Quaternions, 2x2 complex matrices and Lorentz transformations
نویسندگان
چکیده
منابع مشابه
Unimodular Matrices Homomorphic to Lorentz Transformations
deutet und N die oben mit e~lF bezeichnete Größe ist, woraus dann die FREDHOLMsche Lösung der Integralgleichung (15) folgt. Da bei unserem Verfahren derselbe Ausdruck für 5 ( 1 , 1 \ g ) folgt wie bei MATTHEWS und SALAM, so sollte die entsprechende Reihenentwicklung nach Potenzen von g zu der FREDHOLMschen Lösung führen. Dabei müßte eine Identität bestehen zwischen den entsprechenden Koeffizien...
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It is shown that a subgroup of SL(2, H), denoted Spin(2, H) in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally iso-morphic to the restricted Lorentz group, L ↑ +. On the basis of the Dirac theory using the spinor group Spin(2, H), in which the charge conjugation transformation becomes linear in the quaternionic Dirac spinor, it is shown th...
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In these notes we study Lorentz transformations and focus on the group of proper, orthochronous Lorentz transformations, donated by L+. (These Lorentz transformations have determinant one and preserve the direction of time.) The 2×2 matrices with determinant one, denoted SL(2, C), play a key role, as there is a map from SL(2,C) onto L+, that is 2-to-1 and a homomorphism. In this correspondence,...
متن کاملInvolution Matrices of Real Quaternions
An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R.
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ژورنال
عنوان ژورنال: BIBECHANA
سال: 2014
ISSN: 2382-5340,2091-0762
DOI: 10.3126/bibechana.v12i0.11671