1997/07/10 by Shigeki Matsutani · 18 citations
Chemistry · Mathematics · Physics and Astronomy · #Action (physics) #Algebraic and Geometric Analysis #Chemistry #Dirac (video compression format) #Dirac equation #Dirac operator #Gauge theory #Mathematical physics #Operator (biology) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Quantum field theory #Quantum mechanics #String (physics) #math-ph #math.MP
paper · pdf · doi:10.1142/s0129055x99000076
published in Reviews in Mathematical Physics 11(02), 171-186 (World Scientific) · AMS-Tex Use
arxiv created 1997/07/10 · openalex publication_date 1999/02/01 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In previous report (J. Phys. A (1997) 30 4019–4029), I showed that the Dirac operator confined in a surface immersed in ℝ 3 by means of a mass type potential completely exhibits the surface itself and is identified with that of the generalized Weierstrass equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using the Ward–Takahashi identity, I showed that the expectation value of the action of the Dirac field is expressed by the Willmore functional and area of the surface, or the action of Polyakov's extrinsic string.