Related papers: Singularities and diffeomorphisms
Techniques of gauge theory are used to define and compute an invariant of certain diffeomorphisms of 4-manifolds. The invariant vanishes for any diffeomorphism which is smoothly isotopic to the identity. As an application, we give the first…
Spin foams are candidate state-sum models for transition amplitudes in quantum gravity. An active research subject is to identify the possible divergences of spin foam models, or alternatively to show that models are finite. We will discuss…
Gauging a symmetry can be thought of as the insertion of a spacetime-filling defect. Accordingly, we regard each gaugeable symmetry in a theory as defining a $-1$-form symmetry via condensation. The resulting operators, called gauge…
Diffeomorphisms and an internal symmetry (e.g., local Lorentz invariance) are typically regarded as the symmetries of any geometrical gravity theory, including general relativity. In the first-order formalism, diffeomorphisms can be thought…
We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map.…
We give a general description of gauge symmetry breaking using vertical and remainder fluxes in 4D F-theory models. The fluxes can break a geometric gauge group to a smaller group and induce chiral matter, even when the larger group admits…
Diffeomorphism symmetry, the fundamental invariance of general relativity, is generically broken under discretization. After discussing the meaning and implications of diffeomorphism symmetry in the discrete, in particular for the continuum…
The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and…
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…
We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have…
Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties both in canonical and covariant…
Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension…
Gauge symmetries generally appear as a constraint algebra, under which one expects all physical states to be singlets. However, quantum anomalies and boundary conditions introduce central charges and change this picture, thus causing…
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…
Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by Freund (1987}, seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
We analyze approaches to the partial or complete unification of gauge symmetries in theories with dynamical symmetry breaking. Several types of models are considered, including those that (i) involve sufficient unification to quantize…
We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies or hydrodynamics, though using the…
A local gauge symmetry can not possibly be a mere redundancy of the description, provided that 1. charge is nonzero. 2. we also consider divergent gauge transformations, whose brackets with local transformations contain global charge…
We provide a new angle and obtain new results on a class of metrics on length-normalized curves in $d$ dimensions, represented by their unit tangents expressed as a function of arc-length, which are functions from the unit interval to the…