Related papers: Lagrangians with Riemann Zeta Function
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.…
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…
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…
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…
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…
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…
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 collective effects taking into account all primes…
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 theories. This approach is motivated by the…
This thesis aims to study nonlocal Lagrangians with a finite and an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for…
This article aims to study non-local Lagrangians with an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for them. In…
The spectral zeta functions have been found many application in several branches of modern physics, including the quantum field theory, the string theory and the cosmology. In this paper, we shall consider the spectral zeta functions and…
We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a…
We give an explicit formula for the subalgebra zeta function of a general 3-dimensional Lie algebra over the p-adic integers $\mathbb{Z}_p$. To this end, we associate to such a Lie algebra a ternary quadratic form over $\mathbb{Z}_p$. The…
This is an integrated part of our Geo-Arithmetic Program. In this paper we introduce and hence study non-abelian zeta functions and more generally non-abelian $L$-functions for number fields, based on geo-arithmetical cohomology,…
In a recent paper Z\'u\~niga-Galindo and the author begun the study of the local zeta functions for Laurent polynomials. In this work we continue this study by giving a very explicit formula for the local zeta function associated to a…
We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis formulated in terms of integrals of the…
We obtain explicit expressions for the determinants of the Laplacians on zero and one forms for an infinite class of three dimensional lens spaces $L(p,q)$. These expressions can be combined to obtain the Ray-Singer torsion of these lens…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
The purpose of this article is to initiate a study of a class of Lorentz invariant, yet tractable, Lagrangian Field Theories which may be viewed as an extension of the Klein-Gordon Lagrangian to many scalar fields in a novel manner. These…
Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property. This notion has its roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics, in the theory of…