Related papers: Symmetry vs Symmetry
Spontaneous symmetry breaking is a well-understood mechanism for generating distinct phases of matter. Recently, the notion of symmetry has been broadened to include operations without inverses, leading to the concept of non-invertible…
We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that…
We analyse symmetry breaking in general gauge theories paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: a Euclidean metric associated with the scalar…
One cannot yet point to any firm string prediction. While many approximate string ground states are known with interesting properties, we do not have any argument that one or another describes what we observe around us, and for reasons…
The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking…
Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…
Physics takes for granted that interacting physical systems with no common history are independent, before their interaction. This principle is time-asymmetric, for no such restriction applies to systems with no common future, after an…
Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure,…
If supersymmetric particles are discovered, an important problem will be to determine how supersymmetry has been broken. At collider energies, supersymmetry breaking can be parameterised by soft supersymmetry breaking parameters. Several…
I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April,…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
Let $S(H)$ be the set of all self-adjoint bonded linear operators on $H$ and $\mathcal{V} \subset S(H)$ a subset that is pertinent in mathematical foundations of quantum mechanics. A symmetry is a bijective map $\phi :\mathcal{V} \to…
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in spectra, ground state spins and isospins is discovered in both odd and even-particle systems. Various types…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
\noindent In our contribution to this volume we deal with \emph{discrete} symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
The concept of (global) gauge symmetry breaking plays an important role in many areas of physics. Since the corresponding symmetry is a gauge symmetry, its breaking is actually gauge-dependent. Thus, it is possible to design gauges which…
A mechanism of supersymmetry breaking in two or four-dimensions is given, in which the breaking is related to the Fermat's last theorem. It is shown that supersymmetry is exact at some irrational number points in parameter space, while it…