ar X iv : h ep - t h / 04 11 09 0 v 1 8 N ov 2 00 4 The Bargmann - Wigner Equations in Spherical Space
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چکیده
1 Abstract The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of parameters characterizing them. For spheres embedded in three, four and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two point function shown to vanish at one loop order. The Bargmann-Wigner (BW) equations [1,2] are a means of generating wave equations for higher spin fields. For spin s, a totaly symmetric 2s component spinor ψ α 1 α 2 ...α 2s is taken to satisfy the 2s equations (iγ · ∂ + m) α,β ψ βα 2 ···α 2s = 0. .. (iγ · ∂ + m) α 2s β ψ α 1 α 2 ···β = 0. (1) (We work in Euclidean space with γ-matrix conventions given in the appendix.) Before adapting this procedure to spherical space, we will demonstrate how eq. (1) can be used in the case s = 1 to generate the Maxwell equations. By eqs. (A.15) and (A.16), we see that
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تاریخ انتشار 2004