Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Nonperturbative results for two-index conformal windows

Via large and small N c relations we derive nonperturbative results about the conformal window of two-index theories. Using Schwinger-Dyson methods as well as four-loops results we estimate subleading corrections and show that naive large number of colors extrapolations are unreliable when N c is less than about six. Nevertheless useful nonper-turbative inequalities for the size of the conformal windows, for any number of colors, can be derived. By further observing that the adjoint conformal window is independent of the number of colors we argue, among other things, that: the large N c two-index conformal window is twice the conformal window of the adjoint representation (which can be determined at small N c) expressed in terms of Dirac fermions; lattice results for adjoint matter can be used to provide independent information on the conformal dynamics of two-index theories such as SU(N c) with two and four symmetric Dirac flavors.

Casimir effect with quantized charged spinor matter in background magnetic field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged spinor matter field confined between two parallel neutral plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the Dirac Hamiltonian operator be self-adjoint. It is shown that, in the case of a sufficiently strong magnetic field and a sufficiently large separation of the plates, the generalized Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates. The detection of this effect seems to be feasible in the foreseeable future.

BPA qualtitative and quantitative assessment associated with orthodontic bonding in vivo

OBJECTIVE To assess the in vivo amount of BPA released from a visible light-cured orthodontic adhesive, immediately after bracket bonding. METHODS 20 orthodontic patients were recruited after obtaining informed consent. All patients received 24 orthodontic brackets in both dental arches. In Group A (11 patients), 25 ml of tap water were used for mouth rinsing, whereas in Group B (9 patients) a simulated mouth rinse formulation was used: a mixture of 20 ml de-ionized water plus 5 ml absolute ethanol. Rinsing solutions were collected before, immediately after placing the orthodontic appliances and after washing out the oral cavity and were then stored in glass tubes. Rinsing was performed in a single phase for 60s with the entire volume of each liquid. The BPA analysis was performed by gas chromatography-mass spectrometry. RESULTS An increase in BPA concentration immediately after the 1st post-bonding rinse was observed, for both rinsing media, which was reduced after the 2nd post-bonding rinse. Water exhibited higher levels of BPA concentration than water/ethanol after 1st and 2nd post-bonding rinses. Two-way mixed Repeated Measures ANOVA showed that the primary null hypothesis declaring mean BPA concentration to be equal across rinsing medium and rinsing status was rejected (p-value <0.001). The main effects of the rinsing medium and status, as well as their interaction were found to be statistically significant (p-values 0.048, <0.001 and 0.011 respectively). SIGNIFICANCE A significant pattern of increase of BPA concentration, followed by a decrease that reached the initial values was observed. The amount of BPA was relatively low and far below the reference limits of tolerable daily intake.

Comparison of different lattice definitions of the topological charge

We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the HermitianWilson- Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.