KMS Of Academy of mathematics and systems sciences, CAS
The Yang-Mills fields on the Minkowski space | |
Lu, QK | |
1998-10-01 | |
Source Publication | SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY |
ISSN | 1006-9283 |
Volume | 41Issue:10Pages:1061-1067 |
Abstract | Let the coordinate x = (x(0), x(1), x(2), x(3)) of the Minkowski space M-4 be arranged into a matrix H-x = ((x0 + x1)(x2 - ix3) (x2 + ix3)(x0 - x1)). Then the Minkowski metric can be written as ds(2) = n(jk)dx(j)dx(k) = det dH(x). Imbed the space of 2 x 2 Hermitian matrices into the complex Grassmann manifold F(2, 2), the space of complex 4-planes passing through the origin of C-2 x 4. The closure (M) over bar(4) of M-4 in F(2, 2)is the compactification of M4. It is known that the conformal group acts on (M) over bar(4). It has already been proved that on F(2, 2) there is an su(2)-connection B(Z , dZ) = Gamma(Z, dZ)(dagger) - tr[Gamma(Z, dZ) - Gamma(Z, dZ)(dagger)]/2 I, where Z is a 2 x 2 complex matrix and Z(dagger) the complex conjugate and transposed matrix of Z. Restrict this connection to (M) over bar(4): C(H-x, dH(x)) = [B(Z, dZ)](Z = Hx) = C-j(x)dx(j), which is an su(2)-connection on (M) over bar(4). It is proved that its curvature form( ) F : = dC + C Lambda C = 1/2 [partial derivative C-k/partial derivative x(j) - partial derivative C-j/partial derivative x(k) + CjCk - CkCj] dx(j) Lambda dx(k) = : F(jk)dx(j) Lambda dx(k) satisfies the Yang-Mills equation eta(kl)[partial derivative F-jk/partial derivative x(l) + CiFjk - FjkCl] = 0. |
Keyword | Yang-Mills fields Minkowski space Lorentz manifold |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000076532700007 |
Publisher | SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/13524 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Lu, QK |
Affiliation | 1.Shantou Univ, Inst Math, Shantou 515063, Peoples R China 2.Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China |
Recommended Citation GB/T 7714 | Lu, QK. The Yang-Mills fields on the Minkowski space[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,1998,41(10):1061-1067. |
APA | Lu, QK.(1998).The Yang-Mills fields on the Minkowski space.SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,41(10),1061-1067. |
MLA | Lu, QK."The Yang-Mills fields on the Minkowski space".SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY 41.10(1998):1061-1067. |
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