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The Yang-Mills fields on the Minkowski space
Lu, QK
1998-10-01
Source PublicationSCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
ISSN1006-9283
Volume41Issue:10Pages:1061-1067
AbstractLet 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.
KeywordYang-Mills fields Minkowski space Lorentz manifold
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000076532700007
PublisherSCIENCE PRESS
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/13524
Collection中国科学院数学与系统科学研究院
Affiliation1.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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