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- Thread starter Loren Booda
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selfAdjoint

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Couldn't local Dirac singularities in my proposed field represent also

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selfAdjoint

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Loren, go back and look at the integral I posted, notice that f(x) in there. It could be anything. What the Dirac δ does is to pick out a particular value of any function that you integrate. Dirac modelled it on the finite case of a vector like (0,1,0). If you inner multiply that by any arbitrary vector (a,b,c) you get

(a,b,c)(0,1,0) = 0*a + 1*b + 0*c = b

(so it picks out the second component, and if you used a 1 in a different place you would pick out a different component. Now in QM math the integral of the product of two "functions" is an inner product in the algebra of those functions, so δ(x-a) in the integral picks out the "a-value component" of the function.

(a,b,c)(0,1,0) = 0*a + 1*b + 0*c = b

(so it picks out the second component, and if you used a 1 in a different place you would pick out a different component. Now in QM math the integral of the product of two "functions" is an inner product in the algebra of those functions, so δ(x-a) in the integral picks out the "a-value component" of the function.

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