Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians

The spacetime dependent lagrangian formalism of references [1-2] is used to obtain is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field,{\it viz.} $\phi_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge).The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct $D$-brane actions. The formalism is also used to obtain the Deser-Gomberoff-Henneaux-Teitelboim results [10] for dyon charge quantisation in abelian $p$-form theories in dimensions $D=2(p+1)$ for both even and odd $p$. PACS: 11.15.-q,11.27.+d,11.10.EfComment: Latex, 15 pages, a comprehensive paper incorporating material of hep-th/0210051, hence title and abstracts modified, typos correcte

The Hawking temperature in the context of dark energy

An emergent gravity metric incorporating $k-$essence scalar fields $\phi$ having a Born-Infeld type lagrangian is mapped into a metric whose structure is similar to that of a blackhole of large mass $M$ that has swallowed a global monopole. However, here the field is not that of a monopole but rather that of a $k-$essence scalar field. If $\phi_{emergent}$ be solutions of the emergent gravity equations of motion under cosmological boundary conditions at $\infty$, then for $r\rightarrow\infty$ the rescaled field $\frac {\phi_{emergent}}{2GM-1}$ has exact correspondence with $\phi$ with $\phi(r,t)=\phi_{1}(r)+\phi_{2}(t)$. The Hawking temperature of this metric is $T_{\mathrm emergent}= \frac{\hbar c^{3}}{8\pi GM k_{\mathrm B}}(1-K)^{2}\equiv \frac{\hbar}{8\pi GM k_{\mathrm B}}(1-K)^{2}$, taking the speed of light $c=1$. Here $K=\dot\phi_{2}^{2}$ is the kinetic energy of the $k-$essence field $\phi$ and $K$ is always less than unity, $k_{\mathrm B}$ is the Boltzmann constant. This is phenomenologically interesting in the context of Belgiorno {\it et al's} gravitational analogue experiment.Comment: 6 pages, latex, To appear in Euro Physics Letters. arXiv admin note: text overlap with arXiv:1009.4634 by other author

Three Flavoured neutrino oscillations and the Leggett Garg Inequality

Three flavoured neutrino oscillations are investigated in the light of the Leggett-Garg inequality. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified. The results obtained are: (a) The maximum violation of the Leggett Garg Inequality (LGI) is $2.17036$ for neutrino path length $L_{1}=140.15$ Km and $\Delta L=1255.7$ Km.(b) Presence of the mixing angle $\theta_{13}$ enhances the maximum violation of LGI by $4.6\%$.(c) The currently known mass hierarchy parameter $\alpha = 0.0305$ increases the the maximum violation of LGI by $3.7\%$. (d)Presence of CP violating phase parameter enhances the maximum violation of LGI by $0.24\%$, thus providing an \textit{alternative indicator of CP violation} in 3-flavoured neutrino oscillations.Comment: 8 pages, 5 figures, late