Geodesic
Rigged Hilbert Space of Free Coherent States and $p$-Adic Numbers
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 2, pp. 229-239 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the rigged Hilbert space of free coherent states. We prove that this rigged Hilbert space is isomorphic to the space of generalized functions over a $p$-adic disk. We discuss the relation of the described isomorphism of rigged Hilbert spaces and noncommutative geometry and show that the considered example realizes the isomorphism between the noncommutative line and the $p$-adic disk.
Keywords: $p$-adic numbers, noncommutative geometry. 
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S. V. Kozyrev. Rigged Hilbert Space of Free Coherent States and $p$-Adic Numbers. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 2, pp. 229-239. http://geodesic.mathdoc.fr/item/TMF_2003_135_2_a3/

[1] S. V. Kozyrev, TMF, 110:2 (1997), 334 ; q-alg/9701015 | DOI | MR | Zbl

[2] S. V. Kozyrev, Infin. Dimens. Anal. Quantum Probab., 1:2 (1998), 349 ; E-print q-alg/9706020 | DOI | MR | Zbl

[3] V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adicheskii analiz i matematicheskaya fizika, Nauka, M., 1994 | MR

[4] I. V. Volovich, Class. Q Grav., 4 (1987), L83 | DOI | MR

[5] P. G. O. Freund, M. Olson, Phys. Lett. B, 199 (1987), 186 ; V. S. Vladimirov, I. V. Volovich, Commun. Math. Phys., 123 (1989), 659 ; I. Ya. Aref'eva, B. Dragovic, P. Frampton, I. V. Volovich, Mod. Phys. Lett. A, 6 (1991), 4341 ; В. С. Владимиров, УМН, 43 (1989), 17 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl

[6] A. Khrennikov, $p$-Adic Valued Distributions in Mathematical Physics, Kluwer, Dordrecht, 1994 | MR | Zbl

[7] S. Albeverio, A. Khrennikov, Int. J. Mod. Phys., 10:13/14 (1998), 1665 ; A. N. Kochubei, “Additive and multiplicative fractional differentiations over the field of $p$-adic numbers”, $p$-Adic Functional Analysis, Proc. of the 4th Int. Conf. (Nijmegen, Netherlands, June 3–7, 1996), Lect. Notes Pure Appl. Math., 192, eds. W. H. Schikhof, C. Perez-Garcia, J. Kakol, Dekker, New York, 1997, 275 | MR | MR | Zbl

[8] V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, J. Phys. A, 32 (1999), 8785 ; ; G. Parisi, N. Sourlas, European Phys. J. B, 14 (2000), 535 ; E-print cond-mat/9904360E-print cond-mat/9906095 | DOI | MR | Zbl | DOI | MR

[9] S. V. Kozyrev, Izv. RAN. Ser. matem., 66:2 (2002), 149 ; E-print math-ph/0012019 | DOI | MR | Zbl

[10] S. V. Kozyrev, The noncommutative replica approach, E-print cond-mat/0110238

[11] I. Ya. Aref'eva, I. V. Volovich, Nucl. Phys. B, 462 (1996), 600 ; R. Gopakumar, D. Gross, Nucl. Phys. B, 451 (1995), 379 ; M. R. Douglas, M. Li, Phys. Lett. B, 348 (1995), 360 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR

[12] L. Accardi, Y. G. Lu, Commun. Math. Phys., 180 (1996), 605 ; L. Accardi, Y. G. Lu, I. V. Volovich, Quantum Theory and its Stochastic Limit, Springer, Berlin, 2002 ; Interacting Fock Spaces and Hilbert Module Extensions of the Heisenberg Commutation Relations, Publ IIAS, Kyoto, 1997; Л. Аккарди, И. В. Волович, С. В. Козырев, ТМФ, 116:3 (1998), 401 ; D. Voiculescu, K. J. Dykema, A. Nica, Free Random Variables, CRM Monograph Series, 1, AMS, Providence, RI, 1992 ; M. Bozejko, R. Speicher, Commun. Math. Phys., 137 (1991), 519 | DOI | MR | Zbl | MR | Zbl | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl