Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models

We present a detailed study of quantized noncompact, nonlinear SO(1,N) sigma-models in arbitrary space-time dimensions D \geq 2, with the focus on issues of spontaneous symmetry breaking of boost and rotation elements of the symmetry group. The models are defined on a lattice both in terms of a transfer matrix and by an appropriately gauge-fixed Euclidean functional integral. The main results in all dimensions \geq 2 are: (i) On a finite lattice the systems have infinitely many nonnormalizable ground states transforming irreducibly under a nontrivial representation of SO(1,N); (ii) the SO(1,N) symmetry is spontaneously broken. For D =2 this shows that the systems evade the Mermin-Wagner theorem. In this case in addition: (iii) Ward identities for the Noether currents are derived to verify numerically the absence of explicit symmetry breaking; (iv) numerical results are presented for the two-point functions of the spin field and the Noether current as well as a new order parameter; (v) in a large N saddle-point analysis the dynamically generated squared mass is found to be negative and of order 1/(V \ln V) in the volume, the 0-component of the spin field diverges as \sqrt{\ln V}, while SO(1,N) invariant quantities remain finite.Comment: 60 pages, 12 Figures, AMS-Latex; v2: results on vacuum orbit and spontaneous symmetry breaking extended to all dimension

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

Severely Impaired Learning and Altered Neuronal Morphology in Mice Lacking NMDA Receptors in Medium Spiny Neurons

The striatum is composed predominantly of medium spiny neurons (MSNs) that integrate excitatory, glutamatergic inputs from the cortex and thalamus, and modulatory dopaminergic inputs from the ventral midbrain to influence behavior. Glutamatergic activation of AMPA, NMDA, and metabotropic receptors on MSNs is important for striatal development and function, but the roles of each of these receptor classes remain incompletely understood. Signaling through NMDA-type glutamate receptors (NMDARs) in the striatum has been implicated in various motor and appetitive learning paradigms. In addition, signaling through NMDARs influences neuronal morphology, which could underlie their role in mediating learned behaviors. To study the role of NMDARs on MSNs in learning and in morphological development, we generated mice lacking the essential NR1 subunit, encoded by the Grin1 gene, selectively in MSNs. Although these knockout mice appear normal and display normal 24-hour locomotion, they have severe deficits in motor learning, operant conditioning and active avoidance. In addition, the MSNs from these knockout mice have smaller cell bodies and decreased dendritic length compared to littermate controls. We conclude that NMDAR signaling in MSNs is critical for normal MSN morphology and many forms of learning

Altered mRNA Editing and Expression of Ionotropic Glutamate Receptors after Kainic Acid Exposure in Cyclooxygenase-2 Deficient Mice

Kainic acid (KA) binds to the AMPA/KA receptors and induces seizures that result in inflammation, oxidative damage and neuronal death. We previously showed that cyclooxygenase-2 deficient (COX-2−/−) mice are more vulnerable to KA-induced excitotoxicity. Here, we investigated whether the increased susceptibility of COX-2−/− mice to KA is associated with altered mRNA expression and editing of glutamate receptors. The expression of AMPA GluR2, GluR3 and KA GluR6 was increased in vehicle-injected COX-2−/− mice compared to wild type (WT) mice in hippocampus and cortex, whereas gene expression of NMDA receptors was decreased. KA treatment decreased the expression of AMPA, KA and NMDA receptors in the hippocampus, with a significant effect in COX-2−/− mice. Furthermore, we analyzed RNA editing levels and found that the level of GluR3 R/G editing site was selectively increased in the hippocampus and decreased in the cortex in COX-2−/− compared with WT mice. After KA, GluR4 R/G editing site, flip form, was increased in the hippocampus of COX-2−/− mice. Treatment of WT mice with the COX-2 inhibitor celecoxib for two weeks decreased the expression of AMPA/KA and NMDAR subunits after KA, as observed in COX-2−/− mice. After KA exposure, COX-2−/− mice showed increased mRNA expression of markers of inflammation and oxidative stress, such as cytokines (TNF-α, IL-1β and IL-6), inducible nitric oxide synthase (iNOS), microglia (CD11b) and astrocyte (GFAP). Thus, COX-2 gene deletion can exacerbate the inflammatory response to KA. We suggest that COX-2 plays a role in attenuating glutamate excitotoxicity by modulating RNA editing of AMPA/KA and mRNA expression of all ionotropic glutamate receptor subunits and, in turn, neuronal excitability. These changes may contribute to the increased vulnerability of COX-2−/− mice to KA. The overstimulation of glutamate receptors as a consequence of COX-2 gene deletion suggests a functional coupling between COX-2 and the glutamatergic system

Effects of Subthalamic Nucleus Lesions and Stimulation upon Corticostriatal Afferents in the 6-Hydroxydopamine-Lesioned Rat

Abnormalities of striatal glutamate neurotransmission may play a role in the pathophysiology of Parkinson's disease and may respond to neurosurgical interventions, specifically stimulation or lesioning of the subthalamic nucleus (STN). The major glutamatergic afferent pathways to the striatum are from the cortex and thalamus, and are thus likely to be sources of striatal neuronally-released glutamate. Corticostriatal terminals can be distinguished within the striatum at the electron microscopic level as their synaptic vesicles contain the vesicular glutamate transporter, VGLUT1. The majority of terminals which are immunolabeled for glutamate but are not VGLUT1 positive are likely to be thalamostriatal afferents. We compared the effects of short term, high frequency, STN stimulation and lesioning in 6-hydroxydopamine (6OHDA)-lesioned rats upon striatal terminals immunolabeled for both presynaptic glutamate and VGLUT1. 6OHDA lesions resulted in a small but significant increase in the proportions of VGLUT1-labeled terminals making synapses on dendritic shafts rather than spines. STN stimulation for one hour, but not STN lesions, increased the proportion of synapses upon spines. The density of presynaptic glutamate immuno-gold labeling was unchanged in both VGLUT1-labeled and -unlabeled terminals in 6OHDA-lesioned rats compared to controls. Rats with 6OHDA lesions+STN stimulation showed a decrease in nerve terminal glutamate immuno-gold labeling in both VGLUT1-labeled and -unlabeled terminals. STN lesions resulted in a significant decrease in the density of presynaptic immuno-gold-labeled glutamate only in VGLUT1-labeled terminals. STN interventions may achieve at least part of their therapeutic effect in PD by normalizing the location of corticostriatal glutamatergic terminals and by altering striatal glutamatergic neurotransmission