When is Multimetric Gravity Ghost-free?

We study ghosts in multimetric gravity by combining the mini-superspace and the Hamiltonian constraint analysis. We first revisit bimetric gravity and explain why it is ghost-free. Then, we apply our method to trimetric gravity and clarify when the model contains a ghost. More precisely, we prove trimetric gravity generically contains a ghost. However, if we cut the interaction of a pair of metrics, trimetric gravity becomes ghost-free. We further extend the Hamiltonian analysis to general multimetric gravity and calculate the number of ghosts in various models. Thus, we find multimetric gravity with loop type interactions never becomes ghost-free.Comment: 22 pages, 6 figure

Anomalous magnetization process in frustrated spin ladders

We study, at T=0, the anomalies in the magnetization curve of the S=1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the M=\Ms/2 plateau, where \Ms is the saturation magnetization. We use analytical methods (degenerate perturbation theory and non-Abelian bosonization) as well as numerical methods (level spectroscopy and density matrix renormalization group), which lead to the consistent conclusion with each other. We also touch on the M=\Ms/4 and M=(3/4)\Ms plateaux and cusps.Comment: 4 pages, 7 figures (embedded), Conference paper (Highly Frustrated Magnetism 2003, 26-30th August 2003, Grenoble, France

Tuberous Sclerosis 2 Gene Is Expressed at High Levels in Specific Types of Neurons in the Mouse Brain

Tuberous sclerosis (TSC) is an autosomal dominant disorder characterized by mental retardation, epilepsy and hamartomatous growth in many tissues. The gene (TSC2) encoding a tumor suppressor protein whose mutations cause TSC, has been demonstrated to be expressed at high levels in the adult and developing brain, raising the question of whether or not the TSC2 gene product has unique roles in differentiation related to cytoskeletal interactions within the central nervous system, in addition to a tumor suppressor function. To determine the expression of TSC2 in functionally distinct neuron types of the mouse brain, we carried out in situ hybridization with digoxigenin-labeled riboprobes for the detection of TSC2 mRNA. High levels of the TSC2 gene were in neurons of the pyramidal and dentate granular layer in the hippocampus, cerebellar Purkinje cells, neurons of the piriform cortex, motor neurons in the medulla and interneurons in the striatum, while intermediate levels were in cortical neurons, striatal neurons, septal neurons, thalamic neurons and neurons in the substantia nigra compacta. Thus, the high expression of the TSC2 gene has restricted distribution in specific neuronal types which are characterized by well-developed dendrites and rich in use-dependent long-term changes in synaptic efficacy. These results suggest that the function of the TSC2 gene product may be involved on a cellular basis in neuronal plasticity and relevant to mental retardation observed in TSC patients