Related papers: Symmetries in the \bm{g_{9/2}} shell
If our 3+1-dimensional universe is a brane or domain wall embedded in a higher dimensional space, then a phenomenon we term the ``clash of symmetries'' provides a new method of breaking some continuous symmetries. A global $G_{\text{cts}}…
Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the…
We define a perturbatively calculable quantity--the on-shell correlator--which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the case of flat and anti-de Sitter space, on-shell correlators…
Let $f(n)$ denote the number of 1-shell totally symmetric plane partitions of weight $n$. Recently, Hirschhorn and Sellers, Yao, and Xia established a number of congruences modulo 2 and 5, 4 and 8, and 25 for $f(n)$, respectively. In this…
The symmetries of the $t=1$ and $t=0$ pair-fields are different. The consequences for rotational spectra are discussed. For $t=1$, the concept of spontaneous breaking and subsequent restoration of the isospin symmetry turns out to be…
We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion--free and some types of them have to be locally flat. We prove that each symmetry…
Detailed description of nuclei necessitates model Hamiltonians which break most dynamical symmetries. Nevertheless, generalized notions of partial and quasi dynamical symmetries may still be applicable to selected subsets of states, amidst…
Let $X_{2k}$ be a set of $2k$ labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of $X_{2k}$. Two such matchings, $M$ and $M'$, are disjoint compatible if they do not have…
This is the second in a pair of articles that classify the configuration space and kinematic symmetry groups for $N$ identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries…
Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is…
The one-dimensional harmonic oscillator in a box problem is used to introduce the concept of a mixed-mode shell-model scheme. The method combines low-lying ``pure mode'' states of a system to achieve a better description in situations where…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
The symmetries of the sdg-IBM, the interacting boson model with s, d and g bosons, are studied as regards the occurrence of shapes with octahedral symmetry. It is shown that no sdg-IBM Hamiltonian with a dynamical symmetry displays in its…
A geometric interpretation is given of matrix elements of a short-range interaction between states that are written in terms of aligned neutron-proton pairs.
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
In nuclear physics a magic number is defined as the nucleon number, which is separated by a significantly large single-particle energy gap from the next nucleon. Magic numbers define the nuclear shells, which are considered to be active,…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
Investigating the CKM matrix in different parametrization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal. Using those relations,…
Modern nucleon-nucleon (NN) potentials, which accurately fit the nucleon-nucleon scattering phase shifts, contain terms which break isospin symmetry. The effects of these symmetry violating terms on the bulk properties of nuclear matter are…
The symmetry energy in nuclei is studied using a monopole-monopole two boby interaction which has an isospin dependent term. A Hartree theory is developed for this interaction which has an oscillator shell model basis with corresponding…