共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we study some p-adic invariant and fermionic p-adic integrals on ?p associated with trigonometric functions. By using these p-adic integrals we represent several trigonometric functions as a formal power series involving either Bernoulli or Euler numbers. In addition, we obtain some identities relating various special numbers like zigzag, some ‘trigonometric’, Bernoulli, Euler numbers, and Euler numbers of the second kind. 相似文献
2.
Branko Dragovich 《Czechoslovak Journal of Physics》2006,56(10-11):1137-1142
Adelic quantum mechanics is form-invariant under an interchange of real andp-adic number fields as well as rings ofp-adic integers. We also show that in adelic quantum mechanics Feynman’s path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers. 相似文献
3.
《Physics letters. [Part B]》1988,214(3):339-349
Different possibilities to construct p-adic superstring amplitudes are discussed. To describe one of these possibilities we formulate a p-adic generalization of the conformal technique. p-adic conformal rules allow us to explicitly write down the amplitude for massless particles. They do not have the form of the usual kinematical factors multiplied by the p-adic modification of the usual amplitudes. The relation between open and closed p-adic superstring amplitudes is discussed. 相似文献
4.
5.
《Physics letters. [Part B]》1988,201(3):306-310
The field of p-adic complex numbers has a much richer structure than the field of ordinary complex numbers. This is used in order to extend the powerful tools of two-dimensional conformal field theories to higher dimensions. It is thus proposed that critical systems in more than two dimensions be first studied over the p-adics and then, if possible, recovered by the adelic construction. It is further argued that this higher-dimensional p-adic analyticity may be the key to membrane theories. A natural ansatz for three-brane tree-scattering amplitudes, where p-adic analyticity is instrumental, is given as an explicit example. 相似文献
6.
We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of Calabi–Yau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on p-adic cohomology. We discuss a p-adic interpretation of the conjecture about integrality of Gopakumar–Vafa invariants. 相似文献
7.
We study a class of nonlocal systems which can be described by a local scalar field diffusing in an auxiliary radial dimension. As examples p-adic, open and boundary string field theory are considered on Minkowski, Friedmann–Robertson–Walker and Euclidean metric backgrounds. Starting from distribution-like initial field configurations which are constant almost everywhere, we construct exact and approximate nonlocal solutions. The Euclidean p-adic lump is interpreted as a solitonic brane, and the Euclidean kink of supersymmetric open string field theory as an instanton. Some relations between solutions of different string theories are highlighted also thanks to a reformulation of nonlocal systems as fixed points in a renormalization group flow. 相似文献
8.
《Physics letters. [Part B]》1988,215(2):260-264
We stress the use of modular forms in obtaining adelic formulations of field theoretical problems. Supersymmetry then appears in the real section with thep-adic parts as arithmetic completions. We first show how the Casimir effect is naturally interpreted adelically and the coefficient arises from dimensional analysis. We then suggest looking at the zero slope limit of adelic string amplitudes. Finally, we interpret the rationality of the critical exponents for conformal field theories in terms of p-adic analyticity of correlation functions. 相似文献
9.
《Physics letters. [Part B]》1987,199(2):186-190
A full set of factorized, dual, crossing-symmetric tree-level N-point amplitudes is constructed for non-archimedean closed strings. Momentum components and space-time coordinates are still valued in the field of real numbers, quantum amplitudes in that of complex numbers. It is the world-sheet parameters, which one integrates over, that become p-adic. For the closed string the parameters are valued in quadratic extensions of the fields Qp of p-adic numbers (p = prime). 相似文献
10.
《Physica A》1995,215(4):577-587
During the last years large interest was shown in p-adic quantum models (especially, in string theory). As usual, new physical models generate new mathematical methods. In our case a new type of stochastics, p-adic stochastics, was arisen inside p-adic quantum physics. We apply this stochastics to propose a justification of the Einstein-Podolsky-Rosen theory of hidden variables, which was in large contradiction with the Bell type inequality. Our main result is the following: if we consider a p-adic probability distribution of hidden variables, then there are no problems with Bell's inequality. 相似文献
11.
《Physics letters. [Part B]》1988,209(4):445-450
Some remarkable properties of the adelic string amplitudes for the physical domain of the Mandelstam variables are considered. It is shown that the p-adic four-point functions are always negative. Also, a formula is obtained which expresses the product of moduli of the p-adic amplitudes and the Veneziano amplitude in terms of the zeta functions. This product is absolutely convergent unlike the divergent product of these amplitudes without moduli, recently considered by Freund and Witten. Using the zeta function representation, p-adic interpolation of the Veneziano amplitude is also considered. 相似文献
12.
It is shown that some Gaussian and non-Gaussian scaling invariant p-adic field theories are invariant under the group of transformations which conserve the p-adic norm of the cross-ratio of any four points. This group can be treated as a p-adic conformal group. It has a continuation on the Bruhat—Tits tree, being an automorphism group of that tree. The models also have tree continuation, in particular the binary correlation function of the tree model is a spherical function. 相似文献
13.
The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which
the exponents have a cubic singularity, arising from the coalescence of two saddle points in an asymptotic analysis. Pearcey
functions are given by integrals in which the exponents have a quartic singularity, arising from the coalescence of three
saddle points. A corresponding Pearcey kernel appears in a random matrix model and a Brownian motion model for a fixed time. This paper derives an extended Pearcey kernel by scaling the Brownian motion model at several times, and a system of partial differential equations whose solution determines
associated distribution functions. We expect there to be a limiting nonstationary process consisting of infinitely many paths,
which we call the Pearcey process, whose space-time correlation functions are expressible in terms of this extended kernel. 相似文献
14.
An extension of the formalism of quantum mechanics to the case where the canonical variables are valued in a field ofp-adic numbers is considered. In particular the free particle and the harmonic oscillator are considered. In classicalp-adic mechanics we consider time as ap-adic variable and coordinates and momentum orp-adic or real. For the case ofp-adic coordinates and momentum quantum mechanics with complex amplitudes is constructed. It is shown that the Weyl representation is an adequate formulation in this case. For harmonic oscillator the evolution operator is constructed in an explicit form. For primesp of the form 4l+1 generalized vacuum states are constructed. The spectra of the evolution operator have been investigated. Thep-adic quantum mechanics is also formulated by means of probability measures over the space of generalized functions. This theory obeys an unusual property: the propagator of a massive particle has power decay at infinity, but no exponential one. 相似文献
15.
In this paper, we study the chaotic behavior of the p-adic Ising-Potts mapping associated with the p-adic Ising model on the Cayley tree. As an application of this result, we are able to show the existence of periodic (with any period) p-adic quasi Gibbs measures for the model. 相似文献
16.
A. Torre 《Applied physics. B, Lasers and optics》2010,99(4):775-799
We present a comparison of the evolution features, in terms of the intensity moments up to the second order, of what are here
referred to as Ai-Gauss and Bi-Gauss
wave functions, which originate from source functions consisting of Gaussian-like modulated Airy patterns (of the first and second kind).
Both have already been considered in the literature, the former being in particular analysed in detail. A paraxial-optics
oriented view of the cos-like Airy–Hardy integrals, which stand out as a generalization of the well-known Airy integral, is
also developed. 相似文献
17.
18.
《Physics letters. [Part B]》1988,213(3):260-262
For the p-adic bosonic string, a simple regularization procedure is applied to the four-particle adelic formula. Arguments that have been made against the validity of the five-particle adelic formula are criticised. 相似文献
19.
Yu. A. Glukhov V. P. Rudakov K. P. Artemov A. S. Demyanova A. A. Ogloblin S. A. Goncharov A. Izadpanakh 《Physics of Atomic Nuclei》2007,70(1):1-7
An investigation of refractive effects in heavy-ion scattering is continued. For the elastic scattering of 16O nuclei on a 13C target at E(16O) = 132 MeV, the differential cross sections are measured for the first time in addition to previous measurements for targets from the carbon isotopes 12C and 14C. Airy structures that are similar for all isotopes and which have close cross sections are observed and are found to be consistent with the energy systematics of Airy minima that were obtained previously. The volume integrals of the real and imaginary parts of the optical potentials found in the present study are nearly identical for all of the isotopes considered here and are also in good agreement with the systematics obtained previously. 相似文献
20.
Farrukh Mukhamedov 《Mathematical Physics, Analysis and Geometry》2013,16(1):49-87
In the present paper, we study a new kind of p-adic measures for q?+?1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition. 相似文献