Abstract
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” 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.
| Original language | English |
|---|---|
| Article number | 135 |
| Journal | Universe |
| Volume | 5 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2019 Jun |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
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Quaternion electromagnetism and the relation with two-spinor formalism. / Hong, In Ki; Kim, Choong Sun.
In: Universe, Vol. 5, No. 6, 135, 06.2019.Research output: Contribution to journal › Article
TY - JOUR
T1 - Quaternion electromagnetism and the relation with two-spinor formalism
AU - Hong, In Ki
AU - Kim, Choong Sun
PY - 2019/6
Y1 - 2019/6
N2 - 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” 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.
AB - 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” 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.
UR - http://www.scopus.com/inward/record.url?scp=85067651801&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85067651801&partnerID=8YFLogxK
U2 - 10.3390/universe5060135
DO - 10.3390/universe5060135
M3 - Article
AN - SCOPUS:85067651801
VL - 5
JO - Universe
JF - Universe
SN - 2218-1997
IS - 6
M1 - 135
ER -