New Type Of Symmetry Research Articles

Quantum mechanics and symmetries

Symmetries have always played an important role in physics. With quantum mechanics, however, the interplay between physics and symmetries has reached a new dimension. The very structure of quantum mechanics invites the application of group theoretical methods to an extent that physicists would have been led to invent various concepts of group theory, such as Lie groups, by quantum mechanics had they not been known before. Symmetries are also a direct mediator between experimental facts and the theoretical structure of a theory. This is the case because there is a direct connection between symmetries and conservation laws. Space-time symmetries are an obvious example. Conservation of energy, momentum and angular momentum are linked to invariance under time translation, space translation and rotation in space. It was in atomic physics that space-time symmetries became significant, but they are as important in nuclear physics and in all the physics discovered after that. In nuclear physics, however, a new concept of symmetries, symmetries in an internal space, was discovered with the introduction of isospin. All our socalled fundamental models describing what we know about strong-weak and electromagnetic interactions are built on symmetries in space-time and internal spaces. These symmetries are not only used to extract information from a theory, they are also used to construct these theories, and this for good reasons. It turned out that only theories possessing such symmetries make sense as quantum field theories. Thus symmetries are not only a good tool to deal with quantum field theoretical models, they are necessary to define such models. Following this line of thought, a new type of symmetry, the socalled supersymmetry, proved to be extremely successfull. Quantum theory seems to have a very deep relation to supersymmetry. Thus it is not surprising that the most promising fundamental models of physics are based on supersymmetry, even when they go beyond a local quantum field theory, as string theory does.

Quantum mechanics and symmetries

AbstractSymmetries have always played an important role in physics. With quantum mechanics, however, the interplay between physics and symmetries has reached a new dimension. The very structure of quantum mechanics invites the application of group theoretical methods to an extent that physicists would have been led to invent various concepts of group theory, such as Lie groups, by quantum mechanics had they not been known before.Symmetries are also a direct mediator between experimental facts and the theoretical structure of a theory. This is the case because there is a direct connection between symmetries and conservation laws. Space‐time symmetries are an obvious example. Conservation of energy, momentum and angular momentum are linked to invariance under time translation, space translation and rotation in space.It was in atomic physics that space‐time symmetries became significant, but they are as important in nuclear physics and in all the physics discovered after that. In nuclear physics, however, a new concept of symmetries, symmetries in an internal space, was discovered with the introduction of isospin. All our socalled fundamental models describing what we know about strong‐weak and electromagnetic interactions are built on symmetries in space‐time and internal spaces. These symmetries are not only used to extract information from a theory, they are also used to construct these theories, and this for good reasons. It turned out that only theories possessing such symmetries make sense as quantum field theories. Thus symmetries are not only a good tool to deal with quantum field theoretical models, they are necessary to define such models.Following this line of thought, a new type of symmetry, the socalled supersymmetry, proved to be extremely successfull. Quantum theory seems to have a very deep relation to supersymmetry. Thus it is not surprising that the most promising fundamental models of physics are based on supersymmetry, even when they go beyond a local quantum field theory, as string theory does.

Rayleigh–Taylor instability in the presence of a density transition layer

A new type of symmetry for the Rayleigh equation is found. For small Atwood number an analytic solution is obtained for a smoothly varying density profile. The spectra of unstable modes are defined. It is shown that a transition layer with finite width can undergo stratification, and velocity shear between new-formed sublayers forms.

Differential Operators, Symmetries and the Inverse Problem for Second-Order Differential Equations

Abstract With each second-order differential equation Z in the evolution space J 1(M n+1) we associate, using the natural f(3, −1)-structure and the f(3, 1)-structure K, a group of automorphisms of the tangent bundle T (J 1(M n+1)), with isomorphic to a dihedral group of order 8. Using the elements of and the Lie derivative, we introduce new differential operators on J 1(M n+1) and new types of symmetries of Z. We analyze the relations between the operators and the “dynamical” connection induced by Z. Moreover, we analyze the relations between the various symmetries, also in connection with the inverse problem for Z. Both the approach based on the Poincare–Cartan two forms and the one relying on the introduction of the so-called metrics compatible with Z are explicitly worked out.

A new type of symmetry in electron-polar-molecule scattering

An adiabatic treatment of the electron-molecule angular wavefunction yields a novel classification scheme.

Electron scattering from diatomic polar molecules. II. Treatment by frame transformations

The theory of Chang and Fano is applied to electron scattering by polar molecules. For collision energy $Eg{E}_{min}$ the problem can be treated accurately without numerical radial integration; the solution is presented in a form suited to an $R$-matrix treatment of the molecular core. The value of ${E}_{min}$ (in a.u.) is determined through $D\frac{\mathrm{Bj}}{{E}_{min}}l\ensuremath{\delta}\ensuremath{\ll}1$; when $\frac{E}{{E}_{min}}\ensuremath{\approx}\mathrm{a}\mathrm{few}$ eV, more extensive calculation is required beyond the bodyframe Born-Oppenheimer region. For this purpose a generalization of the Chang-Fano theory is developed. It consists of an adiabatic continuous transformation of frame, the frame used at each electron-molecule distance $r$ being determined directly by the dynamics of the problem. This procedure generates a coordination diagram for the known solutions to limiting cases, a diagram analogous to that used in quantum chemistry for connecting the united-atom and separated-atom limits of molecular-orbital theory. A new type of symmetry in the problem is made apparent. Preliminary discussion is made of the applicability of this method to more general problems of close coupling in the asymptotic region.

Linear Symmetries of Scattering Amplitudes

AbstractIf we define, roughly, linear symmetries as those symmetries which lead to linear relationships among scattering amplitudes, we are then faced with the question whether we already know all possible types of linear symmetries or whether there are new types of symmetries which we can yet discover. We argue that for an important class of these symmetries there can be no new types of symmetries, except for one which we call scaling symmetry. We also attempt to point out all types of symmetries which other classes have. In analyzing the above question we are led to a simple and consistent formalism for describing linear symmetries which takes linearity as the starting point for dealing with these symmetries. In this approach all linear symmetries are formally treated on an equal footing. General results on linear symmetries are derived: These symmetries are then classified into three main classes, and an effort is made to discover the characteristic properties of the individual classes.