Related papers: Pure shape dynamics: General framework
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…
Recent studies have highlighted the sensitivity of active matter to boundaries and their geometries. Here we develop a general theory for the dynamics and statistics of active particles on curved surfaces and illustrate it on two examples.…
The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…
The idea of defining a gravitational singularity as an obstruction to the dynamical evolution of a test field (described by a PDE) rather than the dynamical evolution of a particle (described by a geodesics) is explored. In particular, the…
This article contains our comments and views on the status of the current understanding of phase transitions in systems with only hard-core interactions, based on our work in this area. The equation of state for the hard sphere gas in…
The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive…
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…
The notions of pure states and inherent structures, i.e. stable configurations against 1-spin flip are discussed. We explain why these different concepts accidentally coincide in mean-field models with infinite connectivity and present an…
The concept of a physical space, which actualizes Euclidean geometry, is not confined to the statics of solids but extensible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of…
We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently-introduced Generalized Hydrodynamics (GHD). The method allows to…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
We attempt to reveal the geometry, emerged from the entanglement structure of any general $N$-party pure quantum many-body state by representing entanglement entropies corresponding to all $2^N $ bipartitions of the state by means of a…
Kendall's Similarity Shape Theory for constellations of points in the carrier space $\mathbb{R}^n$ was developed for use in Probability and Statistics. It was subsequently shown to reside within (Classical and Quantum) Mechanics'…
In this paper, we aim to model 3D scene geometry, appearance, and physical information just from dynamic multi-view videos in the absence of any human labels. By leveraging physics-informed losses as soft constraints or integrating simple…
We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity…
It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial derivative of the state. This higher spatial derivative (termed…
This article examines how the physical presence of field energy and particulate matter could influence the topological properties of space time. The theory is developed in terms of vector and matrix equations of exterior differential forms.…
New construction of 4D dynamical space-time (DST) has been proposed in the framework of unification of relativity and quantum theory. Such unification is based solely on the fundamental notion of generalized coherent state (GCS) of N-level…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive…