Related papers: p-Adic physics below and above Planck scales

String theory suggests modifications of our spacetime such as extra dimensions and the existence of a mininal length scale. In models with addidional dimensions, the Planck scale can be lowered to values accessible by future colliders.…

We derive supersymmetric quantum mechanics of n BPS objects with 3n position degrees of freedom and 4n fermionic partners with SO(4) R-symmetry. The potential terms, essential and sufficient for the index problem for non-threshold BPS…

We derive a power series formula for the $p$-adic regulator on the higher dimensional algebraic K-groups of number fields. This formula is designed to be well suited to computer calculations and to reduction modulo powers of $p$. In…

The traditional formulation of the ultimate goal of physics (in the narrower sense of axiomatic theory) involves the derivation of physical laws from first principles. Though, such option doesn't make things easier since the task of the…

Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…

We point out the conceptual problems related to the application of the standard notion of mass to quarks and recall the arguments that there should be a close connection between the properties of elementary particles and the arena used for…

In 2014, Darmon and Rotger defined the Garrett-Rankin triple product $p$-adic $L$- function and related it to the image of certain diagonal cycles under the $p$-adic Abel- Jacobi map. We introduce a new $p$-adic triple symbol based on this…

Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…

I propose that physical theories defined over finite places (including $p$-adic fields) can be used to construct conventional theories over the reals, or conversely, that certain theories over the reals "decompose" over the finite places,…

One of the deepest insights from the general theory of relativity is the relational nature of spacetime. While it is a generally agreed on that the nature of spacetime must be drastically different at the Planck scale, it has been a common…

We define the resultant of two power series with coefficients in the ring of integers of a $p$-adic field. In order to do this, we prove a universal version of the Weierstrass preparation theorem.

Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption…

Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree--like behavior…

We argue that the hierarchy problem of the standard model of particle physics can be solved by adding a state-dependent term to the Higgs sector. We present an example of a scalar field with a Higgs-like potential with an additional term…

We investigate a gravitational model based on local Lorentz invariance and general coordinate invariance. The model incorporates classical scale invariance, which forbids dimensionful parameters, and the irreversible vierbein postulate,…

Theories in which gravity is weaker on cosmological scales have been proposed to explain the observed acceleration of the universe. The nonlinear regime in such theories is not well studied, though it is likely that observational tests of…

We propose higher-order generalizations of Jacobsthal's $p$-adic approximation for binomial coefficients. Our results imply explicit formulae for linear combinations of binomial coefficients $\binom{ip}{p}$ ($i=1,2,\dots$) that are…

The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…

In this article we construct a large class of interacting Euclidean quantum field theories, over a p-adic space time, by using white noise calculus. We introduce p-adic versions of the Kondratiev and Hida spaces in order to use the Wick…

We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…