The problems of the non-archimedean analysis generated by quantum physics
Khrennikov, A.Yu
Annales mathématiques Blaise Pascal, Tome 2 (1995), p. 181-190 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1995-01-01
@article{AMBP_1995__2_1_181_0,
     author = {Khrennikov, A.Yu},
     title = {The problems of the non-archimedean analysis generated by quantum physics},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {2},
     year = {1995},
     pages = {181-190},
     mrnumber = {1342814},
     zbl = {0868.46058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_1995__2_1_181_0}
}

Khrennikov, A.Yu. The problems of the non-archimedean analysis generated by quantum physics. Annales mathématiques Blaise Pascal, Tome 2 (1995) pp. 181-190. http://gdmltest.u-ga.fr/item/AMBP_1995__2_1_181_0/

1. Vladimirov V. S. and Volovich I.V., p-adic quantum mechanics. Commun. Math. Phys., 123, 659-676 (1989). | MR 1006299 | Zbl 0688.22004

2. Vladimirov V. S. , Volovich I.V., and Zelenov E.I., p-adic Numbers in Mathematical Physics, World Scientific Publ., Singapoure (1993) | MR 1288093 | Zbl 0812.46076

3. Volovich I.V. , Number Theory as the Ultimate Physical Theory, CERN, Geneva. Preprint TH. 4781/87 (1987).

4. Volovich I.V., p-adic string. Class. Quant. Gra. , 4, 83-87 (1987). | MR 895889

5. Volovich I.V. , Harmonic analysis and p-adic strings. Lett. Math. Phys., 16 , 61-64 (1988). | MR 958464 | Zbl 0668.43006

6. Freund P. G. O. and Olson M. , Non-Archimedean strings. Phys. Lett. B, 199, 186-190 (1987). | MR 919703

7. Freund P. G. O. and Witten E. , Adelic string amplitudes. Phys. Lett. B , 199, 191-195 (1987). | MR 919704

8. Gervais J.L. , p-adic analyticity and Virasoro algebras for conformal theories in more than two dimensions. Phys. Lett. B . 201, 306-310 (1988). | MR 927481

9. Aref'Eva I.Ya. Dragovic B., and Volovich I.V. , Open and closed p-adic strings and quadratic extensions of number fields. Phys. Lett. B ., 200, 512-516 (1988). | MR 926670

10. Beltrametti E. and Cassinelli G., Quantum mechanics and p-adic numbers. Found. Phys., 2, 1-7, (1972). | MR 331996

11. Frampton P. H. and Okada Y. , p-adic string N-point function. Phys. Rev. Lett. B , 60, 484-486 (1988). | MR 925747

12. Khrennikov A.Yu. Generalized functions and Gaussian functional integrals with respect to non-Archimedean functional spaces. Izv. Akad. Nauk SSSR, Ser. Mat., 55, No. 4, 780-814 (1991). | MR 1137586 | Zbl 0755.46047

13. Khrennikov A.Yu. Endo M. , The unboundedness of the p-adic Gaussian distribution. Izv. Akad. Nauk SSSR, Ser. Mat. . 56. No. 4, 456-476 (1992).

14. Khrennikov A.Yu. , Axiomatics of the p-adic theory of probabilities. Dokl. Acad. Nauk SSSR, sr. Matem., 326, No. 5, 1075-1079 (1992). | MR 1198776

15. Khrennikov A.Yu. , p-adic quantum mechanics with p-adic valued functions. J. Math. Phys., 32. No. 4, 932-937 (1991). | MR 1097779 | Zbl 0746.46067

16. Khrennikov A.Yu. , p-adic valued distributions in mathematical physics , Kluwer Academic Publ. , Dordrecht, 1994 | MR 1325924 | Zbl 0833.46061

17. Cianci R. and Khrennikov A.Yu. , p-adic superanalysis, 1. Infinitely generated Banach superalgebras and algebraic groups. J. Math. Phys., 34. No. 5, 1995-1999, (1993). | MR 1214503 | Zbl 0809.46091

18. Cianci R. and Khrennikov A.Yu. , Can p-adic numbers be useful to regularize divergent expectation values of quantum observables ? Preprint, Depart. Math., Univ. Genova, November (1993). To be published in Int. J. of Theor. Phys., 1994. | MR 1285249 | Zbl 0842.60096

19. Khrennikov A.Yu. , Generalized functions with non-Archimedean values and their applications to quantum mechanics and field theory. Analysis-3, Modern Mathematics and its Applications , VINITI, Moscow (1993) .

20. Krennikov A.Yu. ,Gauge connection between real and p-adic space-time , Proc . of Marcel Grossmann Meeting on General Relativity , Kyoto , 1991 , ( Sato H . Nakamura T . ) . World scientific publ. Singapore, 498-500 (1992) | MR 1236881

21. Khrennikov A.Yu. ,p-adic theory of probability and its applications. A principle of the statistical stabilization of frequencies. Teoret. and Matem. Fizika, 97, No 3 , 348-363 (1993). | MR 1257875 | Zbl 0839.60005