Renormalization of Poincare Transformations in Hamiltonian Semiclassical Field Theory

Semiclassical Hamiltonian field theory is investigated from the axiomatic point of view. A notion of a semiclassical state is introduced. An "elementary" semiclassical state is specified by a set of classical field configuration and quantum state in this external field. "Composed" semiclassical states viewed as formal superpositions of "elementary" states are nontrivial only if the Maslov isotropic condition is satisfied; the inner product of "composed" semiclassical states is degenerate. The mathematical proof of Poincare invariance of semiclassical field theory is obtained for "elementary" and "composed" semiclassical states. The notion of semiclassical field is introduced; its Poincare invariance is also mathematically proved.Comment: LaTeX, 40 pages; short version of hep-th/010307

Heisenberg Evolution WKB and Symplectic Area Phases

The Schrodinger and Heisenberg evolution operators are represented in quantum phase space by their Weyl symbols. Their semiclassical approximations are constructed in the short and long time regimes. For both evolution problems, the WKB representation is purely geometrical: the amplitudes are functions of a Poisson bracket and the phase is the symplectic area of a region in phase space bounded by trajectories and chords. A unified approach to the Schrodinger and Heisenberg semiclassical evolutions is developed by introducing an extended phase space. In this setting Maslov's pseudodifferential operator version of WKB analysis applies and represents these two problems via a common higher dimensional Schrodinger evolution, but with different extended Hamiltonians. The evolution of a Lagrangian manifold in the extended phase space, defined by initial data, controls the phase, amplitude and caustic behavior. The symplectic area phases arise as a solution of a boundary condition problem. Various applications and examples are considered.Comment: 32 pages, 7 figure

A coordinated DNA damage response promotes adult quiescent neural stem cell activation

Stem and differentiated cells frequently differ in their response to DNA damage, which can determine tissue sensitivity. By exploiting insight into the spatial arrangement of subdomains within the adult neural subventricular zone (SVZ) in vivo, we show distinct responses to ionising radiation (IR) between neural stem and progenitor cells. Further, we reveal different DNA damage responses between neonatal and adult neural stem cells (NSCs). Neural progenitors (transit amplifying cells and neuroblasts) but not NSCs (quiescent and activated) undergo apoptosis after 2 Gy IR. This response is cell type- rather than proliferationdependent and does not appear to be driven by distinctions in DNA damage induction or repair capacity. Moreover, exposure to 2 Gy IR promotes proliferation arrest and differentiation in the adult SVZ. These 3 responses are ataxia telangiectasia mutated (ATM)- dependent and promote quiescent NSC (qNSC) activation, which does not occur in the subdomains that lack progenitors. Neuroblasts arising post-IR derive from activated qNSCs rather than irradiated progenitors, minimising damage compounded by replication or mitosis. We propose that rather than conferring sensitive cell death, apoptosis is a form of rapid cell death that serves to remove damaged progenitors and promote qNSC activation. Significantly, analysis of the neonatal (P5) SVZ reveals that although progenitors remain sensitive to apoptosis, they fail to efficiently arrest proliferation. Consequently, their repopulation occurs rapidly from irradiated progenitors rather than via qNSC activation