Noncommutative Mathematics for Quantum Systems

(Dana P.) #1
References 115

[Maa92] H. Maassen. Addition of freely independent random variables. J.
Funct. Anal., 106(2): 409–438, 1992.


[Mac98] S. MacLane.Categories for the working mathematician, volume 5
ofGraduate texts in mathematics. Springer-Verlag, Berlin, 2
edition, 1998.


[Maj95] S. Majid, Foundations of quantum group theory. Cambridge
University Press, 1995.


[McC92] K. McClanahan. C∗-algebras generated by elements of a unitary
matrix.J. Funct. Anal.107 (1992), no. 2, 439–457.


[Mer85] N.D. Mermin. Is the moon there when nobody looks? Rreality and
quantum theory.Physics Today, 38(4): 38–47, 1985.


[Mey95] P.-A. Meyer.Quantum Probability for Probabilists, volume 1538
ofLecture Notes in Math. Springer-Verlag, Berlin, 2nd edition,
1995.


[Mur97] N. Muraki. Noncommutative Brownian motion in monotone Fock
space.Comm. Math. Phys., 183(3): 557–570, 1997.


[Mur00] N. Muraki. Monotonic convolution and monotone L ́evy-Hincinˇ
formula. Preprint, 2000.


[Mur02] N. Muraki. The five independences as quasi-universal products.Inf.
Dim. Anal., quant. probab. and rel. fields, 5(1): 113–134, 2002.


[Mur03] N. Muraki. The five independences as natural products. Inf. Dim.
Anal., quant. probab. and rel. fields, 6(3): 337–371, 2003.


[Mur13] N. Muraki. A simple proof of the classification theorem for positive
natural products.Probab. Math. Stat., 33(2): 315–326, 2013.


[MT04] G.J. Murphy and L. Tuset. Aspects of compact quantum group theory,
Proc. Amer. Math. Soc.132 (2004), no. 10, 3055–3067.


[MvD98] A. Maes and A. Van Daele. Notes on Compact Quantum Groups,
Nieuw Arch. Wisk.(4) 16 (1998), no. 1–2, 73–112.


[nlab Gl] http://ncatlab.org/nlab/show/Gleason’s+theorem,
Version of January 11, 2014.


[nlab KS] http://ncatlab.org/nlab/show/Kochen-Specker+
theorem, Version of January 11, 2014.


[NS06] A. Nica and R. Speicher. Lectures on the combinatorics of free
probability. London Mathematical Society Lecture Note Series, 335.
Cambridge University Press, Cambridge, 2006.

Free download pdf