179 research outputs found
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.Comment: 10 pages. Presented at the 2nd Conf. on SFT and Related Topics,
Moscow, April 2009. Submitted to Theor. Math. Phy
Nonlocal Dynamics of p-Adic Strings
We consider the construction of Lagrangians that might be suitable for
describing the entire -adic sector of an adelic open scalar string. These
Lagrangians are constructed using the Lagrangian for -adic strings with an
arbitrary prime number . 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.Comment: 8 page
p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency
The classical and quantum formalism for a p-adic and adelic harmonic
oscillator with time-dependent frequency is developed, and general formulae for
main theoretical quantities are obtained. In particular, the p-adic propagator
is calculated, and the existence of a simple vacuum state as well as adelic
quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical
phase are noted.Comment: 10 page
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.Comment: 13 pages, 2 table
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
in its argument. Construction of the corresponding Lagrangians L starts
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. 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.Comment: 13 pages, submitted to Theoretical and Mathematical Physic
Functional Classical Mechanics and Rational Numbers
The notion of microscopic state of the system at a given moment of time as a
point in the phase space as well as a notion of trajectory is widely used in
classical mechanics. However, it does not have an immediate physical meaning,
since arbitrary real numbers are unobservable. This notion leads to the known
paradoxes, such as the irreversibility problem. A "functional" formulation of
classical mechanics is suggested. The physical meaning is attached in this
formulation not to an individual trajectory but only to a "beam" of
trajectories, or the distribution function on phase space. The fundamental
equation of the microscopic dynamics in the functional approach is not the
Newton equation but the Liouville equation for the distribution function of the
single particle. The Newton equation in this approach appears as an approximate
equation describing the dynamics of the average values and there are
corrections to the Newton trajectories. We give a construction of probability
density function starting from the directly observable quantities, i.e., the
results of measurements, which are rational numbers.Comment: 8 page
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page
Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time
It is known that no length or time measurements are possible in sub-Planckian
regions of spacetime. The Volovich hypothesis postulates that the
micro-geometry of spacetime may therefore be assumed to be non-archimedean. In
this letter, the consequences of this hypothesis for the structure,
classification, and conformal symmetry of elementary particles, when spacetime
is a flat space over a non-archimedean field such as the -adic numbers, is
explored. Both the Poincar\'e and Galilean groups are treated. The results are
based on a new variant of the Mackey machine for projective unitary
representations of semidirect product groups which are locally compact and
second countable. Conformal spacetime is constructed over -adic fields and
the impossibility of conformal symmetry of massive and eventually massive
particles is proved
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