By David I. Olive, Peter C. West

This is often the 1st systematic advent to electromagnetic duality and its generalizations. The authors, major figures during this intriguing new region of mathematical physics, describe the elemental principles, most recent advancements, and a few previous paintings whose importance has just recently turn into obvious. This quantity can be crucial analyzing for all these operating in mathematical physics.

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One may investigate the motion of several well-separated kinks and antikinks as a motion of weakly interacting point particles. It is also possible to model the motion of kinks when they are close together, and to study the way a kink and antikink annihilate into radiation. In ref. 9) where K denotes a kink and K an antikink. Thè annihilation sets up a large amplitude oscillation of the unique discrete mode of oscillation of the remaining kink, at frequency 2y/3aX, which slowly radiates away because of the nonlinearities.

However, if 6 = ir, then as they approach, the monopole doesn't know how to twist relative to the antimonopole, and they reach an unstable equilibrium. The precise properties of this solution are known, following a numerical study by Rüber [10]. (/ am grateful to W. ) The solution is axisymmetric, and the monopole and antimonopole are not particularly close, nor much distorted. There is no net magnetic charge, but there is a magnetic dipole moment. 7 times the mass of one monopole. 6 Multimonopoles We return now to the Bogomol'nyi équation BÌ = DÌ4>.

4) can be interpreted as a Legendre transformation. 15) With these definitions, the dual of the dual of a function equals the original function. 1 In general, the dual Lagrangian is a very different function from the original Lagrangian. 15) is introduced to avoid overcounting when summing over the indices of the antisymmetric tensors F and Fp. Gaillard & Zumino 1 46 which must be independent of c, since G is. The above argument can be inverted. 18) with c = 1, or Ld(S, Fd) = -L ( - i - F D ) = -L ( - i , G ) .