Quaternion Electromagnetism and the Relation with Two-Spinor Formalism
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/5/6/135 |
| _version_ | 1811263152623452160 |
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| author | In Ki Hong Choong Sun Kim |
| author_facet | In Ki Hong Choong Sun Kim |
| author_sort | In Ki Hong |
| collection | DOAJ |
| description | By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary “<i>i</i>” should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotation. |
| first_indexed | 2024-04-12T19:40:50Z |
| format | Article |
| id | doaj.art-5ed3e29cd6c94eed9829fad96afd1348 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-12T19:40:50Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-5ed3e29cd6c94eed9829fad96afd13482022-12-22T03:19:06ZengMDPI AGUniverse2218-19972019-06-015613510.3390/universe5060135universe5060135Quaternion Electromagnetism and the Relation with Two-Spinor FormalismIn Ki Hong0Choong Sun Kim1Department of Phyics and IPAP, Yonsei University, Seoul 03722, KoreaDepartment of Phyics and IPAP, Yonsei University, Seoul 03722, KoreaBy using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary “<i>i</i>” should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotation.https://www.mdpi.com/2218-1997/5/6/135quaternionelectromagnetismrepresentation theoryCayley-Dickson algebraspecial relativitytwistor theory |
| spellingShingle | In Ki Hong Choong Sun Kim Quaternion Electromagnetism and the Relation with Two-Spinor Formalism Universe quaternion electromagnetism representation theory Cayley-Dickson algebra special relativity twistor theory |
| title | Quaternion Electromagnetism and the Relation with Two-Spinor Formalism |
| title_full | Quaternion Electromagnetism and the Relation with Two-Spinor Formalism |
| title_fullStr | Quaternion Electromagnetism and the Relation with Two-Spinor Formalism |
| title_full_unstemmed | Quaternion Electromagnetism and the Relation with Two-Spinor Formalism |
| title_short | Quaternion Electromagnetism and the Relation with Two-Spinor Formalism |
| title_sort | quaternion electromagnetism and the relation with two spinor formalism |
| topic | quaternion electromagnetism representation theory Cayley-Dickson algebra special relativity twistor theory |
| url | https://www.mdpi.com/2218-1997/5/6/135 |
| work_keys_str_mv | AT inkihong quaternionelectromagnetismandtherelationwithtwospinorformalism AT choongsunkim quaternionelectromagnetismandtherelationwithtwospinorformalism |