Random Matrix Theory and Quantum Chromodynamics

Akemann G (2017)
In: Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Schehr G, Altland A, Fyodorov YV, O'Connell, N, Cugliandolo LF (Eds); Oxford: Oxford Univ. Press: 228-282.

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Schehr, Grégory ; Altland, Alexander ; Fyodorov, Yan V. ; O'Connell,, Neil ; Cugliandolo, Leticia F.
Abstract
These notes are based on the lectures delivered at the Les Houches Summer School in July 2015. They are addressed at a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian Unitary Ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in Quantum Chromodynamics with three colours in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. We also give some open random matrix problems.
Publishing Year
Conference
104. Les Houches Summer School
Location
Les Houches
Conference Date
2015-07-06 – 2015-07-31
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Akemann G. Random Matrix Theory and Quantum Chromodynamics. In: Schehr G, Altland A, Fyodorov YV, O'Connell, N, Cugliandolo LF, eds. Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Oxford: Oxford Univ. Press; 2017: 228-282.
Akemann, G. (2017). Random Matrix Theory and Quantum Chromodynamics. In G. Schehr, A. Altland, Y. V. Fyodorov, N. O'Connell,, & L. F. Cugliandolo (Eds.), Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015 (pp. 228-282). Oxford: Oxford Univ. Press.
Akemann, G. (2017). “Random Matrix Theory and Quantum Chromodynamics” in Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015, Schehr, G., Altland, A., Fyodorov, Y. V., O'Connell,, N., and Cugliandolo, L. F. eds. (Oxford: Oxford Univ. Press), 228-282.
Akemann, G., 2017. Random Matrix Theory and Quantum Chromodynamics. In G. Schehr, et al., eds. Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Oxford: Oxford Univ. Press, pp. 228-282.
G. Akemann, “Random Matrix Theory and Quantum Chromodynamics”, Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015, G. Schehr, et al., eds., Oxford: Oxford Univ. Press, 2017, pp.228-282.
Akemann, G.: Random Matrix Theory and Quantum Chromodynamics. In: Schehr, G., Altland, A., Fyodorov, Y.V., O'Connell,, N., and Cugliandolo, L.F. (eds.) Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. p. 228-282. Oxford Univ. Press, Oxford (2017).
Akemann, Gernot. “Random Matrix Theory and Quantum Chromodynamics”. Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Ed. Grégory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell,, and Leticia F. Cugliandolo. Oxford: Oxford Univ. Press, 2017. 228-282.
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