
| url | http://link.springer.com/article/10.1140/epjc/s10052-018-5844-7 |
| work_keys_str_mv | AT cfurey su3ctimessu2ltimesu1ylefttimesu1xrightsu3csu2lu1yu1xasasymmetryofdivisionalgebraicladderoperators |