More details can be found in the references below and the other references are mainly contained therein. Reports on mathematical physics vol 84, issue 1, pages 1. Spin networks in quantum gravity lorente, miguel, journal of. This latter approach will allow to show that padic integers form a ring, denoted by zp. The first 30 years article in p adic numbers ultrametric analysis and applications 92 may 2017 with 250 reads how we measure reads. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin. The method suggested is analogous to lagranges formulation of a path integral used in ordinary quantum mechanics. International conference on padic mathematical physics and. But recently new models of the quantum physics were proposed on the basis of p adic numbers field qp. Lately p adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the nonarchimedean geometry of spacetime at small distances. Padic analysis and mathematical physics by v s vladimirov. Click download or read online button to get introduction to p adic analytic number theory book now. Lately p adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin.
Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non archimedean. In this paper we consider a new geometric approach to madelungs quantum hydrodynamics qhd based on the theory of a gauge connection. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the nonarchimedean geometry of spacetime at small distances. These draft works include course notes, textbooks, and research expositions in progress. Introduction to p adic analytic number theory download. Communications in mathematical physics project euclid. Read on padic mathematical physics, padic numbers, ultrametric analysis, and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Pdf on padic mathematical physics igor volovich and s. Michele nardelli, on the link between the structure of abranes observed in the homological mirror symmetry and the classical theory of automorphic forms. The usual meaning taken for padic analysis is the theory of padicvalued functions on spaces of interest. This item appears in the following collections academic publications 176382 academic output radboud university. Mathematical connections with the padic strings and the zeta strings. What are p adic numbers, p adic analysis, p adic physics, p adic probability.
There are various attemptsspeculationsproposals to use padic numbers in. Among the main achievements of this new branch of contemporary mathematical physics are padic and adelic quantum me. Feb 08, 2009 read on p adic mathematical physics, p adic numbers, ultrametric analysis, and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Padic analysis and mathematical physics soviet and east. Box 57, 11001 belgrade, serbia and montenegro abstract padic mathematical physics emerged as a result of e orts to nd a nonarchimedean approach to the spacetime and string dynamics at. Apr 27, 2009 tion to some aspects of padic mathematical physics could be helpful for the readers of the. American mathematical society, providence, ri, 2009. Historically, this research was inspired by the discovery that the veneziano amplitude of the open bosonic string, which is calculated using an integral over the real numbers, can be generalized to the p adic numbers. Southeastern european network in mathematical and theoretical physics nis, serbia international center for mathematical modeling in physics, engineering, economics, and cognitive science linnaeus university, vaxjokalmar, sweden email. The construction of qp is very similar to the construction of p is a fixed prime number, p 2.
Coverage touches on a wide variety of topics, including. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. Electronic publications 80624 freely accessible full text publications plus those not yet available due to embargo. Analysis and mathematical physics amp publishes current research results as well as selected highquality survey articles in real, complex, harmonic, and geometric analysis originating and or having applications in mathematical physics. The author honors pythagoras in naming the ratios of the 12 schematic. Bounds of padic weighted hardycesaro operators and their commutators on padic weighted spaces of morrey types nguyen minh chuong, ha duy hung and nguyen thi hong 5 february 2016 padic numbers, ultrametric analysis, and applications, vol. The planck constants hierarchy produces dimensionless ratios, that allow for the first time the theoretical calculation of constants, e. Hensel 1904 in connection with problems of the pure theory of numbers. Analysis of business connections utilizing theory of topology of random graphs in padic mathematical physics, khrennikov, z. Nonexistence of arithmetic fake compact hermitian symmetric spaces of type other than an n. Padic analysis and mathematical physics weikung books. The goal of this paper is to report on a formalization of the padic numbers in the setting of the second authors univalent foundations program. Padicnumbersanintroductionuniversitext download free. Probably, you have never used any padic nonrational.
This site is like a library, use search box in the widget to get ebook that you want. Unlike previous similar approaches this connection is no longer an exact differential, instead allowing for a constant curvature and endowing qhd with intrinsic nonzero holonomy through the use of only singlevalued phasefactors. Padic analysis and mathematical physics weikung books on. This formalization, which has been verified in the coq proof assistant, provides an approach to the p adic numbers in constructive algebra and analysis. Regarding the second question what is the most convincing justification in physics that we need to work over the field of real or complex numbers i would like to quote freeman dyson in birds and frogs. And in the second section we show that pdf present a wave function using rescaled plasma dispersion function such that we define it.
The steady progress of physics requires for its theoretical formulation a mathematics that gets continually more advanced. One of its main achievements is a successful formulation and development of p adic and adelic quantum mechanics, which have complexvalued wave functions of p adic and adelic arguments, respectively. Analysis on the field of padic numbers padic analysis. Heegner points and sylvesters conjecture, with john voight, arithmetic geometry, clay mathematics proceedings, 8. Quantum ergodicity at a finite energy level tate, tatsuya, journal of the mathematical society of japan, 1999. Analysis on the field of padic numbers padic analysis and. The goal of this paper is to report on a formalization of the p adic numbers in the setting of the second authors univalent foundations program. For an overview of applications of p adic numbers in physics i would refer to the wikipedia and physics. The journal promotes dialog among specialists in these areas. In mathematics, padic analysis is a branch of number theory that deals with the mathematical analysis of functions of padic numbers the theory of complexvalued numerical functions on the padic numbers is part of the theory of locally compact groups. International conference on padic mathematical physics. Spin networks in quantum gravity lorente, miguel, journal of geometry and symmetry in physics, 2006.
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