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.

Pelvic floor muscle displacement during voluntary and involuntary activation in continent and incontinent women: a systematic review.

INTRODUCTION Investigations of the dynamic function of female pelvic floor muscles (PFM) help us to understand the pathophysiology of stress urinary incontinence (SUI). Displacement measurements of PFM give insight into muscle activation and thus help to improve rehabilitation strategies. This systematic review (PROSPERO 2013: CRD42013006409) was performed to summarise the current evidence for PFM displacement during voluntary and involuntary activation in continent and incontinent women. METHODS MEDLINE, EMBASE, Cochrane and SPORTDiscus databases were searched using selected terminology reflecting the PICO approach. Screening of Google Scholar and congress abstracts added to further information. Original articles investigating PFM displacement were included if they reported on at least one of the aims of the review, e.g., method, test position, test activity, direction and quantification of displacement, as well as the comparison between continent and incontinent women. Titles and abstracts were screened by two reviewers. The papers included were reviewed by two individuals to ascertain whether they fulfilled the inclusion criteria and data were extracted on outcome parameters. RESULTS Forty-two predominantly observational studies fulfilled the inclusion criteria. A variety of measurement methods and calculations of displacement was presented. The sample was heterogeneous concerning age, parity and continence status. Test positions and test activities varied among the studies. CONCLUSIONS The findings summarise the present knowledge of PFM displacement, but still lack deeper comprehension of the SUI pathomechanism of involuntary, reflexive activation during functional activities. We therefore propose that future investigations focus on PFM dynamics during fast and stressful impact tasks.

Gauging MSSM global symmetries and SUSY breaking in de Sitter vacuum

We elaborate on a recent study of a model of supersymmetry breaking we proposed recently, in the presence of a tunable positive cosmological constant, based on a gauged shift symmetry of a string modulus, external to the Standard Model (SM) sector. Here, we identify this symmetry with a global symmetry of the SM and work out the corresponding phenomenology. A particularly attracting possibility is to use a combination of Baryon and Lepton number that contains the known matter parity and guarantees absence of dimension-four and -five operators that violate B and L.