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DECOMPOSITION OF THE SEMI-SIMPLE GROUP CONNECTION AND COSMIC STRINGS IN THE LORENTZ SPACETIME

PENG-MING ZHANG

Department of Mathematics, Lanzhou University, Lanzhou, 730000, P. R. China

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YI-SHI DUAN

Institute of Theoretical Physics, Lanzhou University, Lanzhou, 730000, P. R. China

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, and

JI-RONG REN

Institute of Theoretical Physics, Lanzhou University, Lanzhou, 730000, P. R. China

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https://doi.org/10.1142/S0217732304013623Cited by:2 (Source: Crossref)

Abstract

In a previous paper, we addressed the method of Abelian decomposition to the case of SU(N) Yang–Mills theory. Here, we extend the decomposition method further to the general case. With the Cartan–Weyl basis we decompose semisimple group connection and discuss the SO(3,1) group in particular. In terms of the vierbein projection, we propose two two-forms as the U(1) gauge fields in the SO(3,1) gauge theory and show that these two-forms are just the different cosmic string tensors. Meanwhile, these two-forms indicate that the cosmic strings appear naturally in the Lorentz spacetime, i.e. the torsion in the Riemann–Cartan spacetime is not necessary for the cosmic strings.

Keywords:

PACS: 02.20.Qs, 11.27.+d

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