We derive an asymptotic expansion for off-diagonal coherent-state matrix elements of nonpolynomial operators in gauge theories admitting holomorphic coherent-state representations. The derivation combines stationary-phase analysis with an operator-level treatment of the Taylor remainder, and yields explicit semiclassical error control under stated assumptions. As a primary application, we formulate the expansion for volume and flux related operators in loop quantum gravity and compare it with the standard diagonal expansion proposed by Giesel and Thiemann [Classical Quantum Gravity 24, 2565 (2007)]. By organizing the expansion around the genuine off-diagonal Berezin symbol rather than a diagonal expectation value, the resulting formula preserves the full holomorphic structure of the geometric phase and reproduces benchmark matrix elements accurately in the numerical regimes tested here, particularly when the coherent-state labels are well separated. We also investigate the behavior of the new expansion formula at small-volume configurations by computing diagonal physical volume expectation values, and detect a loss of accuracy at $t=1$ only when the physical face area is as small as $A_{\mathrm{phys}}\sim 1$ for the regular 3-valent configuration.

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• Gauge theories
• Loop quantum gravity