Back-Reaction on the Topological Degrees of Freedom in (2+1)-Dimensional Spacetime

We investigate the back-reaction effect of the quantum field on the topological degrees of freedom in (2+1)-dimensional toroidal universe, ${\cal M} \simeq T^2\times {\bf R}$. Constructing a homogeneous model of the toroidal universe, we examine explicitly the back-reaction effect of the Casimir energy of a massless, conformally coupled scalar field, with a conformal vacuum. The back-reaction causes an instability of the universe: The torus becomes thinner and thinner as it evolves, while its total 2-volume (area) becomes smaller and smaller. The back-reaction caused by the Casimir energy can be compared with the influence of the negative cosmological constant: Both of them make the system unstable and the torus becomes thinner and thinner in shape. On the other hand, the Casimir energy is a complicated function of the Teichm\"uller parameters $(\tau^1, \tau^2)$ causing highly non-trivial dynamical evolutions, while the cosmological constant is simply a constant. Since the spatial section is a 2-torus, we shall write down the partition function of this system, fixing the path-integral measure for gravity modes, with the help of the techniques developed in string theories. We show explicitly that the partition function expressed in terms of the canonical variables corresponding to the (redundantly large) original phase space, is reduced to the partition function defined in terms of the physical-phase-space variables with a standard Liouville measure. This result is compatible with the general theory of the path integral for the 1st-class constrained systems.Comment: 42 pages, phyzzx.tex, Figures will be sent on reques

Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added reference

Site-specific translocation and evidence of postnatal origin of the t(1;19) E2A-PBX1 fusion in childhood acute lymphoblastic leukemia

The t(1;19) translocation yields a fusion between E2A and PBX1 genes and occurs in 5% of acute lymphoblastic leukemia in children and adults. We used chromosomal translocations and Ig heavy chain (IGH)/T cell antigen receptor (TCR) rearrangements to develop an understanding of the etiology and natural history of this subtype of leukemia. We sequenced the genomic fusion between E2A and PBX1 in 22 preB acute lymphoblastic leukemias and two cell lines. The prenatal origin of the leukemia was assessed in 15 pediatric patients by screening for the clonotypic E2A-PBX1 translocation in neonatal blood spots, or Guthrie cards, obtained from the children at the time of birth. Two patients were determined to be weakly positive for the fusion at the time of birth, in contrast to previously studied childhood leukemia fusions, t(12;21), t(8;21), and t(4;11), which were predominantly prenatal. The presence of extensive N-nucleotides at the point of fusion in the E2A-PBX1 translocation as well as specific characteristics of the IGH/TCR rearrangements provided additional evidence for a postnatal, preB cell origin. Intriguingly, 16 of 24 breakpoints on the 3.2-kb E2A intron 14 were located within 5 bp, providing evidence for a site-specific recombination mechanism. Breakpoints on the 232-kb PBX1 intron 1 were more dispersed but highly clustered proximal to exon 2. In sum, the translocation breakpoints displayed evidence of unique temporal, ontological, and mechanistic formation than the previously analyzed pediatric leukemia translocation breakpoints and emphasize the need to differentiate cytogenetic and molecular subgroups for studies of leukemia causality