Related papers: On 4-dimensional Lorentz-structures, Dark energy a…
We discovered that abnormal Mott physics can emerge even in weakly correlated 4f fermions through their interplay with topological singularity. Employing ab initio many-body perturbation theory combined with dynamical mean field theory, we…
The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or…
Time is the odd dimension out: Unlike space, it follows the arrow of time, forbidding back-reflections and requiring momentum yet not energy conservation. Tailored temporal variations manipulate momentum bands and engineer waves in time. We…
Recent work on exotic smooth R^4's, i.e. topological R^4 with exotic differential structure, shows the connection of 4-exotics with the codimension-1 foliations of $S^{3}$, SU(2) WZW models and twisted K-theory $K_{H}(S^{3})$, $H\in…
In this paper we compute the corrections to the black-body force (BBF) potential due to spacetime geometry and topology. This recently discovered attractive force on neutral atoms is caused by the thermal radiation emitted from black bodies…
Studying spacetimes with continuous symmetries by dimensional reduction to a lower dimensional spacetime is a well known technique in field theory and gravity. Recently, its use has been advocated in numerical relativity as an efficient…
In this first paper, we demonstrate a theorem that establishes a first step toward proving a necessary topological condition for the occurrence of first or second order phase transitions: we prove that the topology of certain submanifolds…
Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing…
The local and global properties of the Goetz thick plane domain wall space-time are studied. It is found that when the surface energy of the wall is greater than a critical value $\sigma_{c}$, the space-time will be closed by intermediate…
I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are…
For homogeneous higher gradient elasticity models we discuss frame-indifference and isotropy requirements. To this end, we introduce the notions of local versus global SO(3)-invariance and identify frame-indifference (traditionally) with…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
We study wormhole geometries embedded in an expanding universe within a four-scalar non-linear $\sigma$ model, where the target-space metric is identified with the spacetime Ricci tensor. In this framework, wormholes can remain stable even…
This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing…
A short survey of exotic smooth structutes on 4-manifolds is given with a special emphasis on the corresponding cork structures. Along the way we discuss some of the more recent results in this direction, obtained jointly with R.Matveyev,…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
In the context of N=4 supergravity in four dimensions, we present an exact classical solution that leads to spacetime-dependent electromagnetic couplings and discuss the ensuing Lorentz-violating effects. We comment briefly on experimental…
Energy minimizing harmonic maps between manifolds are known to be smooth outside a rectifiable set of codimension $3$, called the singular set. The possibility that this set is not a manifold, but has arbitrarily many small gaps in it, is…
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…
We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is…