Search results for "symmetry group"
showing 10 items of 41 documents
On the role of symmetry in solving maximum lifetime problem in two-dimensional sensor networks
2016
We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group $G$ can be utilized to simplify its solution. We prove, that for a $G$-invariant maximum lifetime problem there exists a $G$-invariant solution. Constrains which follow from the $G$-invariance allow to reduce the problem and its solution to a subset, an optimal fundamental region of the sensor network. We analyze in detail solutions of the maximum lifetime problem invariant under a group of isometry transformations of a two dimensional Euclidean plane.
Infinite sets of conservation laws for linear and nonlinear field equations
1984
The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the ‘coupling constant’) the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant u…
Quasimolecular resonances in terms of dipole and quadrupole interacting bosons
1986
The energy spectrum of the /sup 12/C+ /sup 12/C resonances is described with the interacting boson (quadrupole) model. The Hamiltonians corresponding to the three dynamical symmetries and to the general case of the model are used. The results are compared with the similar calculations within the nuclear vibron (dipole) model. Based on the present experimental data no choice can be made between the dipole and quadrupole descriptions, but in both cases the best fit is quite close to the dynamical symmetry corresponding to a soft vibrator.
Twists in Ferromagnetic Monolayers With Trigonal Prismatic Symmetry
2018
Two-dimensional materials such as graphene or hexagonal boron nitride are indispensable in industry. The recently discovered 2D ferromagnetic materials also promise to be vital for applications. In this work, we develop a phenomenological description of non-centrosymmetric 2D ferromagnets with trigonal prismatic crystal structure. We chose to study this special symmetry group since these materials do break inversion symmetry and therefore, in principle, allow for chiral spin structures such as magnetic helices and skyrmions. However, unlike all non-centrosymmetric magnets known so far, we show that the symmetry of magnetic trigonal prismatic monolayers neither allow for an internal relativi…
Symmetries and Symmetry Groups in Quantum Physics
2013
When one talks about discrete or continuous groups which are to describe symmetries of quantum systems, one must first identify the objects on which the elements of these groups are acting.
Quantization as a consequence of the group law
1982
A method of gemetric quantization which solely makes use of the structure of the symmetry group of the dynamical system is proposed; the classical limit is discussed along similar lines. The method is applied to two examples, the free particle and the harmonic oscillator.
Higher Order Integrability in Generalized Holonomy
2004
Supersymmetric backgrounds in M-theory often involve four-form flux in addition to pure geometry. In such cases, the classification of supersymmetric vacua involves the notion of generalized holonomy taking values in SL(32,R), the Clifford group for eleven-dimensional spinors. Although previous investigations of generalized holonomy have focused on the curvature \Rm_{MN}(\Omega) of the generalized SL(32,R) connection \Omega_M, we demonstrate that this local information is incomplete, and that satisfying the higher order integrability conditions is an essential feature of generalized holonomy. We also show that, while this result differs from the case of ordinary Riemannian holonomy, it is n…
AdS$_3$ solutions with exceptional supersymmetry
2018
Among the possible superalgebras that contain the AdS$_3$ isometries, two interesting possibilities are the exceptional $F(4)$ and $G(3)$. Their R-symmetry is respectively SO(7) and $G_2$, and the amount of supersymmetry ${\cal N}=8$ and ${\cal N}=7$. We find that there exist two (locally) unique solutions in type IIA supergravity that realize these superalgebras, and we provide their analytic expressions. In both cases, the internal space is obtained by a round six-sphere fibred over an interval, with an O8-plane at one end. The R-symmetry is the symmetry group of the sphere; in the $G(3)$ case, it is broken to $G_2$ by fluxes. We also find several numerical ${\cal N}=1$ solutions with $G_…
Clusterization in the shape isomers of the 56Ni nucleus
2011
The interrelation of the quadrupole deformation and clusterization is investigated in the example of the ${}^{56}$Ni nucleus. The shape isomers, including superdeformed and hyperdeformed states, are obtained as stability regions of the quasidynamical U(3) symmetry based on a Nilsson calculation. Their possible binary clusterizations are investigated by considering both the consequences of the Pauli exclusion principle and the energetic preference.
Accidental stability of dark matter
2013
We propose that dark matter is stable as a consequence of an accidental Z(2) that results from a flavour symmetry group which is the double-cover group of the symmetry group of one of the regular geometric solids. Although model-dependent, the phenomenology resembles that of a generic >inert Higgs> dark matter scheme.