Remark 3.23 . [04CV]
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Remark 3.23.
We suggested in section 2.10 that the Solomon functional is essentially the logarithm of the tunneling amplitude between Lagrangian branes. Pushing forth with this physics analogy, we may regard the elementary functional as a semiclassical approximation,4444 44 The elementary functional is proportional to the period integrals over the cycles , which may be regarded as coming from integration over the moduli of constant maps. Such integrals are regarded as more classical then those involving nontrivial holomorphic curves. and as quantum fluctuation effects. Our main assertion then becomes that quantitative almost calibratedness with some extra hypotheses imply the a priori bound on the quantum fluctuation effects. The author is not aware of previous suggestions in the physics literature, but Jake Solomon’s formal Riemannian picture in section 2.8 may offer partial explanations for the relevance of the almost calibrated condition.