Double Cones are Intervals

  • V. S. Sunder
Part of the Operator Theory Advances and Applications book series (OT, volume 207)


The purpose of this short note is to point out the following fact and some of its pleasant ‘consequences’: the so-called double-cones in (4-dimensional) Minkowski space are nothing but the intervals (A, B) = {C ∋ H 2: A < C < B} in the space H2 of 2 × 2 complex Hermitian matrices, where we write X < Y if (Y − X) is positive-definite.

Mathematics Subject Classification (2000)



Minkowski space light cones Hermitian matrices positive-definite matrices 


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  1. [PRH]
    Paul R. Halmos, Finite-dimensional vector spaces, van Nostrand, Princeton, 1958.zbMATHGoogle Scholar
  2. [BAU]
    H. Baumgaertel, Operator algebraic Methods in Quantum Field Theory. A Set of Lectures, (Akademie Verlag, 1995).Google Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • V. S. Sunder
    • 1
  1. 1.The Institute of Mathematical SciencesChennaiIndia

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