Related papers: Dimensional Reduction without Extra Continuous Dim…
We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver…
We consider the dilaton gravity models derived by reductions of generalized theories of gravity and study one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully…
A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model…
Exotic duality suggests a link between gauge theories for differential p-forms and tensor fields of mixed symmetry [D-2,p] in D spacetime dimensions. On the other hand, standard Hodge duality relates p-form to (D-p-2)-form gauge potentials…
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…
Models that involve extra dimensions have introduced completely new ways of looking up on old problems in theoretical physics. The aim of the present notes is to provide a brief introduction to the many uses that extra dimensions have found…
We study, using the example of general covariance, to what extent a would-be non-abelian extension of free field abelian gauge theory can be helped by a field redefinition; answer - not much! However, models resulting from dimensional…
In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…
Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the…
A discrete field formalism exposes the physical meaning and origins of gauge fields, their symmetries and singularities. They represent a lack of a stricter field-source coherence.
Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this…
We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
In this paper we provide an alternative reduction theory for real, binary forms with no real roots. Our approach is completely geometric, making use of the notion of hyperbolic center of mass in the upper half-plane. It appears that our…
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles…
This paper describes and proves a canonical procedure to decouple perturbations and optimize their gauge around backgrounds with one non-homogeneous dimension, namely of co-homogeneity 1, while preserving locality in this dimension.…
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…