Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-01-28
Ann. Phys. 323 (2008) 2107--2114
Physics
High Energy Physics
High Energy Physics - Theory
11 pages
Scientific paper
10.1016/j.aop.2008.06.002
The decomposition of $Spin^{c}(4)$ gauge potential in terms of the Dirac 4% -spinor is investigated, where an important characterizing equation $\Delta A_{\mu}=-\lambda A_{\mu}$ has been discovered. Here $\lambda $ is the vacuum expectation value of the spinor field, $\lambda =\Vert \Phi \Vert ^{2}$, and $A_{\mu}$ the twisting U(1) potential. It is found that when $\lambda $ takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.
Duan Yi-Shi
Liu Xin
Yang Wen-Li
Zhang Yao-Zhong
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