Abstract
It is shown that to each locally normal state of a boson system one can associate a point process that can be interpreted as the position distribution of the state. The point process contains all information one can get by position measurements and is determined by the latter. On the other hand, to each so-called Σc-point processQ we relate a locally normal state with position distributionQ.
Similar content being viewed by others
References
O. Bratteli and D. W. Robinson,Operator Algebras and Quantum Statistical Mechanics I, II (Springer-Verlag, New York, 1979, 1981).
G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley-Interscience, New York, 1972).
K.-H. Fichtner and W. Freudenberg, On a probabilistic model of infinite quantum mechanical particle systems,Math. Nachr. 121:171–210 (1985).
K.-H. Fichtner and W. Freudenberg, Point process and normal states of boson systems, Preprint, Naturwissenschaftlich-Technisches Zentrum Leipzig (1986).
K.-H. Fichtner and W. Freudenberg, Point processes and states of infinite boson systems, Preprint, Naturwissenschaftlich-Technisches Zentrum Leipzig (1986).
A. Guichardet,Symmetric Hilbert Spaces and Related Topics (Lecture Notes in Mathematics 231, Springer-Verlag, Berlin, 1972).
R. L. Hudson and P. D. F. Ion, The Feynman-Kac formula for a canonical quantum-mechanical Wiener process, Preprint, Sonderforschungsbereich 123, Universität Heidelberg 21 (1979).
O. Kallenberg,Random Measures (Akademie-Verlag, Berlin, and Academic Press, New York, 1983).
H. Maasen, Quantum Markov processes on Fock space described by integral kernels, inQuantum Probability and Applications II, L. Accardi and W. von Waldenfelds, eds. (Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1985), pp. 361–374.
K. Matthes, J. Kerstan, and J. Mecke,Infinitely Divisible Point Processes (Wiley, New York, 1978).
M. Reed and B. Simon,Methods of Modern Mathematical Physics 1 (Academic Press, New York, 1972).
D. Ruelle,Statistical Mechanics, Rigorous Results (Benjamin, New York, 1969).
D. Ruelle, Equilibrium statistical mechanics of infinite systems, inStatistical Mechanics and Quantum Field Theory, C., de Witt and R. Stora, eds. (Gordon and Breach, New York, 1971), pp. 215–240.
A. Wakolbinger and G. Eder, A conditionΣ cλ for point processes,Math. Nachr. 116:209–232 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fichtner, K.H., Freudenberg, W. Point processes and the position distribution of infinite boson systems. J Stat Phys 47, 959–978 (1987). https://doi.org/10.1007/BF01206171
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01206171