On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3

Abstract

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Willmore surface is expressed by volume of a subspace of the moduli of the MNV equation.

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References in corpus (3)

• Conformal invariant functionals of immersions of tori into R^3
• Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-
• Immersion Anomaly of Dirac Operator on Surface in R^3

Cited by in corpus (8)

• Statistical Mechanics of Non-stretching Elastica in Three Dimensional Space
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• Gauss Optics and Gauss Sum on an Optical Phenomena
• On an Algebraic Essential of Submanifold Quantum Mechanics
• Weierstrass Relation for a Submanifold $S^k$ in $\EE^n$ Coming from Submanifold Dirac Operator
• On the Moduli of a quantized loop in P and KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I
• Submanifold Dirac Operator with Torsion