• Corpus ID: 16499990

Some Lagrangians with Zeta Function Nonlocality

  title={Some Lagrangians with Zeta Function Nonlocality},
  author={Branko Dragovich},
  journal={arXiv: High Energy Physics - Theory},
  • B. Dragovich
  • Published 4 May 2008
  • Mathematics
  • arXiv: High Energy Physics - Theory
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… 


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

The p-adic sector of the adelic string

We study the construction of Lagrangians that can be considered the Lagrangians of the p-adic sector of an adelic open scalar string. Such Lagrangians are closely related to the Lagrangian for a

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

Nonlocal Field Theory and p-Adic Strings

We consider nonlocal fleld theory aspects of some p-adic strings. In particular, Lagrangians of p-adic open scalar strings, for single p as well as for collective primes p, are reviewed. They contain

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

The Fibonacci’s zeta function. Mathematical connections with some sectors of String Theory

In this paper we have described, in the Section 1, the Fibonacci’s zeta function and the Euler-Mascheroni constant and in the Section 2, we have described some sectors of the string theory: zeta

On the Riemann Hypothesis. Formulas explained - ψ(x) as equivalent RH. Mathematical connections with “Aurea” section and some sectors of String Theory.

In this work the authors will examine the themes of RH, equivalent RH and GRH. The authors will explain some formulas and will show other special functions that are usually introduced with the PNT

From $p$-Adic to Zeta Strings

This article is related to construction of zeta strings from $p$-adic ones. In addition to investigation of $p$-adic string for a particular prime number $p$, it is also interesting to study

Links between string theory and the Riemann’s zeta function

There is a connection between string theory and the Riemann’s zeta function: this is an interesting way,because the zeta is related to prime numbers and we have seen on many occasions how nature

Dynamics with infinitely many derivatives: variable coefficient equations

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory



Zeta-nonlocal scalar fields

AbstractWe consider some nonlocal and nonpolynomial scalar field models originating from p-adic string theory. An infinite number of space-time derivatives is determined by the operator-valued

Exact noncommutative solitons in p-adic strings and BSFT

The tachyon field of p-adic string theory is made noncommutative by replacing ordinary products with noncommutative products in its exact effective action. The same is done for the boundary string

Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field

Nonlinear Dynamics Equation in p-Adic String Theory

We investigate nonlinear pseudodifferential equations with infinitely many derivatives. These are equations of a new class, and they originally appeared in p-adic string theory. Their investigation

Bouncing and accelerating solutions in nonlocal stringy models

A general class of cosmological models driven by a nonlocal scalar field inspired by string field theories is studied. In particular cases the scalar field is a string dilaton or a string tachyon. A

On Exact Tachyon Potential in Open String Field Theory

In these notes we revisit the tachyon lagrangian in the open string field theory using background independent approach of Witten from 1992. We claim that the tree level lagrangian (up to second order

Route to nonlocal cosmology

An analytic approach to phenomenological models inspired by cubic string field theory is introduced and applied to some examples. We study a class of actions for a minimally coupled, homogeneous

p-Adic and Adelic Quantum Mechanics

p-Adic mathematical physics emerged as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale. One of its main achievements is a successful

Adelic Harmonic Oscillator

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the

Zeta Strings

We introduce nonlinear scalar field models for open and open-closed strings with spacetime derivatives encoded in the operator val-ued Riemann zeta function. The corresponding two Lagrangians are