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We develop a new semiclassical approach, which starts with the density matrixgiven by the Euclidean time path integral with fixed coinciding endpoints, andproceed by identifying classical (minimal Euclidean action) path, to bereferred to as {\it flucton}, which passes through this endpoint. Fluctuationsaround flucton path are included, by standard Feynman diagrams, previouslydeveloped for instantons. We calculate the Green function and evaluate the oneloop determinant both by direct diagonalization of the fluctuation equation,and also via the trick with the Green functions. The two-loop corrections areevaluated by explicit Feynman diagrams, and some curious cancellation oflogarithmic and polylog terms is observed. The results are fully consistentwith large-distance asymptotics obtained in quantum mechanics. Two classicexamples -- quartic double-well and sine-Gordon potentials -- are discussed indetail, while power-like potential and quartic anharmonic oscillator arediscussed in brief. Unlike other semiclassical methods, like WKB, we do not usethe Schr\"{o}dinger equation, and all the steps generalize to multi-dimensionalor quantum fields cases straightforwardly.

Quantum and thermal fluctuations in quantum mechanics and field theories from a new version of semiclassical theory