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Doi (Kyoto U.), Takumi Iritani (YITP","submitted_at":"2014-04-25T18:16:53Z","abstract_excerpt":"We derive an analytical gauge-invariant formula between the Polyakov loop $L_P$ and the Dirac eigenvalues $\\lambda_n$ in QCD, i.e., $L_P \\propto \\sum_n \\lambda_n^{N_t -1} \\langle n|\\hat U_4|n \\rangle$, in ordinary periodic square lattice QCD with odd-number temporal size $N_t$. Here, $|n\\rangle$ denotes the Dirac eigenstate, and $\\hat U_4$ temporal link-variable operator. This formula is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\\rangle$. 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