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A simple analytic proof of the formula known as the non-Abelian Stokes theorem is given. It is explicitly shown that the consistency of the formula is guaranteed by the Bianchi identity for the gauge field. An attempt is made to construct the Lagrangian for the gauge field in terms of loop variables.doi:10.1143/ptp.99.691 fatcat:dllaodqfb5atnpu6z6uk7okqf4