Inner products of resonance solutions in 1-D quantum barriers

The properties of a prescription for the inner products of the resonance (Gamow states), scattering (Dirac kets), and bound states for 1-dimensional quantum barriers are worked out. The divergent asypmtotic behaviour of the Gamow states is regularized using a Gaussian convergence factor first introduced by Zel'dovich. With this prescription, most of these states (with discrete complex energies) are found to be orthogonal to each other, to the bound states, and to the Dirac kets, except when they are neighbors, in which case the inner product is divergent. Therefore, as it happens for the continuum scattering states, the norm of the resonant ones remains non-calculable. Thus, they exhibit properties half way between the (continuum real) Dirac-delta orthogonality and the (discrete real) Kronecker-delta orthogonality of the bound states.Comment: 13 pages, 2 figure

Advances in cyclin-dependent kinase inhibitors for the treatment of melanoma

Despite the recent advances in the treatment of malignant melanoma with immunotherapy and BRAF/MEK targeted agents, advanced disease still beholds a poor prognosis for a significant proportion of patients. Cyclin dependent kinase (CDK) inhibitors have been investigated as novel melanoma therapeutics throughout a range of phase 1 and 2 trials, as single agents and in combination with established treatments. Areas covered: This article summarises the rationale for, and development of CDK inhibitors in melanoma, with their evolution from pan-CDK inhibitors to highly specific agents, throughout clinical trials and finally their potential future use. Expert opinion: Whilst CDK inhibitors have been practice changing in breast cancer management, their efficacy is yet to be proven in melanoma. Combination with BRAF/MEK inhibitors has been hindered by dose limiting toxicities, but their role may yet to be found within the spectrum of biomarker derived personalised melanoma management. The effect that CDK inhibitors can have as an adjunct to immunotherapy also remains to be seen

Gauge Fixing in Higher Derivative Gravity

Linearized four-derivative gravity with a general gauge fixing term is considered. By a Legendre transform and a suitable diagonalization procedure it is cast into a second-order equivalent form where the nature of the physical degrees of freedom, the gauge ghosts, the Weyl ghosts, and the intriguing "third ghosts", characteristic to higher-derivative theories, is made explicit. The symmetries of the theory and the structure of the compensating Faddeev-Popov ghost sector exhibit non-trivial peculiarities.Comment: 21 pages, LaTe

Gauge fixing in higher derivative field theories

Higher Derivative (HD) Field Theories can be transformed into second order equivalent theories with a direct particle interpretation. In a simple model involving abelian gauge symmetries we examine the fate of the possible gauge fixings throughout this process. This example is a useful test bed for HD theories of gravity and provides a nice intuitive interpretation of the "third ghost" occurring there and in HD gauge theories when a HD gauge fixing is adopted.Comment: 16 pages, Latex,( Preprint imaff 93/10