Charged spinning fluids in general relativity

The treatment of neutral spinning fluids in general relativity due to Ray and Smalley is generalized, by considering the fluid as charged and having a magnetic dipole moment proportional to the spin.     

Charged perfect fluids in the presence of a cosmological constant

We consider the static and spherically symmetric field equations of general relativity for charged perfect fluid spheres in the presence of a cosmological constant. Following work by Florides (J Phys A Math Gen 16:1419–1433, 1983) we find new exact solutions of the field equations, and discuss their mass radius ratios. These solutions, for instance, require the charged Nariai metric to be the vacuum part of the spacetime. We also find charged generalizations of the Einstein static universe and speculate that the smallness problem of the cosmological constant might become less problematic if charge is taken into account.     

Comparative analysis of symmetries for the models of mechanics of nonuniform fluids

The symmetries for the main models of mechanics of binary fluids are calculated by the methods of the theory of continuous groups. The fundamental system of the differential form of the main conservation laws is characterized by the ten-parametric Galilean group. The Navier-Stokes set of equations possesses an extended set of symmetries with infinite dimensionality. Simplification of the model changes the order of the set of equations of motion, which leads to the impossibility to take into account the complete set of boundary conditions and formation of discontinuities in solutions for reduced models.     

Phase transitions, interfacial fluctuations and hidden symmetries for fluids near structured walls

Fluids adsorbed at micro-patterned and geometrically structured substrates can exhibit novel phase transitions and interfacial fluctuation effects distinct from those characteristic of wetting at planar, homogeneous walls. We review recent theoretical progress in this area paying particular attention to filling transitions pertinent to fluid adsorption near wedges, which have highlighted a deep connection between geometrical and contact angles. We show that filling transitions are not only characterized by large scale interfacial fluctuations leading to universal critical singularities but also reveal hidden symmetries with short-ranged critical wetting transitions and properties of dimensional reduction. We propose a non-local interfacial model which fulfills all these properties and throws light on long-standing problems regarding the order of the 3D short-range critical wetting transition.     

Role of molecular symmetries in magneto-spatial dispersional change of the refractive index in fluids

Variations in refractive index due to the (B⁰ · k) effect are calculated for a circularly polarized light wave. The effect is related with the mechanism of nonlinear electron distortion in a field B⁰ described by an i-tensor of rank 4 and the reorientation mechanism represented by the product of two c-tensors, of ranks 3 and 1. The magnetic classes of molecules admitting of these mechanisms are determined.     

Hadrons and broken symmetries with WASA-at-COSY

The WASA Detector Facility is an internal experiment at the cooler synchrotron (COSY) in Jülich, Germany. The COSY accelerator provides proton and deuteron beams with momenta up to 3.7 GeV/c giving access to hadron physics including the strange quark sector. The physics program with the WASA detector involves hadron dynamics and hadron structure. Key experiments address fundamental symmetries and symmetry violations via the study of rare and not-so-rare meson decays. From the very first production run, results on the Dalitz plot slope parameter in the isospin violating η → 3π ⁰ decay have been obtained. The 3π ⁰ final state is also used to study meson production mechanisms. Investigations of other decay modes of the η-meson address C, P, and T symmetries and combinations. Higher orders in chiral perturbation theory are probed with the η → π ⁰ decay. The status and plans for studying hadron structure with Dalitz decays of mesons are presented.     

Schrödinger operators with symmetries

We consider the stationary Schrödinger operator H of a many-body system M with two-body rotation invariant interactions. The operator H is reduced with respect to the symmetries of permutation of identical particles, rotations and reflections, into a direct sum of operators H^τ̃, where τ̃ is an index of the irreducible representations of the symmetry group of the system.The spectra of the operators H^τ̃ were investigated in a series of papers of G.M. Zislin and A.G. Sigalov ([20], [21], [31]-[35]). In a recent paper [3] we have developed the spectral theory of these operators on the basis of the Weinberg equations.In the present work we complete and simplify this theory. In particular we treat in detail the case where the given system can be decomposed into two identical subsystems. For such systems there is a certain coupling between permutation and rotation-reflection symmetries, because a permutation, which interchanges the two subsystems, imposes a reflection on the relative position vector of the two centers of mass. This requires a modification of the theorem on essential spectrum as formulated in [3] in the case where such a division is not possible. The importance of this special case, as exemplified by diatomic molecules, fully justifies such a detailed treatment.This special case was treated by Zislin [34] under the assumption that the interactions are essentially multiplicative, relatively compact two-body interactions. Our method allows for general relatively compact two-body interactions, and can without difficulty be generalized to many-body interactions.Moreover, the method based on the Weinberg equation is suitable for a further analysis of the spectra of these operators.     

Primeval symmetries

A detailed examination of the Killing equations in Robertson–Walker coordinates shows how the addition of matter and/or radiation to a de Sitter Universe breaks the symmetry generated by four of its Killing fields. The product \(U = a^2 \,{\dot H}\) of the squared scale parameter by the time-derivative of the Hubble function encapsulates the relationship between the two cases: the symmetry is maximal when U is a constant, and reduces to the six-parameter symmetry of a generic Friedmann–Robertson–Walker model when it is not. As the fields physical interpretation is not clear in these coordinates, comparison is made with the Killing fields in static coordinates, whose interpretation is made clearer by their direct relationship to the Poincaré group generators via Wigner–Inönú contractions.     

Bifurcation symmetries

The bifurcation of one mode into several branches frequently generates symmetries among the branches. These symmetries are “naturally broken”. After a look at some simple examples, we study a model where the bifurcation symmetry has some features of a flavor symmetry.     

Charged sphere of shear-free fluids with $$\frac{\partial}{\rho} \partial r \leq 0$$

The Einstein-Maxwell equations for non-static charged shear-free spherically symmetric perfect fluid distribution reduce to a second-order non-linear differential equation in the radial parameter. Several solutions of this equation have been obtained in earlier work without considering the general requirement for physical relevance of the solutions. Generally physically acceptable relativistic fluid models demand that the solutions satisfy the reality conditions ρ ≥ 0, p ≥ 0, ρ _r ≤ 0, etc. throughout the fluid model. In this article the expression for density gradient ρ _x (or ρ _r ) has been utilized to produce charged shear-free relativistic fluid models with non-positive density gradient (NDG)ρ _r ≤ 0. Eventually, we have found that none of the Riccati solutions have NDG including Vaidya metric. Also, the solutions with NDG neither possess Lie-symmetries nor Painlevé property. Further, it is observed that the solutions with NDG have no uncharged analogue.     

Dressing symmetries

We study the group of dressing transformations in soliton theories. We show that it is generated by the monodromy matrix. This provides a new proof of their Lie-Poisson property. We treat in detail the examples of the Toda field theories and the Heisenberg model. We show that the group of dressing transformations is the classical precursor of the various manifestations of quantum groups in these models, e.g. algebraic Bethe ansatz, non-local currents, or quantum group symmetries. Finally, we define field multiplets supporting a linear representation of the dressing group and we show that their exchange algebras are encoded in the classical double.Communicated by K. Gawedzki     

Tetrad symmetries

It is shown that ifG is a subgroup of the group of motions of a given space-time then a tetrad can be chosen which is symmetric under the subgroup if and only if the rank of the generators ofG is equal to the order ofG. As an example such a tetrad is constructed for the TypeN twisting empty space-time admitting a two-parameter group of motions.     

Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C_2v$C_{2v}$ exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry.