Abstract
The decomposition of Spin c ( 4 ) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Δ A μ = - λ A μ has been discovered. Here, λ is the vacuum expectation value of the spinor field, λ = ∥ Φ ∥ 2 , and A μ the twisting U ( 1 ) potential. It is found that when λ 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
