Related papers: Notes on Global Stress and Hyper-Stress Theories
Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
We briefly review the description of the internal sector of supergravity theories in the language of generalised geometry and how this gives rise to a description of supersymmetric backgrounds as integrable geometric structures. We then…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
This paper concerns the quantisation of a rigid body in the framework of ``covariant quantum mechanics'' on a curved spacetime with absolute time. The basic idea is to consider the multi-configuration space, i.e. the configuration space for…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
We study the contribution to the entanglement entropy of (2+1)-dimensional conformal field theories coming from a sharp corner in the entangling surface. This contribution is encoded in a function $a(\theta)$ of the corner opening angle,…
Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniform local nature, are obtained for the existence…
The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method for mixed elasticity. As the name suggests, the tangential component of the displacement vector as well as the normal-normal component of the stress…
The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments…
Tangent stabilised large strain isotropic elasticity was recently proposed by Poya et al. [1] wherein by working directly with principal stretches the entire eigenstructure of constitutive and geometric/initial stiffness terms were found in…
We study the dynamics generated by return maps associated with nested convex bodies and growing domains satisfying the geometric normal property in the plane. These maps are defined by transporting boundary points along normal directions to…
For the case of a first-class constrained system with an equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations $G$ is…
The configuration-space topology in canonical General Relativity depends on the choice of the initial data 3-manifold. If the latter is represented as a connected sum of prime 3-manifolds, the topology receives contributions from all…
The conditions under which a given manifold $M$ may be given a tangent bundle or a cotangent bundle structure are analyzed. This is an important property arising in different contexts. For instance, in the study of integrability of a given…
The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…