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By Um C.-I., Yeon K.-H., George T.F.

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This provided an unambiguous evidence that meson-exchange currents are real in Nature. We now realize that this is no big deal in the present understanding of nuclear dynamics. Here the mesons that mediate both the nuclear force and the exchange currents are particles that are observed on-shell, so there is nothing so unusual about it although it required a precise understanding of one-body processes and a systematic chiral counting before multi-body processes could be sorted out. The situation with quarks and gluons is a totally different matter.

The metric is g µν = diag(1, −1) with Lorentz indices µ, ν = 0, 1 and the γ matrices are in Weyl representation, γ0 = γ 0 = σ1 , γ1 = −γ 1 = −iσ2 , γ5 = γ 5 = σ3 with the usual Pauli matrices σi . 5in 22 ws-book975x65 Chiral Nuclear Dynamics II introducing a fictitious field θ, iθ(x)γ5 ¯ ψ(x) = χ(x)e ¯ . 7) d2 xχγ ¯ µ (i∂µ + Vµ + Aµ γ5 − ∂µ θ(x)γ5 ) χ S = where J is the Jacobian of the transformation which can be readily calculated: J = exp i d2 x 1 1 ∂µ θ∂ µ θ + 2π π µν Vµ ∂ν θ − 1 Aµ ∂ µ θ π . 6).

40) We thus learn that the quark charge is partitioned into the bag and outside of the bag, without however any dependence of the total on the size or location of the bag boundary. This partition is exact. In the (1+1)-dimensional case, one can calculate other physical quantities such as the energy, response functions and, more generally, partition functions and show that the physics does not depend upon the presence of the bag. We could work with quarks alone, or pions alone or any mixture of the two.

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