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Quantum measure theory

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Mathematica Slovaca

Abstract

We first present some basic properties of a quantum measure space. Compatibility of sets with respect to a quantum measure is studied and the center of a quantum measure space is characterized. We characterize quantum measures in terms of signed product measures. A generalization called a super-quantum measure space is introduced. Of a more speculative nature, we show that quantum measures may be useful for computing and predicting elementary particle masses.

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References

  1. BAUER, H.: Measure and Integration Theory, Walter de Gruyter, Berlin-New York, 2001.

    MATH  Google Scholar 

  2. CRAVEN, B.: Lebesgue Measure and Integral, Pitman, Mansfield, MA, 1982.

    MATH  Google Scholar 

  3. GELL-MANN, M.— HARTLE, J. B.: Classical equations for quantum systems, Phys. Rev. D (3) 47 (1993), 3345–3382.

    Article  MathSciNet  Google Scholar 

  4. GRIFFITHS, R. B.: Consistent histories and the interpretation of quantum mechanics, J. Statist. Phys. 36 (1984), 219–272.

    Article  MATH  MathSciNet  Google Scholar 

  5. GUDDER, S.: A histories approach to quantum mechanics, J. Math. Phys. 39 (1998), 5772–5788.

    Article  MATH  MathSciNet  Google Scholar 

  6. PHILLIPS, E. R.: An Introduction to Analysis and Integration Theory, Intext, London, 1971.

    MATH  Google Scholar 

  7. RUDOLF, O.— WRIGHT, J. D.: Homogeneous decoherence functionals in standard and history quantum mechanics, Comm. Math. Phys. 35 (1999), 249–267.

    Article  Google Scholar 

  8. SALGADO, R.: Some identities for the quantum measure and its generalizations, Modern Phys. Lett. A 17 (2002), 711–728.

    Article  MATH  MathSciNet  Google Scholar 

  9. SORKIN, R.: Quantum mechanics as quantum measure theory, Modern Phys. Lett. A 9 (1994), 3119–3127.

    Article  MATH  MathSciNet  Google Scholar 

  10. SORKIN, R.: Quantum mechanics without the wave function, J. Phys. A 40 (2007), 3207–3231.

    Article  MATH  MathSciNet  Google Scholar 

  11. SURYA, S.— WALLDEN, P.: Quantum covers in quantum measure theory. arXiv: quant-ph 0809.1951 (2008).

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Authors and Affiliations

  1. Department of Mathematics, University of Denver, Denver, Colorado, 80208, USA

    Stan Gudder

Authors
  1. Stan Gudder
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Correspondence to Stan Gudder.

Additional information

Communicated by Anatolij Dvurečenskij

Dedicated to Professor Sylvia Pulmannová on the occasion of her 70th birthday

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Gudder, S. Quantum measure theory. Math. Slovaca 60, 681–700 (2010). https://doi.org/10.2478/s12175-010-0040-8

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  • DOI: https://doi.org/10.2478/s12175-010-0040-8

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