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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

The origin of dynamical symmetries in nonrelativistic mechanics

K. H. Mariwalla

Published Feb 1, 1975• 7 citations
Publisher
DOI
10.1007/bf02780743

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Optoelectronic functional materials are divided into two categories as electronic functional material and photonic functional material. And the comparison of the two materials exhibits that the theory of electronic functional material, solid-state quantum mechanics, has developed quite ripe, but the theory of photonic functional material is still in the classical stage or quasi-classical stage. While today, photonic functional material has gradually developed into microscopic field, the deficiency of quantum mechanics in its theory has confined the development of photonic functional material. The optical theory in this paper is different from the traditional optical theory that originates from wave optics, but originates from ray optics and introduces quantum mechanics into ray optics, thus sets up the formula of ray optics quantum mechanics. The conclusion exhibits great symmetry between ray optics quantum mechanics and solid-state quantum mechanics. Nonrelativistic ray optics quantum mechanics is set up on the condition that light is confined near the axis. This paper introduces the construction of ray optics quantum mechanics concisely, and its main equations as well.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 26, 2006•0 citations
We solve the SU(N)-invariant Yang-Baxter equations imposing only the unitarity condition. The usual S matrices should satisfy the crossing symmetry which originates from the CPT invariance of relativistic quantum-field theory. In this paper, we consider nonrelativistic SU(N)-invariant factorizable S matrices by relaxing the crossing symmetry and making the amplitudes for creating and annihilating new particles vanish and find that these S matrices are exactly the same as those of the multicomponent Calogero-Sutherland model, the quantum-mechanical model with the hyperbolic potential between particles and antiparticles. This particular solution is of interest since it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the SU(N)-invariant Yang-Baxter equations. \textcopyright{} 1996 The American Physical Society.
A striking result from nonrelativistic quantum mechanics is the monogamy of entanglement, which states that a particle can be maximally entangled only with one other party, not with several ones. While there is the exact quantitative relation for three qubits and also several inequalities describing monogamy properties, it is not clear to what extent exact monogamy relations are a general feature of quantum mechanics. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. They come about through the curious relationship between the nonrelativistic quantum mechanics of qubits and Minkowski space. We elucidate the origin of entanglement monogamy from this symmetry perspective and provide recipes to construct new families of such equalities.
Optoelectronic functional materials are divided into two categories as electronic functional material and photonic functional material. And the comparison of the two materials exhibits that the theory of electronic functional material, solid-state quantum mechanics, has developed quite ripe, but the theory of photonic functional material is still in the classical stage or quasi-classical stage. While today, photonic functional material has gradually developed into microscopic field, the deficiency of quantum mechanics in its theory has confined the development of photonic functional material. The optical theory in this paper is different from the traditional optical theory that originates from wave optics, but originates from ray optics and introduces quantum mechanics into ray optics, thus sets up the formula of ray optics quantum mechanics. The conclusion exhibits great symmetry between ray optics quantum mechanics and solid-state quantum mechanics. Nonrelativistic ray optics quantum mechanics is set up on the condition that light is confined near the axis. This paper introduces the construction of ray optics quantum mechanics concisely, and its main equations as well.