Related papers: Do bras and kets have dimensions?
We analyze brane configurations corresponding to non-trivial six dimensional fixed points. Several results previously obtained from a pure field theoretical analysis are rederived in the brane language.
We consider evolution of compact extra dimensions in cosmology and try to see whether wrapped branes can prevent the expansion of the internal space. Some difficulties of Brandenberger and Vafa mechanism for decompactification are pointed…
A pure Dirac's method for abelian and non-abelian massive theories in three dimensions is performed. Our analysis is developed on the extended phase space reporting the relevant structure of the theories, namely, the extended action, the…
Our main goal in this long survey article is to provide an overview of the theory of complex fractal dimensions and of the associated geometric or fractal zeta functions, first in the case of fractal strings (one-dimensional drums with…
There have been several attempts in recent years to extend the notions of symplectic and Poisson structures in order to create a suitable geometrical framework for classical field theories, trying to achieve a success similar to the use of…
I address the issue of spacetime dimensionality within Kaluza-Klein theories and theories with large extra dimensions. I review the arguments explaining the dimensionality of the universe, within the framework of string gas cosmology and…
Extra-dimensions are a common topic in popular descriptions of theoretical physics with which undergraduate student most often have no contact in physics courses. This paper shows how students could be introduced to this topic by presenting…
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states:…
We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as the supergeometric setting. The review is supplemented by a…
The Jackiw-Teitelboim model written as a BF theory in two dimensions is analyzed by using the Dirac's and Faddeev-Jackiw formalism. The analysis consists in finding the full structure of the constraints, the gauge transformations, the…
We give tight bounds on the relation between the primal and dual of various combinatorial dimensions, such as the pseudo-dimension and fat-shattering dimension, for multi-valued function classes. These dimensional notions play an important…
Noticing that the point-form approach referred to in many recent works implies physics described on hyperplanes, an approach inspired from Dirac's one, which involves a hyperboloid surface, is presented. A few features pertinent to this new…
We study the emergence of Dirac fermionic field in the low energy description of non-relativistic dynamical models on graphs admitting continuum limit. The Dirac fermionic field appears as the effective field describing the excitations…
The smallness of the cosmological constant is one of the basic problems in particle physics and cosmology. Various attempts have been made to explain this mystery, but no satisfactory solution has been found yet. The appearance of extra…
The aim of this talk is to provide non-experts with a brief and elementary introduction on the field of extra dimensions. The main motivation for extra dimensions relies on the more fundamental string theories that predict ten (or eleven)…
Higher-dimensional theories with time-like and space-like extra dimensions are compared both from the conceptual and from the phenomenological points of view. In this context causality and unitarity are discussed. It is shown that…
In a companion paper, we introduced a notion of multi-Dirac structures, a graded version of Dirac structures, and we discussed their relevance for classical field theories. In the current paper we focus on the geometry of multi-Dirac…
QED in 2+1 dimensions has long been studied as a model field theory which exhibits both asymptotic freedom and non-trivial IR behaviour. There is also a trend towards viewing it as a candidate low energy effective theory for the pseudogap…
Objects dual to graded algebras are subproduct systems of linear spaces, a purely algebraic counterpart of a notion introduced recently in the context of noncommutative dynamics (Shalit and Solel, Bhat and Mukherjee). A complete…
The most fundamental characteristics of a physical system can often be deduced from its behaviour under discrete symmetry transformations such as time reversal, parity and chirality. Here we review basic symmetry properties of the…