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Quantum Coulomb Gases

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Quantum Many Body Systems

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2051))

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Abstract

The study of large random matrices in physics originated with the work of Eugene Wigner who used them to predict the energy level statistics of a large nucleus. He argued that because of the complex interactions taking place in the nucleus there should be a random matrix model with appropriate symmetries, whose eigenvalues would describe the energy level spacing statistics.

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Notes

  1. 1.

    Strictly speaking, even if we use a relativistic kinetic energy, this Lagrangian is not relativistically invariant. The reason is that we consider the particles as rigid bodies, which do not Lorenz contract as they move. We will here ignore this additional complication. The Lagrangian in the form given here is that of the Abraham model of charged particles [33].

  2. 2.

    The operator inside the square root is defined as a self-adjoint operator by Friedrichs extending it from the domain of smooth functions with compact support.

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Acknowledgement

Many thanks to the organizers for the invitation to give these lectures and in particular to A. Giuliani for the financial support through the ERC starting grant CoMboS-239694.

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  1. Department of Mathematics, University of Copenhagen Universitetsparken 5, 2100, Copenhagen, Denmark

    Jan Philip Solovej

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  1. Jan Philip Solovej
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Correspondence to Jan Philip Solovej .

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Solovej, J.P. (2012). Quantum Coulomb Gases. In: Quantum Many Body Systems. Lecture Notes in Mathematics(), vol 2051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29511-9_3

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