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TMF, 1997, Volume 112, Number 3, Pages 355–374 (Mi tmf1048)  

This article is cited in 10 scientific papers (total in 10 papers)

A representation of quantum field Hamiltonian in a $p$-adic Hilbert space

S. A. Albeverioa, A. Yu. Khrennikovb, R. Ciancic

a Ruhr-Universität Bochum, Mathematischer Institut
b Växjö University
c University of Genova, Department of Mathematics

Abstract: Gaussian measures on infinite-dimensional $p$-adic spaces are introduced and the corresponding $L_2$-spaces of $p$-adic valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in $p$-adic $L_2$-spaces. There is a formal analogy with the usual Segal representation. But there is also a large topological difference: parameters of the $p$-adic infinite-dimensional Weyl group are defined only on some balls (these balls are additive subgroups). $p$-Adic Hilbert space representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. Many Hamiltonians with potentials which are too singular to exist as functions over reals are realized as bounded symmetric operators in $L_2$-spaces with respect to a $p$-adic Gaussian measure.

DOI: https://doi.org/10.4213/tmf1048

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English version:
Theoretical and Mathematical Physics, 1997, 112:3, 1081–1096

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Received: 05.02.1997

Citation: S. A. Albeverio, A. Yu. Khrennikov, R. Cianci, “A representation of quantum field Hamiltonian in a $p$-adic Hilbert space”, TMF, 112:3 (1997), 355–374; Theoret. and Math. Phys., 112:3 (1997), 1081–1096

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\vol 112
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\crossref{https://doi.org/10.1007/BF02583040}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Albeverio, P. E. Kloeden, A. Yu. Khrennikov, “Human memory as a $p$-adic dynamic system”, Theoret. and Math. Phys., 117:3 (1998), 1414–1422  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Kochubei A.N., “Non-Archimedean normal operators”, Journal of Mathematical Physics, 51:2 (2010), 023526  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Ilic-Stepic A., Ognjanovic Z., Ikodinovic N., Perovic A., “A P-Adic Probability Logic”, Math. Log. Q., 58:4-5 (2012), 263–280  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Ilic-Stepic A., Ognjanovic Z., Ikodinovic N., “Conditional P-Adic Probability Logic”, Int. J. Approx. Reasoning, 55:9, SI (2014), 1843–1865  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Stepic A.I., Ognjanovic Z., “Logics For Reasoning About Processes of Thinking With Information Coded By P-Adic Numbers”, Stud. Log., 103:1 (2015), 145–174  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Mukhamedov F., Dogan M., “On P-Adic Lambda-Model on the Cayley Tree II: Phase Transitions”, Rep. Math. Phys., 75:1 (2015), 25–46  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Dragovich B., Khrennikov A.Yu., Misic N.Z., “Summation of P-Adic Functional Series in Integer Points”, Filomat, 31:5 (2017), 1339–1347  crossref  mathscinet  isi  scopus
    8. Saburov M., bin Ismail M.J., “On Square Root Function Over Q(P) and Its Application”, 37Th International Conference on Quantum Probability and Related Topics (Qp37), Journal of Physics Conference Series, 819, eds. Accardi L., Mukhamedov F., Hee P., IOP Publishing Ltd, 2017, UNSP 012028  crossref  mathscinet  isi  scopus  scopus  scopus
    9. Ahmad Mohd Ali Khameini, Liao L., Saburov M., “Periodic P-Adic Gibbs Measures of Q-State Potts Model on Cayley Trees i: the Chaos Implies the Vastness of the Set of P-Adic Gibbs Measures”, J. Stat. Phys., 171:6 (2018), 1000–1034  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    10. Stepic A.I., Ognjanovic Z., “Logics to Formalise P-Adic Valued Probability and Their Applications”, Int. J. Parallel Emerg. Distrib. Syst., 33:3, SI (2018), 257–275  crossref  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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