A Representation of the Lorentz Spin Group and Its Application |
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Authors: | Qi Keng Lu Ke Wu |
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Institution: | (1) Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China;(2) School of Mathematical Science, Capital Normal University, Beijing, 100037, P. R. China |
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Abstract: | For an integer m ≥ 4, we define a set of
matrices γ
j
(m), (j = 0, 1, . . . , m − 1) which satisfy
, where (η
jk
(m))0≤j,k≤m−1 is a diagonal matrix, the first diagonal element of which is 1 and the others are −1,
is a
identity matrix with
being the integer part of
. For m = 4 and 5, the representation
of the Lorentz Spin group is known. For m ≥ 6, we prove that
(i) when m = 2n, (n ≥ 3),
is the group generated by the set of matrices
(ii) when m = 2n + 1 (n ≥ 3),
is generated by the set of matrices
Partially supported by Chinese NNSF Projects (10231050/A010109, 10375038, 904030180) and NKBRPC Project (2004CB318000) |
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Keywords: | Lorentz spin group representation Yang-Mills equation |
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