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We derive the minimal Fock-state expansions of the pion and the photon wavefunctions in light-cone formalism, then we calculate the pion-photon and thephoton-pion transition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma $ and$\gamma ^{\ast}\gamma \to \pi ^{0}$ processes by employing thesequark-antiquark wave functions of the pion and the photon. We find that ourcalculation for the $\gamma ^{\ast}\gamma \to \pi ^{0}$ transition form factoragrees with the experimental data at low and moderately high energy scale.Moreover, the physical differences and inherent connections between thetransition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma $ and $ \gamma^{\ast}\gamma \to \pi ^{0}$ have been illustrated, which indicate that thesetwo physical processes are intrinsically related. In addition, we also discussthe $\pi ^{0}\to \gamma \gamma $ form factor and the decay width $\mathit{\Gamma}(\pi \to \gamma \gamma)$ at $Q^{2}=0$.Comment: 20 pages, 2 figure

Pion-photon and photon-pion transition form factors in the light-cone formalism