Related papers: Do bras and kets have dimensions?
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as…
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…
In this paper, we study the behavior of the eigenvalues of the one and two dimensions of q-deformed Dirac oscillator. The eigensolutions have been obtained by using a method based on the q-deformed creation and annihilation operators in…
We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring…
Embedding of the brane metric into Euclidean (2+4)-space is found. Brane geometry can be visualized as the surface of the hyper-sphere in six dimensions which 'radius' is governed by the cosmological constant. Minkowski space in this…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
This presentation is intended to give a flavour of the physics to be studied and discovered by exploiting the interface between string theory, M-theory and field theory provided by the dynamics of extended objects called `branes', and their…
We present a comprehensive formalism to derive precise expressions for the induced gravity of the braneworld, assuming the dynamics of the Dirac-Nambu-Goto type. The quantum fluctuations of the brane at short distances give rise to…
The 5d dilatonic gravity action with surface counterterms, motivated by the AdS/CFT correspondence and with contributions of brane quantum CFTs is considered with an AdS-like bulk. The role of quantum brane CFT consists in inducing…
The extra space paradigm plays a significant role in modern physics and in cosmology as the specific case. In this review, the relation between the main cosmological parameters - Planck mass and Cosmological constants - and a metric of…
A D-dimensional gravitational model with Gauss-Bonnet and cosmological term is considered. When ansatz with diagonal cosmological metrics is adopted, we overview recent solutions for zero cosmological term and find new examples of solutions…
The paper \cite{Dance0601} tentatively suggested a physical picture that might underlie string theories. The string parameters $\tau $ and $\sigma_i $ were interpreted as spacetime dimensions which a simple quantum mechanical observer can…
We study the cosmology of models with four space and one time dimension where our universe is a 3-brane and report a few results which extend existing work in several directions. Assuming a stable fifth dimension, we obtain a solution for…
Using a global superalgebra with 32 fermionic and 528 bosonic charges, many features of p-brane dualities and hidden dimensions are discussed.
Our primary focus is on the theory of skew braces, specifically exploring their connection with combinatorial solutions to the Yang-Baxter equation. Skew braces have recently emerged as intriguing algebraic structures, and their link to the…
Following is a collection of lecture notes on D-branes, which may be used by the reader as preparation for applications to modern research applications such as: the AdS/CFT and other gauge theory/geometry correspondences, Matrix Theory and…
What is the "right way" to define dimension? Mathematicians working in the early and middle $20$th-century formalized three intuitive definitions of dimension that all turned out to be equivalent on separable metric spaces. But were these…
(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of {\it (Bergmann) observable. This clarification leads to the proposal of a {\it main conjecture}…
It is usually assumed that a ket represents the state of an actually existing particle. But one can show there is no evidence for particles. The particle-like properties of mass, spin and charge, as well as particle-like trajectories, the…
Models with extra dimensions may give new effects visible at future experiments. In these models, bulk fields can develop localized corrections to their kinetic terms which can modify the phenomenological predictions in a sizeable way. We…