Congruence and metaplectic covariance: Rational biquadratic reciprocity and quantum entanglement

Abstract

The purpose of the paper is to elucidate the cyclotomographic applications of the coadjoint orbit methodology to the Legendre-Hilbert-Artin symbolic tower of class field theory in the sense of the theories of Chevalley, Hasse, Weil and Witt. The Witt arithmetics concludes with the law of rational biquadratic reciprocity and quantum entanglement. The purpose of the paper is to elucidate the cyclotomographic applications of the coadjoint orbit methodology to the Legendre-Hilbert-Artin symbolic tower of class field theory in the sense of the theories of Chevalley, Hasse, Weil and Witt. The Witt arithmetics concludes with the law of rational biquadratic reciprocity and quantum entanglement.

Keywords

• Third order principle of spinor triality
• spaces of even and odd half-spinor
• metaplectic Lie group Mp(2, R)
• Hopf principal circle bundle
• the metaplectic coadjoint orbit model
• half-spinor Maslov index
• Witt quartic groups
• Legendre-Hilbert-Artin symbolic tower of class field theory
• valuation and module function
• rational quantum entanglement
• adeles and ideles

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