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Energy from the gauge invariant observables

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For a classical solution vertical bar Psi > in Witten's cubic string field theory, the gauge invariant observable is conjectured to be equal to the difference of the one-point functions of the closed string state corresponding to V, between the trivial vacuum and the one described by vertical bar Psi >. For a static solution vertical bar Psi >, if V is taken to be c (c) over bar partial derivative X-0 partial derivative X-0, the gauge invariant observable is expected to be proportional to the energy of W. We prove this relation assuming that vertical bar Psi > satisfies equation of motion and some regularity conditions. We discuss how this relation can be applied to various solutions obtained recently.

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