Fetching the paper…
Reading the bibliography…
A brief review of some selected topics in p-adic mathematical physics is presented.
G. K. Kalisch, “On p p -adic Hilbert spaces,” Ann. Math. 48
1947
Earlier work this paper cites.
N. N. Bogolyubov, ”On a new method in the theory of superconductivity,” J. Exp. Theor. Phys. 34
1958
Earlier work this paper cites.
A. Weil, “Sur certains groupes d’operateurs unitaires,” Acta Mathematica 111
1964
Earlier work this paper cites.
Z. I. Borevich and I. R. Shafarevich, Number Theory
1966
Earlier work this paper cites.
I. M. Gelfand, M. I. Graev and I. I. Pyatetskii-Shapiro, Representation Theory and Automorphic Functions
1969
Earlier work this paper cites.
J. P. Serre, A Course in Arithmetics
1973
Earlier work this paper cites.
Harish-Chandra, “Harmonic analysis on reductive p p -adic groups,” in Proc. of Symposia in Pure Mathematics
1973
Earlier work this paper cites.
M. R. Herman and J. C. Yoccoz, “Generalization of some theorem of small divisors to non-archimedean fields,” in Geometric Dynamics
1983
Earlier work this paper cites.
V. S. Vladimirov and I. V. Volovich, “Superanalysis. I. Differential calculus,” Theor. Math. Phys. 59
1984
Earlier work this paper cites.
W. H. Schikhof, Ultrametric Calculus
1984
Earlier work this paper cites.
V. S. Vladimirov and I. V. Volovich, “Superanalysis. II. Integral calculus,” Theor. Math. Phys. 60
1985
Earlier work this paper cites.
G. Rammal, M. A. Toulouse and M. A. Virasoro, ”Ultrametricity for physicists,” Rev. Mod. Phys. 58
1986
Earlier work this paper cites.
I. V. Volovich, “Number theory as the ultimate physical theory,” Preprint No. TH 4781/87, CERN, Geneva, (1987)
1987
Earlier work this paper cites.
I. V. Volovich, “ p p -Adic string,” Class. Quant. Grav. 4
1987
Earlier work this paper cites.
M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory: Volumes 1, 2
1987
Earlier work this paper cites.
P. G. O. Freund and M. Olson, “Non-archimedean strings,” Phys. Lett. B 199
1987
Earlier work this paper cites.
P. G. O. Freund and E. Witten, “Adelic string amplitudes,“ Phys. Lett. B 199
1987
Earlier work this paper cites.
I. V. Volovich, “ p p -Adic space-time and string theory,” Theor. Math. Phys. 71
1987
Earlier work this paper cites.
M. Mezard, G. Parisi and M. Virasoro, Spin-Glass Theory and Beyond
1987
Earlier work this paper cites.
P. H. Frampton and Y. Okada, “Effective scalar field theory of p p -adic string,” Phys. Rev. D 37
1988
Earlier work this paper cites.
L. Brekke, P. G. O. Freund, M. Olson and E. Witten, ”Nonarchimedean string dynamics,” Nucl. Phys. B 302
1988
Earlier work this paper cites.
I. V. Volovich, “Harmonic analysis and p p -adic strings,” Lett. Math. Phys. 16
1988
Earlier work this paper cites.
I. Ya. Aref’eva, B. Dragovich and I. V. Volovich, “On the adelic string amplitudes,” Phys. Lett. B 209
1988
Earlier work this paper cites.
I. Ya. Aref’eva, B. Dragovich and I. V. Volovich, “Open and closed p p -adic strings and quadratic extensions of number fields,” Phys. Lett. B 212
1988
Earlier work this paper cites.
I. Ya. Aref’eva, B. Dragovich and I. V. Volovich, “ p p -Adic superstrings,” Phys. Lett. B 214
1988
Earlier work this paper cites.
P. H. Frampton and Y. Okada, “ p p -Adic string N-point function,” Phys. Rev. Lett. 60
1988
Earlier work this paper cites.
G. Parisi, “ p p -Adic functional integral,” Mod. Phys. Lett. A 4
1988
Earlier work this paper cites.
V. S. Vladimirov, “Generalized functions over the field of p p -adic numbers,” Russ. Math. Surv. 43
1988
Earlier work this paper cites.
I. Ya. Aref’eva, B. Dragovich and I. V. Volovich, “On the p p -adic summability of the anharmonic oscillator,” Phys. Lett. B 200
1988
Earlier work this paper cites.
Yu. I. Manin, “Reflections on arithmetical physics,” in Conformal Invariance and String Theory
1989
Earlier work this paper cites.
L. Chekhov, A. Mironov and A. Zabrodin, “Multiloops calculations in p p -adic string theory and Bruhat-Tits trees,” Commun. Math. Phys. 125
1989
Earlier work this paper cites.
P. H. Frampton and H. Nishino, “Theory of p p -adic closed strings,” Phys. Rev. Lett. 62
1989
Earlier work this paper cites.
M. D. Missarov, “Random fields on the adele ring and Wilson’s renormalization group,” Annales de l’institut Henri Poincare (A): Physique Theorique 50
1989
Earlier work this paper cites.
V. S. Vladimirov and I. V. Volovich, “ p p -Adic quantum mechanics,” Comm. Math. Phys. 123
1989
Earlier work this paper cites.
V. S. Vladimirov and I. V. Volovich, “A p p -adic Schrödinger-type equation,” Lett. Math. Phys. 18
1989
Earlier work this paper cites.
D. R. Lebedev and A. Yu. Morozov, “ p p -Adic single-loop calculations,” Theor. Math. Phys. 82
1990
Earlier work this paper cites.
V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, “The spectral theory in the p p -adic quantum mechanics,” Izvestia Akad. Nauk SSSR, Ser. Mat. 54
1990
Earlier work this paper cites.
A. Yu. Khrennikov, “Mathematical methods of the non-archimedean physics,” Uspekhi Mat. Nauk 45
1990
Earlier work this paper cites.
I. Ya. Aref’eva and I. V. Volovich, “Quantum group particles and non-Archimedean geometry,” Phys. Lett. B 268
1991
Earlier work this paper cites.
E. I. Zelenov, “ p p -Adic path integrals,” J. Math. Phys. 32
1991
Earlier work this paper cites.
I. Ya. Aref’eva, B. Dragovich, P. H. Frampton and I. V. Volovich, “The wave function of the Universe and p p -adic gravity,” Int. J. Mod. Phys. A 6
1991
Earlier work this paper cites.
R. S. Ismagilov, “On the spectrum of the self-adjoint operator in L 2 ( K ) L_{2}(K) where K K is a local field; an analog of the Feynman-Kac formula,” Theor. Math. Phys. 89
1991
Earlier work this paper cites.
A. Yu. Khrennikov, “ p p -Adic quantum mechanics with p p -adic valued functions,” J. Math. Phys. 32
1991
Earlier work this paper cites.
A. Yu. Khrennikov, “Real-non-Archimedean structure of space-time,” Theor. Math. Phys. 86
1991
Earlier work this paper cites.
B. Dragovich, “ p p -Adic perturbation series and adelic summability,” Phys. Lett. B 256
1991
Earlier work this paper cites.
V. A. Smirnov, “Calculation of general p p -adic Feynman amplitude,” Comm. Math. Phys. 149
1992
Earlier work this paper cites.
A. N. Kochubei, “Parabolic equations over the field of p p -adic numbers,” Math. USSR Izv. 39
1992
Earlier work this paper cites.
F. Vivaldi and S. Hatjyspyros, “Galois theory of periodic orbits of polynomial maps,” Nonlinearity D 5
1992
Earlier work this paper cites.
L. Brekke and P. G. O. Freund, “ p p -Adic numbers in physics,” Phys. Rep. 233
1993
Earlier work this paper cites.
E. I. Zelenov, “ p p -Adic Heisenberg group and Maslov index,” Commun. Math. Phys. 155
1993
Earlier work this paper cites.
A. N. Kochubei, “A Schrödinger type equation over the field of p p -adic numbers,” J. Math. Phys. 34
1993
Earlier work this paper cites.
S. Haran, “Analytic potential theory over p p -adics,” Ann. Inst. Fourier 43
1993
Earlier work this paper cites.
S. N. Evans, “Local field Brownian motion,” J. Theor. Probab. 6
1993
Earlier work this paper cites.
A. Yu. Khrennikov, “ p p -Adic probability theory and its applications. The principle of statistical stabization of frequencies,” Theor. Math. Phys. 97
1993
Earlier work this paper cites.
V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p p -Adic Analysis and Mathematical Physics
1994
Earlier work this paper cites.
A. Yu. Khrennikov, p p -Adic Valued Distributions in Mathematical Physics
1994
Earlier work this paper cites.
I. V. Volovich, “From p p -adic strings to etale ones,” Trudy Steklov Math. Inst. 203
1994
Earlier work this paper cites.
E. I. Zelenov, “The infinite-dimensional p p -adic symplectic group,” Russian Acad. Sci. Izv. Math. 43
1994
Earlier work this paper cites.
B. Dragovich, “Adelic model of harmonic oscillator,” Theor. Math. Phys. 101
1994
Earlier work this paper cites.
S. Albeverio and W. Karwowski, “A random walk on p p -adic numbers - generator and its spectrum,” Stochastic processes. Theory and Appl. 53
1994
Earlier work this paper cites.
B. Dwork, G. Gerotto and F. J. Sullivan, An Introduction to G-Functions
1994
Earlier work this paper cites.
D. K. Arrowsmith and F. Vivaldi, “Geometry of p p -adic Siegel discs,” Physica D 71
1994
Earlier work this paper cites.
V. S. Anashin, “Uniformly distributed sequences of p p -adic integers,” Mathematical Notes 55
1994
Earlier work this paper cites.
Broken Symmetry. Selected Papers of Y. Nambu
1995
Earlier work this paper cites.
B. Dragovich, “Adelic harmonic oscillator,” Int. J. Mod. Phys. A 10
1995
Earlier work this paper cites.
B. Dragovich, “Adelic wave function of the Universe,” in Proc. Third A. Friedmann Int. Seminar on Grav. and Cosmology
1995
Earlier work this paper cites.
B. Dragovich, “Adelic generalization of wave function of the Universe,” The First Hungarian-Yugoslav Astronomical Conference, Hungary, Baja, April 26-27, 1995. Publ. Obs. Astron. Belgrade 49
1995
Earlier work this paper cites.
A. Escassut, Analytic Elements in p-Adic Analysis
1995
Earlier work this paper cites.
V. S. Anashin, “Uniformly distributed sequences over p p -adic integers,” in Number Theoretic and Algebraic Methods in Computer Science
1995
Earlier work this paper cites.
K. Yasuda, “Additive processes on local fields,” J. Math. Sci. Univ. Tokyo 3
1996
Cited alongside, same era.
S. Albeverio and A. Yu. Khrennikov, “Representation of the Weyl group in spaces of square integrable functions with respect to p p -adic valued Gaussian distributions,” J. Phys. A: Math. Gen. 29
1996
Cited alongside, same era.
A. N. Kochubei, “ p p -Adic commutation relations,” J. Phys. A: Math. Gen. 29
1996
Cited alongside, same era.
V. S. Varadarajan, “Path integrals for a class of p p -adic Schrödinger equations,” Lett. Math. Phys. 39
1997
Cited alongside, same era.
G. Djordjević and B. Dragovich, “ p p -Adic path integrals for quadratic actions,” Mod. Phys. Lett. A 12
1997
Cited alongside, same era.
H. Kaneko and K. Yasuda, “Capacities associated with Dirichlet space on an infinite extension of a local field,” Forum Math. 17
2005
Later among the works it cites.
F. Mukhamedov and U. Rozikov, “On inhomogeneous p p -adic Potts model on a Cayley tree,” Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8
2005
Later among the works it cites.
V. I. Arnold, “Number-theoretic turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics,” J. Math. Fluid Mech. 7
2005
Later among the works it cites.
I. Ya. Aref’eva, “Nonlocal string tachyon as a model for cosmological dark energy,” AIP Conf. Proc. 826
2006
Later among the works it cites.
G. Calcagni, “Cosmological tachyon from cubic string field theory,” JHEP 05
2006
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1997
Cited alongside, same era.
S. Albeverio, R. Cianci and A. Yu. Khrennikov, “On the spectrum of the p p -adic position operator,” J. Phys. A: Math. Gen. 30
1997
Cited alongside, same era.
S. Albeverio, R. Cianci and A. Yu. Khrennikov, “On the Fourier transform and the spectral properties of the p p -adic momentum and Schrodinger operators,” J. Phys. A: Math. Gen. 30
1997
Cited alongside, same era.
B. Dragovich, “On some p p -adic series with factorials,” in p-Adic Functional Analysis
1997
Cited alongside, same era.
A. Yu. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models
1997
Cited alongside, same era.
S. V. Kozyrev, “The space of free coherent states is isomorphic to space of distributions on p p –adic numbers,” Infin. Dimens. Anal. Quantum Prob. 1
1998
Cited alongside, same era.
B. Dragovich, “On generalized functions in adelic quantum mechanics,” Integral Transform. Spec. Funct. 6
1998
Cited alongside, same era.
B. Dragovich, “ p p -Adic and adelic quantum cosmology: p p -Adic origin of dark energy and dark matter,” in p p -Adic Mathematical Physics
2006
Later among the works it cites.
A. Connes and M. Marcolli, “From physics to number theory via noncommutative geometry. Part I: Quantum statistical mechanics of Q-lattices,” in Frontiers in Number Theory, Physics, and Geometry, I
2006
Later among the works it cites.
A. Connes and M. Marcolli, “From physics to number theory via noncommutative geometry. Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory,” in Frontiers in Number Theory, Physics, and Geometry, II
2006
Later among the works it cites.
P. Schneider, “Continuous representation theory of p p -adic Lie groups,” Proc. ICM Madrid 2006, Vol. II, pp. 1261 - 1282 (2006)
2006
Later among the works it cites.
A. Yu. Khrennikov and S. V. Kozyrev, “Ultrametric random field,” Infin. Dimens. Anal. Quan. Prob. Related Topics 9
2006
Later among the works it cites.
2006
Later among the works it cites.
A. Yu. Khrennikov and V. M. Shelkovich, “Distributional asymptotics and p p -adic Tauberian and Shannon-Kotelnikov theorems,” Asymptotical Analysis 46
2006
Later among the works it cites.
S. Fischenko and E. I. Zelenov, “ p p –Adic models of turbulence,” in p p -Adic Mathematical Physics
2006
Later among the works it cites.
A. Yu. Khrennikov and S. V. Kozyrev, “Replica symmetry breaking related to a general ultrametric space I: Replica matrices and functionals,” Physica A: Stat. Mech. Appl. 359
2006
Later among the works it cites.
A. Yu. Khrennikov and S. V. Kozyrev, “Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n → 0 n\to 0 limit,” Physica A: Stat. Mech. Appl. 359
2006
Later among the works it cites.
V. Anashin, “Ergodic transformations in the space of p p -adic integers,” in p p -Adic Mathematical Physics
2006
Later among the works it cites.
A. Yu. Khrennikov, “ p p -Adic information space and gene expression,” in Integrative Approaches to Brain Complexity
2006
Later among the works it cites.
M. Pitkänen, “Could genetic code be understood number theoretically?” Electronic preprint: www.helsinki.fi/ matpitka/pdfpool/genenumber.pdf (2006)
2006
Later among the works it cites.
J. Q. Trelewicz and I. V. Volovich, “Analysis of business connections utilizing theory of topology of random graphs,” in p p -Adic Mathematical Physics
2006
Later among the works it cites.
A. Kh. Bikulov, A. P. Zubarev and L. V. Kaidalova, “Hierarchical dynamical model of financial market near the crash point and p p -adic analysis,” Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya ”Fiziko-Matematicheskie Nauki” 42
2006
Later among the works it cites.
A. Connes, C. Consani and M. Marcolli, “Noncommutative geometry and motives: the thermodynamics of endomotives,” Advances in Mathematics 214
2007
Later among the works it cites.
G. Cornelissen, M. Marcolli, K. Reihani and A. Vdovina, “Noncommutative geometry on trees and buildings,” in Traces in Geometry, Number Theory, and Quantum Fields
2007
Later among the works it cites.
I. Ya. Aref’eva and A. S. Koshelev, “Cosmic acceleration and crossing of w = − 1 w={}-1 barrier in non-local cubic superstring field theory model,” JHEP 0702
2007
Later among the works it cites.
N. Barnaby, T. Biswas and J. M. Cline, “ p p -Adic inflation,” JHEP 0704
2007
Later among the works it cites.
A. S. Koshelev, Non-local SFT tachyon and cosmology,” JHEP 0704
2007
Later among the works it cites.
2007
Later among the works it cites.
G. Calcagni, M. Montobbio and G. Nardelli, “Route to nonlocal cosmology,” Phys. Rev. D 76
2007
Later among the works it cites.
I. Ya. Aref’eva and I. V. Volovich, “Quantization of the Riemann zeta-function and cosmology,” Int. J. Geom. Meth. Mod. Phys. 4
2007
Later among the works it cites.
V. S. Varadarajan, Geometry of Quantum Theory
2007
Later among the works it cites.
H. Kaneko and A. N. Kochubei, “Weak solutions of stochastic differential equations over the field of p p -adic numbers,” Tohoku Math. J. 59
2007
Later among the works it cites.
2007
Later among the works it cites.
F. Murtagh, “On ultrametric algorithmic information,” Computer Journal, in press. (Online, Advance Access, 9 Oct. 2007, http://dx.doi.org/10.1093/comjnl/bxm084)
2007
Later among the works it cites.
S. V. Kozyrev, “Wavelets and spectral analysis of ultrametric pseudodifferential operators,” Sbornik: Mathematics 198
2007
Later among the works it cites.
A. Yu. Khrennikov and S. V. Kozyrev, “Replica symmetry breaking related to a general ultrametric space III: The case of general measure,” Physica A: Stat. Mech. Appl. 378
2007
Later among the works it cites.
A. Yu. Khrennikov, F. M. Mukhamedov and J. F. Mendes, “On p p -adic Gibbs measures of the countable state Potts model on the Cayley tree,” Nonlinearity 20
2007
Later among the works it cites.
J. Silverman, The Arithmetic of Dynamical Systems
2007
Later among the works it cites.
B. Dragovich, A. Khrennikov and D. Mihajlović, “Linear fractional p p -adic and adelic dynamical systems,” Rep. Math. Phys. 60
2007
Later among the works it cites.
A. Yu. Khrennikov, S. V. Kozyrev, “Genetic code on the dyadic plane,” Physica A: Stat. Mech. Appl. 381
2007
Later among the works it cites.
B. Dragovich and D. Joksimović, “On possible uses of p p -adic analysis in econometrics,” Megatrend Revija 4
2007
Later among the works it cites.
S. V. Kozyrev, Methods and Applications of Ultrametric and p p –Adic Analysis: From Wavelet Theory to Biophysics
2008
Later among the works it cites.
A. Connes and M. Marcolli, “Noncommutative geometry, quantum fields, and motives,” Colloquium Publications 55
2008
Later among the works it cites.
M. Baker, J. Teitelbaum, B. Conrad, K. S. Kedlaya and D. S. Thakur, p p -Adic Geometry: Lectures from the 2007 Arizona Winter School
2008
Later among the works it cites.
I. Ya. Aref’eva, L. V. Joukovskaya and S. Yu. Vernov, ”Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric,” J. Phys. A: Math. Theor 41
2008
Later among the works it cites.
N. Barnaby and J. M. Cline, “Predictions for nongaussianity from nonlocal inflation,” JCAP 0806
2008
Later among the works it cites.
B. Dragovich, “Zeta-nonlocal scalar fields,” Theor. Math. Phys. 157
2008
Later among the works it cites.
W. A. Zuniga-Galindo, “Decay of solutions of wave-type pseudo-differential equations over p p -adic fields,” Publ. Res. Inst. Math. Sci. 42
2008
Later among the works it cites.
O. G. Smolyanov and N. N. Shamarov, “Feynman and Feynman-Kac formulas for evolution equations with Vladimirov operator,” Doklady Mathematics 77
2008
Later among the works it cites.
A. N. Kochubei, “A non-Archimedean wave equation,” Pacif. J. Math. 235
2008
Later among the works it cites.
W. A. Zuniga-Galindo, “Parabolic equations and Markov processes over p p -adic fields,” Potential Anal. 28
2008
Later among the works it cites.
S. Albeverio, S. Kuzhel and S. Torba, “ p p -Adic Schrödinger-type operator with point interactions,” J. Math. Anal. Appl. 338
2008
Later among the works it cites.
2008
Later among the works it cites.
2008
Later among the works it cites.
2008
Later among the works it cites.
2008
Later among the works it cites.
S. V. Kozyrev, “Toward an ultrametric theory of turbulence,” Theor. Math. Phys. 157
2008
Later among the works it cites.
V. S. Vladimirov, “On the equations for p p -adic closed and open strings,” p p -Adic Numbers, Ultrametric Analysis and Applications 1
2009
Closest in time.
E. I. Zelenov, “Quantum approximation theorem,” p p -Adic Numbers, Ultrametric Analysis and Applications 1
2009
Closest in time.
V. S. Varadarajan, “Multipliers for the symmetry groups of p p -adic spacetime,” p p -Adic Numbers, Ultrametric Analysis and Applications 1
2009
Closest in time.
T. Digernes, V. S. Varadarajan and D. Weisbart, “Matrix valued Schrödinger operators on local fields,” to be published in Proc. Steklov Math. Inst. 265
2009
Closest in time.
S. Albeverio and Ya. Belopolskaya, “Stochastic processes in ℚ p \mathbb{Q}_{p} associated with systems of nonlinear PDEs,” p p -Adic Numbers, Ultrametric Analysis and Applications, to be published (2009)
2009
Closest in time.
H. Kaneko, “Fractal theoretic aspects of local field,” p p -Adic Numbers, Ultrametric Analysis and Applications 1
2009
Closest in time.
2009
Closest in time.
2009
Closest in time.
A. N. Kochubei, Analysis in Positive Characteristic
2009
Closest in time.
V. Anashin and A. Khrennikov, Applied Algebraic Dynamics
2009
Closest in time.
B. Dragovich and A. Yu. Dragovich, “A p p -adic model of DNA sequence and genetic code,” p p -Adic Numbers, Ultrametric Analysis and Applications 1
2009
Closest in time.
2009
Closest in time.