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Russian Mathematical Surveys, 1990, Volume 45, Issue 4, Pages 87–125
DOI: https://doi.org/10.1070/RM1990v045n04ABEH002378
(Mi rm4756)
 

This article is cited in 45 scientific papers (total in 45 papers)

Mathematical methods of non-Archimedean physics

A. Yu. Khrennikov

Moscow State Institute of Electronic Technology (Technical University)
References:
Received: 19.11.1989
Bibliographic databases:
Document Type: Article
UDC: 512.625.5, 517.982.4, 517.948
Language: English
Original paper language: Russian
Citation: A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125
Citation in format AMSBIB
\Bibitem{Khr90}
\by A.~Yu.~Khrennikov
\paper Mathematical methods of non-Archimedean physics
\jour Russian Math. Surveys
\yr 1990
\vol 45
\issue 4
\pages 87--125
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\crossref{https://doi.org/10.1070/RM1990v045n04ABEH002378}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1075387}
\zmath{https://zbmath.org/?q=an:0722.46040}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1990RuMaS..45...87K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990FK12500002}
Linking options:
  • https://www.mathnet.ru/eng/rm4756
  • https://doi.org/10.1070/RM1990v045n04ABEH002378
  • https://www.mathnet.ru/eng/rm/v45/i4/p79
  • This publication is cited in the following 45 articles:
    1. Paolo Aniello, Sonia L'Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter, “Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups”, Lett Math Phys, 114:3 (2024)  crossref
    2. Paolo Aniello, Stefano Mancini, Vincenzo Parisi, “Quantum mechanics on a p-adic Hilbert space: Foundations and prospects”, Int. J. Geom. Methods Mod. Phys., 21:10 (2024)  crossref
    3. Jawad Ettayb, “On the operator equations ABA = A 2 and BAB = B 2 on non-Archimedean Banach spaces”, Topological Algebra and its Applications, 11:1 (2023)  crossref
    4. Paolo Aniello, Stefano Mancini, Vincenzo Parisi, “Trace class operators and states in p-adic quantum mechanics”, Journal of Mathematical Physics, 64:5 (2023)  crossref
    5. Paolo Aniello, Stefano Mancini, Vincenzo Parisi, “A p-Adic Model of Quantum States and the p-Adic Qubit”, Entropy, 25:1 (2022), 86  crossref
    6. Ilaria Svampa, Stefano Mancini, Andreas Winter, “An approach to p-adic qubits from irreducible representations of SO(3)p”, Journal of Mathematical Physics, 63:7 (2022)  crossref
    7. A. M. Kuz', “Analogue of the integral problem for the partial differential equation over p-adic number field”, Prykl. Probl. Mekh. Mat., 18 (2020)  crossref
    8. Mohd Ali Khameini Ahmad, Lingmin Liao, Mansoor Saburov, “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  crossref
    9. Andrei Khrennikov, “The Present Situation in Quantum Theory and its Merging with General Relativity”, Found Phys, 47:8 (2017), 1077  crossref
    10. Andrew Schumann, “p-Adic valued logical calculi in simulations of the slime mould behaviour”, Journal of Applied Non-Classical Logics, 2015, 1  crossref
    11. Mansoor Saburov, Mohd Ali Khameini Ahmad, “On Descriptions of All Translation Invariant p-adic Gibbs Measures for the Potts Model on The Cayley Tree of Order Three”, Math Phys Anal Geom, 18:1 (2015)  crossref
    12. S. V. Kozyrev, “Methods and Applications of Ultrametric and p-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
    13. S. V. Lyudkovskii, “Topological Transformation Groups of Manifolds over Non-Archimedean Fields, Their Representations, and Quasi-Invariant Measures, II”, Journal of Mathematical Sciences, 150:4 (2008), 2123–2223  mathnet  crossref  mathscinet  elib
    14. M. L. Gorbachuk, V. I. Gorbachuk, “On the Cauchy Problem for Differential Equations in a Banach Space over the Field of p-Adic Numbers”, Proc. Steklov Inst. Math., 245 (2004), 91–97  mathnet  mathscinet  zmath
    15. S. V. Lyudkovskii, “Quasi-invariant and pseudo-differentiable measures with values in non-Archimedean fields on a non-Archimedean Banach space”, J. Math. Sci., 128:6 (2005), 3428–3460  mathnet  crossref  mathscinet  zmath  elib  elib
    16. A. Yu. Khrennikov, “Interpretations of Probability and Their p-Adic Extensions”, Theory Probab Appl, 46:2 (2002), 256  mathnet  crossref  mathscinet  isi
    17. S. A. Albeverio, J. M. Bayod, C. Perez-Garsia, A. Yu. Khrennikov, R. Cianci, “Non-Archimedean analogues of orthogonal and symmetric operators”, Izv. Math., 63:6 (1999), 1063–1087  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. S. A. Albeverio, A. Yu. Khrennikov, R. Cianci, “A representation of quantum field Hamiltonian in a p-adic Hilbert space”, Theoret. and Math. Phys., 112:3 (1997), 1081–1096  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. V. I. Bogachev, “Gaussian measures on linear spaces”, Journal of Mathematical Sciences (New York), 79:2 (1996), 933  crossref  mathscinet  zmath
    20. Andrew Khrennikov, “The ultrametric Hilbert-space description of quantum measurements with a finite exactness”, Found Phys, 26:8 (1996), 1033  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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