Curvature and quantized Arnold strangeness

There are three well-known Arnold’s invariants [Formula: see text], and St (Arnold strangeness) for plane curves. Two of them, text] have been successfully quantized. However, the quantization Arnold strangeness remained unrealized. In this paper, we will express a by integrating curvatures multiplied nontrivial densities. The key here is partition function Shumakovitch which reformulates strangeness. Our quantized includes rotation number, original strangeness, Tabachnikov as coefficients in its Taylor expansion.