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Branko Dragovich

Publications and source records attributed to Branko Dragovich.

At least 37 records · Page 2Linked to original sources
arXiv2012

p-Adic Structure of the Genetic Code

The genetic code is connection between 64 codons, which are building blocks of the genes, and 20 amino acids, which are building blocks of the proteins. In addition to coding amino acids, a few codons code stop signal, which is at the end of genes, i.e. it terminates process of protein synthesis. This article is a review of simple modelling of the genetic code and related subjects by concept of p-adic distance. It also contains some new results. In particular, the article presents appropriate structure of the codon space, degeneration and possible evolution of the genetic code. p-Adic modelling of the genetic code is viewed as the first step in further application of p-adic tools in the information sector of life science.

q-bio.OT↗
arXiv2010

Path Integrals for Quadratic Lagrangians on p-Adic and Adelic Spaces

Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically and obtained expressions are generalized to any finite-dimensional spaces. These general formulas are presented in the form which is invariant under interchange of the number fields ${\mathbb R} \leftrightarrow {\mathbb Q}_p$ and ${\mathbb Q}_p \leftrightarrow {\mathbb Q}_{p'} \, ,\, p\neq p'$. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum phenomena.

math-ph↗
arXiv2010

Nonlocal Dynamics of p-Adic Strings

We consider the construction of Lagrangians that might be suitable for describing the entire $p$-adic sector of an adelic open scalar string. These Lagrangians are constructed using the Lagrangian for $p$-adic strings with an arbitrary prime number $p$. They contain space-time nonlocality because of the d'Alembertian in argument of the Riemann zeta function. We present a brief review and some new results.

hep-th↗
arXiv2009

Genetic Code and Number Theory

Living organisms are the most complex, interesting and significant objects regarding all substructures of the universe. Life science is regarded as a science of the 21st century and one can expect great new discoveries in the near futures. This article contains an introductory brief review of genetic information, its coding and translation of genes to proteins through the genetic code. Some theoretical approaches to the modelling of the genetic code are presented. In particular, connection of the genetic code with number theory is considered and the role of $p$-adic numbers is underlined.

q-bio.OT↗
arXiv2009

On p-Adic Sector of Adelic String

We consider construction of Lagrangians which are candidates for p-adic sector of an adelic open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and contain the Riemann zeta function with the d'Alembertian in its argument. In particular, we present a new Lagrangian obtained by an additive approach which takes into account all p-adic Lagrangians. The very attractive feature of this new Lagrangian is that it is an analytic function of the d'Alembertian. Investigation of the field theory with Riemann zeta function is interesting in itself as well.

hep-th↗
arXiv2009

Towards effective Lagrangians for adelic strings

p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these scalar field theories, obtained Lagrangians are also interesting in themselves.

hep-th↗
arXiv2008

Lagrangians with Riemann Zeta Function

We consider construction of some Lagrangians which contain the Riemann zeta function. The starting point in their construction is p-adic string theory. These Lagrangians describe some nonlocal and nonpolynomial scalar field models, where nonlocality is controlled by the operator valued Riemann zeta function. The main motivation for this research is intention to find an effective Lagrangian for adelic scalar strings.

hep-th↗
arXiv2008

Some Lagrangians with Zeta Function Nonlocality

Some nonlocal and nonpolynomial scalar field models originated from p-adic string theory are considered. Infinite number of spacetime derivatives is governed by the Riemann zeta function through d'Alembertian $\Box$ in its argument. Construction of the corresponding Lagrangians begins with the exact Lagrangian for effective field of p-adic tachyon string, which is generalized replacing p by arbitrary natural number n and then taken a sum of over all n. Some basic classical field properties of these scalar fields are obtained. In particular, some trivial solutions of the equations of motion and their tachyon spectra are presented. Field theory with Riemann zeta function nonlocality is also interesting in its own right.

hep-th↗
arXiv2008

Zeta Nonlocal Scalar Fields

We consider some nonlocal and nonpolynomial scalar field models originated from p-adic string theory. Infinite number of spacetime derivatives is determined by the operator valued Riemann zeta function through d'Alembertian $\Box$ in its argument. Construction of the corresponding Lagrangians L starts with the exact Lagrangian $\mathcal{L}_p$ for effective field of p-adic tachyon string, which is generalized replacing p by arbitrary natural number n and then taken a sum of $\mathcal{L}_n$ over all n. The corresponding new objects we call zeta scalar strings. Some basic classical field properties of these fields are obtained and presented in this paper. In particular, some solutions of the equations of motion and their tachyon spectra are studied. Field theory with Riemann zeta function dynamics is interesting in its own right as well.

hep-th↗
arXiv2007

Adeles in Mathematical Physics

Application of adeles in modern mathematical physics is briefly reviewed. In particular, some adelic products are presented.

math-ph↗
arXiv2007

p-Adic Modelling of the Genome and the Genetic Code

The present paper is devoted to foundations of p-adic modelling in genomics. Considering nucleotides, codons, DNA and RNA sequences, amino acids, and proteins as information systems, we have formulated the corresponding p-adic formalisms for their investigations. Each of these systems has its characteristic prime number used for construction of the related information space. Relevance of this approach is illustrated by some examples. In particular, it is shown that degeneration of the genetic code is a p-adic phenomenon. We have also put forward a hypothesis on evolution of the genetic code assuming that primitive code was based on single nucleotides and chronologically first four amino acids. This formalism of p-adic genomic information systems can be implemented in computer programs and applied to various concrete cases.

q-bio.OT↗
arXiv2007

p-Adic and Adelic Rational Dynamical Systems

In the framework of adelic approach we consider real and p-adic properties of dynamical system given by linear fractional map f (x) = (a x + b)/(c x + d), where a, b, c and d are rational numbers. In particular, we investigate behavior of this adelic dynamical system when fixed points are rational. It is shown that any of rational fixed points is p-adic indifferent for all but a finite set of primes. Only for finite number of p-adic cases a rational fixed point may be attractive or repelling. The present analysis is a continuation of the paper math-ph/0612058. Some possible generalizations are discussed.

math-ph↗
arXiv2007

p-Adic Degeneracy of the Genetic Code

Degeneracy of the genetic code is a biological way to minimize effects of the undesirable mutation changes. Degeneration has a natural description on the 5-adic space of 64 codons $\mathcal{C}_5 (64) = \{n_0 + n_1 5 + n_2 5^2 : n_i = 1, 2, 3, 4 \} ,$ where $n_i$ are digits related to nucleotides as follows: C = 1, A = 2, T = U = 3, G = 4. The smallest 5-adic distance between codons joins them into 16 quadruplets, which under 2-adic distance decay into 32 doublets. p-Adically close codons are assigned to one of 20 amino acids, which are building blocks of proteins, or code termination of protein synthesis. We shown that genetic code multiplets are made of the p-adic nearest codons.

q-bio.GN↗
arXiv2007

Zeta Strings

We introduce nonlinear scalar field models for open and open-closed strings with spacetime derivatives encoded in the operator valued Riemann zeta function. The corresponding two Lagrangians are derived in an adelic approach starting from the exact Lagrangians for effective fields of $p$-adic tachyon strings. As a result tachyons are absent in these models. These new strings we propose to call zeta strings. Some basic classical properties of the zeta strings are obtained and presented in this paper.

hep-th↗
arXiv2006

Linear Fractional p-Adic and Adelic Dynamical Systems

Using an adelic approach we simultaneously consider real and p-adic aspects of dynamical systems whose states are mapped by linear fractional transformations isomorphic to some subgroups of GL (2, Q), SL (2, Q) and SL (2, Z) groups. In particular, we investigate behavior of these adelic systems when fixed points are rational. It is shown that any of these rational fixed points is p-adic indifferent for all but a finite set of primes. Thus only for finite number of p-adic cases a rational fixed point may be attractive or repelling. It is also shown that real and p-adic norms of any nonzero rational fixed point are connected by adelic product formula.

math-ph↗
arXiv2006

Invariance in adelic quantum mechanics

Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-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.

hep-th↗
arXiv2006

A p-Adic Model of DNA Sequence and Genetic Code

Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are nucleotides, codons and genes. We show that a 5-adic model is appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance, is also suitable for genetic code and for a more advanced employment in genomics. We find that genetic code degeneracy is related to the p-adic distance between codons.

q-bio.GN↗