Skip to main content
Log in

Quantum mechanics over non-Archimedean number fields

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. V. S. Vladimirov and I. V. Volovich, Teor. Mat. Fiz.,59, 3 (1984).

    Google Scholar 

  2. I. V. Volovich, “Number theory as ultimate physical theory,” Preprint TH, 4881/81, CERN, Geneva (1987).

    Google Scholar 

  3. V. S. Vladimirov and I. V. Volovich, Dokl. Akad. Nauk SSSR,302, 320 (1988).

    Google Scholar 

  4. V. S. Vladimirov and I. V. Volovich, “p-adic quantum mechanics,” Preprint SMI-01/88, SMI, Moscow (1988); “p-adic Schrödinger type equation,” Preprint NBI-HE-88-77, Copenhagen (1988); I. V. Volovich, Lett. Math. Phys.,16, 61 (1988); P. G. O. Freund and M. Olson, Phys. Lett. B,199, 186 (1987); B. Grossman, Phys. Lett. B,197, 101 (1987); P. G. O. Freund and E. Witten, Phys. Lett. B,199, 191 (1987); I. L. Gervais, Phys. Lett. B,201, 306 (1988).

    Google Scholar 

  5. I. Ya. Aref'eva, I. V. Volovich, and B. G. Dragovic, “Open and closed p-adic strings and quadratic extensions of number fields,” Preprint CERN-TH-5076/88, CERN, Geneva (1988).

    Google Scholar 

  6. Z. I. Borevich and I. R. Shafarevich, The Theory of Numbers [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  7. I. M. Gel'fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Theory of Representations and Automorphic Functions [in Russian], Nauka, Moscow (1966); F. Bruhat, Bull. Soc. Math. France,89, 43 (1961); V. S. Vladimirov, Usp. Mat. Nauk,43, 17 (1988).

    Google Scholar 

  8. I. Fresnel and B. De Mathan, Soc. Math. France Ast., No. 24/25, 139 (1975); Sem. Theor. Numbers, No. 26, 1 (1975–1976): C. F. Woodcock, J. London Math. Soc.,7, 681 (1974);20, 101 (1979); G. F. Borm, p-Adic Fourier Theory, Nijmegen (1988); G. F. Borm, Catholic Univ. Nijmegen Rep. No. 8628 (1986).

    Google Scholar 

  9. A. Yu. Khrennikov, “Quantization on non-Archimedean superspaces,” in: Abstracts of Papers at the Seminar School: Topical Problems of Complex Analysis [in Russian], Tashkent State University (1989), pp. 154–155.

  10. V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  11. A. A. Slavnov and L. D. Faddeev, Gauge Fields, Introduction to Quantum Theory (Frontiers in Physics, Vol. 50), Reading, Mass. (1980); V. N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics [in Russian], Atomizdat, Moscow (1976).

  12. A. Yu. Khrennikov, Izv. Akad. Nauk SSSR, Ser. Mat.,51, 46 (1987); Teor. Mat. Fiz.,66, 339 (1986); Mat. Zametki,37, 735 (1985); Tr. MMO,49, 113 (1986); Dokl. Akad. Nauk SSSR,267, 1313 (1982); Sib. Mat. Zh.,29, No. 4, 180 (1988); Differents. Uravneniya,21, 346 (1985);22, 1596 (1986).

    Google Scholar 

  13. A. F. Monna, Analyse Non-Archimedienne, Berlin (1970).

  14. V. S. Vladimirov and I. V. Volovich, Dokl. Akad. Nauk SSSR,276, 521 (1984);273, 26 (1983); Teor. Mat. Fiz.,60, 169 (1984); B. S. DeWitt, Supermanifolds, Cambridge University Press (1984); A. Rogers, J. Math. Phys.,21, 724 (1980);22, 939 (1981).

    Google Scholar 

  15. A. Yu. Khrennikov, Usp. Mat. Nauk,43, 87 (1988).

    Google Scholar 

  16. A. Yu. Khrennikov, Teor. Mat. Fiz.,73, 420 (1988);80, 226 (1989); Differents. Uravneniya,24, 2144 (1988);25, 505 (1989); Mat. Sbornik,180, 763 (1989); Izv. Akad. Nauk SSSR, Ser. Mat.,54, 576 (1990).

    Google Scholar 

Download references

Authors

Additional information

Institute of Electronic Technology, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 3, pp. 406–418, June, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khrennikov, A.Y. Quantum mechanics over non-Archimedean number fields. Theor Math Phys 83, 623–632 (1990). https://doi.org/10.1007/BF01018032

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01018032

Keywords

Navigation