Fermionic topological charge of families of lattice gauge fields
نویسنده
چکیده
the degree of φ : S → SU(N), where S is the 3sphere “at infinity” in R. The topological charge has a fermionic description: by the Index Theorem, Q = index(%∂ ) where %∂ A is the Dirac operator coupled to A. The situation is similar for gauge fields on compact manifolds such as S, T , . . . Consider now a family A of SU(N) gauge fields on the 4-torus T 4 parameterized by y ∈ Y (a smooth parameter space) with the property that the gauge fields parameterized by boundary points of Y are all gauge equivalent:
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