Related papers: Complex geometry and fundamental physical law
We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a…
We investigate, in the framework of a recently introduced new class of invariant geometrical scalar-tensor theory of gravity, the possibility that a viscous dark fluid can be described in a unified manner by a single scalar field. Thus we…
We develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising components of different topological…
This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable…
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofold formulation of the study of particle interactions and…
In a class of generalized gravity theories with general couplings between the scalar field and the scalar curvature in the Lagrangian, we can describe the quantum generation and the classical evolution of both the scalar and tensor…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
Scalar-tensor theories of gravity that embrace conformal coupling to the scalar curvature are the focal point of cosmology on discussions of inflation and late-time accelerating universe. Although there exists a stringent nucleo-synthesis…
The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy--momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
Novelty alone is not sufficient for innovation. For new ideas and products to thrive, they must find their place within the existing societal fabric, such as institutions, conventions, and infrastructures that have been built over time.…
We present a detailed study of the curvature and symplectic asphericity properties of symmetric products of surfaces. We show that these spaces can be used to answer nuanced questions arising in the study of closed Riemannian manifolds with…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
Ten-dimensional models, arising from a gravitational action which includes terms up to the fourth order in curvature tensor, are discussed. The spacetime consists of one timelike dimension and two maximally symmetric subspaces, filled with…
Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…
We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally…