Conservation laws for the classical Toda field theories

We have performed some explicit calculations of the conservation laws for classical (affine) Toda field theories, and some generalizations of these models. We show that there is a huge class of generalized models which have an infinite set of conservation laws, with their integrated charges being in involution. Amongst these models we find that only the $A_m$ and $A_m^{(1)}$ ($m\ge 2$) Toda field theories admit such conservation laws for spin-3. We report on our explicit calculations of spin-4 and spin-5 conservation laws in the (affine) Toda models. Our perhaps most interesting finding is that there exist conservation laws in the $A_m$ models ($m\ge4)$ which have a different origin than the exponents of the corresponding affine theory or the energy-momentum tensor of a conformal theory.Comment: 9 pages, Late

On the form of local conservation laws for some relativistic field theories in 1+1 dimensions

We investigate the possible form of local translation invariant conservation laws associated with the relativistic field equations \partial\bar\partial\phi_i=-v_i(\bphi) for a multicomponent field \bphi. Under the assumptions that (i)~the $v_i$'s can be expressed as linear combinations of partial derivatives $\partial w_j/\partial\phi_k$ of a set of functions w_j(\bphi), (ii)~the space of functions spanned by the $w_j$'s is closed under partial derivations, and (iii)~the fields \bphi take values in a simply connected space, the local conservation laws can either be transformed to the form $\partial{\bar{\cal P}}=\bar\partial\sum_j w_j {\cal Q}_j$ (where $\bar{\cal P}$ and ${\cal Q}_j$ are homogeneous polynomials in the variables $\bar\partial\phi_i$, $\bar\partial^2\phi_i$,\ldots), or to the parity transformed version of this expression $\partial\equiv(\partial_t+\partial_x)/ \sqrt{2}\rightleftharpoons\bar\partial \equiv (\partial_t-\partial_x)/\sqrt{2}$.Comment: 12 pages, Late

Electromagnetic Casimir energy with extra dimensions

We calculate the energy-momentum tensor due to electromagnetic vacuum fluctuations between two parallel hyperplanes in more than four dimensions, considering both metallic and MIT boundary conditions. Using the axial gauge, the problem can be mapped upon the corresponding problem with a massless, scalar field satisfying respectively Dirichlet or Neumann boundary conditions. The pressure between the plates is constant while the energy density is found to diverge at the boundaries when there are extra dimensions. This can be related to the fact that Maxwell theory is then no longer conformally invariant. A similar behavior is known for the scalar field where a constant energy density consistent with the pressure can be obtained by improving the energy-momentum tensor with the Huggins term. This is not possible for the Maxwell field. However, the change in the energy-momentum tensor with distance between boundaries is finite in all cases.Comment: 16 pages, typos corrected, published versio

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

Radiative Corrections to the Casimir Energy

The lowest radiative correction to the Casimir energy density between two parallel plates is calculated using effective field theory. Since the correlators of the electromagnetic field diverge near the plates, the regularized energy density is also divergent. However, the regularized integral of the energy density is finite and varies with the plate separation L as 1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but more transparent theory of a massless scalar field in 1+1 dimensions confined to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late

Equation of State for Exclusion Statistics in a Harmonic Well

We consider the equations of state for systems of particles with exclusion statistics in a harmonic well. Paradygmatic examples are noninteracting particles obeying ideal fractional exclusion statistics placed in (i) a harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level (LLL) of an exterior magnetic field. We show their identity with (i) the Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in a harmonic well.Comment: latex file, 11 page

Field induced stationary state for an accelerated tracer in a bath

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.Comment: 20 pages, 6 figures v3:minor corrections in sec.III and added reference

ERCC1 expression and RAD51B activity correlate with cell cycle response to platinum drug treatment not DNA repair

Background: The H69CIS200 and H69OX400 cell lines are novel models of low-level platinum-drug resistance. Resistance was not associated with increased cellular glutathione or decreased accumulation of platinum, rather the resistant cell lines have a cell cycle alteration allowing them to rapidly proliferate post drug treatment. Results: A decrease in ERCC1 protein expression and an increase in RAD51B foci activity was observed in association with the platinum induced cell cycle arrest but these changes did not correlate with resistance or altered DNA repair capacity. The H69 cells and resistant cell lines have a p53 mutation and consequently decrease expression of p21 in response to platinum drug treatment, promoting progression of the cell cycle instead of increasing p21 to maintain the arrest. Conclusion: Decreased ERCC1 protein and increased RAD51B foci may in part be mediating the maintenance of the cell cycle arrest in the sensitive cells. Resistance in the H69CIS200 and H69OX400 cells may therefore involve the regulation of ERCC1 and RAD51B independent of their roles in DNA repair. The novel mechanism of platinum resistance in the H69CIS200 and H69OX400 cells demonstrates the multifactorial nature of platinum resistance which can occur independently of alterations in DNA repair capacity and changes in ERCC1