Related papers: Categories and the Foundations of Classical Field …
Subject of this article is the relationship between modern cosmology and fundamental physics, in particular general relativity as a theory of gravity on one side, together with its unique application in cosmology, and the formation of…
This review summarizes Effective Field Theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described, and explicitly…
We define the Grothendieck-Witt category over a fixed ground ring. In order to study the structure of this category, we introduce the general theory of Gysin functors and their associated categories of correspondences. The latter…
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy…
I consider the sense in which teleparallel gravity and symmetric teleparallel gravity may be understood as gauge theories of gravity. I first argue that both theories have surplus structure. I then consider the relationship between…
We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR…
Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974)) generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
Gravitational self-interactions are assumed to be determined by the covariant derivative acting on the Riemann-Christoffel field strength. Once imposed on a metric theory, this Yang-Mills gauge constraint extends the equality of…
The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
The theory of gravitation field within the special theory of relativity is analyzed.
I discuss the ontological assumptions and implications of General Relativity. I maintain that General Relativity is a theory about gravitational fields, not about space-time. The latter is a more basic ontological category, that emerges…
There is a venerable position in the philosophy of space and time that holds that the geometry of spacetime is conventional, provided one is willing to postulate a "universal force field". Here we ask a more focused question, inspired by…
A special-relativistic scalar-vector theory of gravitation is presented which mimics an important class of solutions of Einstein's gravitational field equations. The theory includes solutions equivalent to Schwarzschild, Kerr,…
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
From a gauge $SU(2,2|2)$ model with broken supersymmetry, we construct an action for $SU(2)\times U(1)$ Yang-Mills theory coupled to gravity and matter. The connection components for AdS boosts and special conformal translations are…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.