320 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
Petrology and Structure of the Cascade River Schist, in the Sibley Creek Area, Northern Cascades, Washington
The focus of this study is on the protolith types, metamorphism and structure of the Cascade River Schist in the Sibley Creek area of the North Cascades, Washington. The two general lithologic packages are an arc and ocean floor unit termed the Cascade River and Napeequa units, respectively, by Tabor and others (in press). The Cascade River unit has a recognizable stratigraphy which is inverted and repeated across strike from the southwestern to northeastern sides of the field area, apparently as a result of macroscopic synclinal folding. The Napeequa unit lies on top of the Cascade River unit, in the center of the sync line, probably as a result of thrust faulting.
Metamorphic zones and facies in the field area increase from the biotite zone of the greenschist facies, west of the Le Conte fault, to the garnet and staurolite-kyanite zones of the epidote amphibolite facies east of the fault. The greenschist facies is estimated to be metamorphosed at pressures of 3-5 Kb, and temperatures of 450-500 C and the amphibolite facies at 8-10 kb and 600-700 C. Structural control of the greenschist-anphibolite facies transition by the Le Conte fault is suggested by the first appearance of the garnet and oligoclase with the fault, as well as a P-T differential across the fault, which suggests considerable dip-slip displacement across the fault.
The metamorphic structures in the field area consist of: 1) a synmetamorphic first deformation characterized by steeply dipping S-tectonites containing weakly defined down-dip mineral lineations and flattened conglomerate clasts, and 2) a late-metamorphic and commonly retrogressive second deformation characterized by steeply dipping L-Stectonites containing a sub-horizontal stretching lineation, prolate spheroidal conglomerate clasts, and dextral kinematic indicators. Later post-metamorphic structures are folds and faults related to forceful enplacement of the 73 Ma Hidden Lake pluton and Eocene strike-slip offset along the Le Conte fault
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
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
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
Mumford dendrograms and discrete p-adic symmetries
In this article, we present an effective encoding of dendrograms by embedding
them into the Bruhat-Tits trees associated to -adic number fields. As an
application, we show how strings over a finite alphabet can be encoded in
cyclotomic extensions of and discuss -adic DNA encoding. The
application leads to fast -adic agglomerative hierarchic algorithms similar
to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint
of -adic geometry, to encode a dendrogram in a -adic field means
to fix a set of -rational punctures on the -adic projective line
. To is associated in a natural way a
subtree inside the Bruhat-Tits tree which recovers , a method first used by
F. Kato in 1999 in the classification of discrete subgroups of
.
Next, we show how the -adic moduli space of
with punctures can be applied to the study of time series of
dendrograms and those symmetries arising from hyperbolic actions on
. In this way, we can associate to certain classes of dynamical
systems a Mumford curve, i.e. a -adic algebraic curve with totally
degenerate reduction modulo .
Finally, we indicate some of our results in the study of general discrete
actions on , and their relation to -adic Hurwitz spaces.Comment: 14 pages, 6 figure
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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