Related papers: This Week's Finds in Mathematical Physics (1-50)
In Chapter 1 I present the current picture of the universe and briefly review the cosmological constant problem and some of the theories proposed to solve it. The following Chapters essentially contain the published papers with some…
Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must…
We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing $\mathcal{R}^5$ terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes.…
Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
In these notes we will review some approaches to 2+1 dimensional gravity and the way it is coupled to point-particles. First we look into some exact static and stationary solutions with and without cosmological constant. Next we study the…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
Modern material science has been revolutionized by the discovery of novel topological states of quantum matter, which sheds new lights on solving long-standing scientific challenges. However, the exotic quantum phenomena are typically…
This lecture consists of two parts. The first is a (totally unsystematic) survey of some of the high points in the evolution of gravity and its successors, primarily in the course of the past century. The second summarizes some new work on…
We present the summary of the general discussion on the probabilistic foundations of quantum theory that took place during the round table at the Int. Conf. "Foundations of Probability and Physics", V\"axj\"o, Sweden-2000. It is possible to…
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
In this article it is reported a formulation of the solenoidal nature of quantum electronic currents at the nanoscale whose divergence is expressed as the coupling of a magnetic field, interacting with a quantum body, and a weighted Cern…
We study the mathematical foundations of physics. We reconstruct textbook quantum theory from a single symmetric monoidal functor $GNS : \mathbf{Phys} \longrightarrow \ast\mathbf{Mod}$, based on the Gelfand-Naimark-Segal construction and…
This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational…
The present thesis deals with some properties of classical and quantum scalar fields in an inhomogeneous and/or time-dependent background, focusing on models where the latter can be described as a curved space-time with an event horizon.…
The first free comprehensive textbook on quantum (and classical) field theory. The approach is pragmatic, rather than traditional or artistic: It includes practical techniques, such as the 1/N expansion (color ordering) and spacecone…
This is the Preface to the special issue of 'International Journal of Geometric Methods in Modern Physics', v.3, N.1 (2006) dedicated to the 50th aniversary of gauge gravitation theory. It addresses the geometry underlying gauge gravitation…
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory…