Deformed oscillators algebra formulation of the nonlinear Schrödinger hierarchy and of its symmetry

We present a self-contained formulation of the Nonlinear Schrödinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y(gl_N) and finite W(gl_pN, N.gl_p) algebras is also illustrated in this framework.     

Model-independent analysis of tri-bimaximal mixing: A softly-broken hidden or an accidental symmetry?

To address the issue of whether tri-bimaximal mixing (TBM) is a softly-broken hidden or an accidental symmetry, we adopt a model-independent analysis in which we perturb a neutrino mass matrix leading to TBM in the most general way but leave the three texture zeros of the diagonal charged lepton mass matrix unperturbed. We compare predictions for the perturbed neutrino TBM parameters with those obtained from typical SO(10) grand unified theories with a variety of flavor symmetries. Whereas SO(10) GUTs almost always predict a normal mass hierarchy for the light neutrinos, TBM has a priori no preference for neutrino masses. We find, in particular for the latter, that the value of |U_e3| is very sensitive to the neutrino mass scale and ordering. Observation of |U_e3|²>0.001 to 0.01 within the next few years would be incompatible with softly-broken TBM and a normal mass hierarchy and would suggest that the apparent TBM symmetry is an accidental symmetry instead. No such conclusions can be drawn for the inverted and quasi-degenerate hierarchy spectra.     

Hidden conformal symmetry of rotating black holes in the five-dimensional Gödel universe

We have investigated the hidden conformal symmetry of generic non-extremal rotating black holes in the five-dimensional Gödel universe. In a range of parameters, the low-frequency massless scalar wave equation in the “near region” can be described by an SL(2, R) _L × SL(2, R) _R conformal symmetry. We further found that the microscopic entropy via Cardy formula matches the macroscopic Bekenstein-Hawking entropy and the absorption cross section for the massless scalar also agrees with the one for the two dimensional finite temperature conformal field theory (CFT). All these evidences support the conjecture that the generic non-extremal rotating black hole immersed in the Gödel universe can be dual to a two dimensional finite temperature CFT. In addition, we have reformulated the first laws of thermodynamics associated with the inner and outer horizons of the rotating Gödel-type black holes into the forms of conformal thermodynamics.     

“Hidden momentum” in magnets and interaction energy

Coleman and Van Vleck's formula for the mass center associated with the Darwin Lagrangian entails an interesting corollary to an earlier remark by De Broglie and Brillouin.     

Universal volume of groups and anomaly of Vogel’s symmetry

We show that integral representation of universal volume function of compact simple Lie groups gives rise to six analytic functions on \({ CP }^2\), which transform as two triplets under group of permutations of Vogel’s projective parameters. This substitutes expected invariance under permutations of universal parameters by more complicated covariance. We provide an analytic continuation of these functions and calculate their change (anomaly) under permutations of parameters (Vogel’s symmetry). This last relation is universal generalization, for an arbitrary simple Lie group and, moreover, to an arbitrary point in Vogel’s plane, of the Kinkelin’s reflection relation on Barnes’ \(G(1+N)\) function. Kinkelin’s relation gives asymmetry of the \(G(1+N)\) function (which is essentially reciprocal of the volume function for \({ SU }(N)\) groups) under \(N\leftrightarrow -N\) transformation (which is equivalent of the permutation of Vogel’s parameters for \({ SU }(N)\) groups), and coincides with above-mentioned anomaly of permutations at the \({ SU }(N)\) line on Vogel’s plane. Our results also give an anomaly of Vogel’s symmetry of the universal partition function of Chern–Simons theory on three-dimensional sphere. This effect is analogous to modular covariance, instead of invariance, of partition functions of appropriate gauge theories under modular transformation of couplings.     

“Minus c” symmetry in classical electrodynamics and quantum theory

A symmetry associated with the inversion of the speed of light is considered.     

Density functional theory of transition metal phthalocyanines,II: electronic structure of MnPc and FePc—symmetry and symmetry breaking

We present a two-part systematic density functional theory (DFT) study of the electronic structure of selected transition metal phthalocyanines. We use a semi-local generalized gradient approximation (GGA) functional, as well as several hybrid exchange-correlation functionals, and compare the results to experimental photoemission data. Here, we study the intermediate spin systems MnPc and FePc. We show that DFT calculations of these systems are extremely sensitive to the choice of functional and basis set with respect to the obtained electronic configuration and to symmetry breaking. Interestingly, all simulated spectra are in good agreement with experiment despite the differences in the underlying electronic configurations.     

A new “dual” symmetry structure of the KP hierarchy

A new infinite set of commuting additional (“ghost”) symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to a new double-KP hierarchy embedding “ghost” and original KP-type Lax hierarchies connected to each other via a “duality” mapping exchanging the isospectral and “ghost” “times”. A new representation of the 2D Toda lattice hierarchy as a special Darboux-Bäcklund orbit of the double-KP hierarchy is found and parametrized entirely in terms of (adjoint) eigenfunctions of the original KP subsystem.     

Lie symmetry and Mei continuum conservation law of system＊

Lie symmetry and Mei conservation law of continuum Lagrange system are studied in this paper. The equation of motion of continuum system is established by using variational principle of continuous coordinates. The invariance of the equation of motion under an infinitesimal transformation group is determined to be Lie-symmetric. The condition of obtaining Mei conservation theorem from Lie symmetry is also presented. An example is discussed for applications of the results.     

Form invariance and Lie symmetry of equations of non—holonomic systems

In this paper,we study the relation between the form invariance and Lie symmetry of non-holonomic systems.Firstly,we give the definitions and criteria of the form invariance and Lie symmetry in the systems.Next,their relation is deduced.We show that the structure equation and conserved quantity of the form invariance and Lie symmetry of non-holonomic systems have the same form.Finally,we give an example to illustrate the application of the result.     

Constraints on the nuclear symmetry energy and its density slope from the α decay process

We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process.Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state(EOS). Each EOS is characterized by a particular symmetryenergy coefficient(a_(sym)) and a corresponding density-slope parameter L. The stepwise trends of the neutron(proton) skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life T_α with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value a_(sym) = 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay,yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.     

Decompositions of the Kadomtsev–Petviashvili equation and their symmetry reductions

Starting with a decomposition conjecture, we carefully explain the basic decompositions for the Kadomtsev–Petviashvili(KP) equation as well as the necessary calculation procedures, and it is shown that the KP equation allows the Burgers–STO(BSTO) decomposition, two types of reducible coupled BSTO decompositions and the BSTO–KdV decomposition. Furthermore, we concentrate ourselves on pointing out the main idea and result of B?cklund transformation of the KP equation based on a special superpositi...     

Chiral (γ5) symmetry of massless fields and neutrino theory of photons

It is shown that the field theory of massless particles has the internal symmetry groupG=U(1) AutU(1). The ₅ and dual transformations of neutrino and electromagnetic fields are particular cases of the transformations of this group. TheCP transformations of massless field can also be included in the transformations of this group. The following formulation of Pryce (1938) theorem is given: Statistical properties of the composite photon in the neutrino theory of light are inconsistent with chiral (₅) symmetry of neutrino and electromagnetic fields.     

On the zero fluctuation of the “microscopic free energy” and its potential use

The fluctuations of the microscopic free energy calculated with the ensemble probability are shown to be zero. We suggest that this result be used for estimating approximate free energies calculated on the basis of the minimum free energy principle. As an example the estimation is performed with respect to a certain computer simulation of the square Ising lattice. The zero fluctuations also can be used to obtain relations among fluctuations with the accurate ensemble probability distribution.     

z→-z symmetry of spin-orbit coupling and weak localization in graphene

We show that the influence of spin-orbit (SO) coupling on the weak-localization effect for electrons in graphene depends on the lack or presence of z→-z symmetry in the system. While, for z→-z asymmetric SO coupling, disordered graphene should display a weak antilocalization behavior at lowest temperature, z→-z symmetric coupling leads to an effective saturation of decoherence time which can be partially lifted by an in-plane magnetic field, thus tending to restore the weak-localization effect.     

New interaction solutions and nonlocal symmetry of an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form

The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method. The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables. The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly. Many new interaction solutions among soliton and other types of interaction solutions for th...     

The double Lagrangian its applications with U（1, J） symmetry and to the cosmology

By introducing the double complex scalar field, this paper constructs the double Lagrangian with the potential V（Ф（J）,Ф（J）） = V（│Ф（J）│）, which not only can describe the evolution of quintom Universe, but also can naturally give the spintessence and hessence Universe. Furthermore, the U（1, J） symmetry of the double complex Lagrangian is verified, and the total conserved charge within the physical volume is derived by means of the Norther theorem. Moreover, it can point out that the ＇imaginary motion＇ of the angular parameter in Ref.[14], in fact, is only a real phase displacement in our model.     

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form.