Runaway modes in model field theories

Within the framework of linear quantum field theories, a general study is presented of the existence and removal of runaway modes—solutions of the equations of motion which exhibit a real exponential time dependence. It is hoped that this work will yield insight into the corresponding problem in physically realistic theories. It is shown that runaway modes occur only when the Hamiltonian is not positive definite, and that they occur in linear quantum theories whenever they appear in the corresponding classical theories. Three methods are proposed for eliminating these unphysical modes One is the analog of the method used by Dirac in classical electron theory; the other two are believed to be new

Black Holes, Wormholes, and the Disappearance of Global Charge

One of the paradoxes associated with the theory of the formation and subsequent Hawking evaporation of a black hole is the disappearance of conserved global charges. It has long been known that metric fluctuations at short distances (wormholes) violate global-charge conservation; if global charges are apparently conserved at ordinary energies, it is only because wormhole-induced global-charge-violating terms in the low-energy effective Lagrangian are suppressed by large mass denominators. However, such suppressed interactions can become important at the high energy densities inside a collapsing star. We analyze this effect for a simple model of the black-hole singularity. (Our analysis is totally independent of any detailed theory of wormhole dynamics; in particular it does not depend on the wormhole theory of the vanishing of the cosmological constant.) We find that in general all charge is extinguished before the infalling matter crosses the singularity. No global charge appears in the outgoing Hawking radiation because it has all gone down the wormholes.Comment: 12 pages (1 figure available upon request); HUTP-93/A01

What Becomes of Global Color

The recent demise of certain global unbroken symmetry generators in the presence of a grand unified magnetic monopole leads us to consider more carefully the notion of charges associated with gauge symmetries. It turns out that global transformations associated with the generators of the gauge group, and their charges, make sense only for extended systems which are sufficiently localized. GUT monopoles fail this criterion. Detailed consideration of the monopole-antimonopole system helps remove apparent paradoxes related to the chromodyon excitations of a single monopole and agrees with the previous result that some, but not all, of the states naively expected do exist. The remaining states ns needed to fill out color multiplets are spread throughout space; they are recovered as long-lived excitations when an antimonopole is brought in from infinity

Globular Clusters and Dwarf Spheroidal Galaxies

Traditionally globular clusters and dwarf spheroidal galaxies have been distinguished by using one or more of the following criteria: (1) mass, (2) luminosity, (3) size, (4) mass-to-light ratio and (5) spread in metallicity. However, a few recently discovered objects show some overlap between the domains in parameter space that are occupied by galaxies and clusters. In the present note it is shown that ellipticity can, in some cases, be used to help distinguish between globular clusters and dwarf spheroidal galaxies.Comment: MNRAS (Letters), in pres

Possible alternative mechanism to SUSY: conservative extensions of the Poincar\'e group

A group theoretical mechanism is outlined, which can indecomposably extend the Poincar\'e group by the compact internal (gauge) symmetries at the price of allowing some nilpotent (or, more precisely: solvable) internal symmetries in addition. Due to the presence of this nilpotent part, the prohibitive argument of the well known Coleman-Mandula and McGlinn no-go theorems do not go through. In contrast to SUSY or extended SUSY, in our construction the symmetries extending the Poincar\'e group will be all internal, i.e. they do not act on the spacetime, merely on some internal degrees of freedom -- hence the name: conservative extensions of the Poincar\'e group. Using the Levi decomposition and O'Raifeartaigh theorem, the general structure of all possible conservative extensions of the Poincar\'e group is outlined, and a concrete example group is presented with U(1) being the compact gauge group component. It is argued that such nilpotent internal symmetries may be inapparent symmetries of some more fundamental field variables, and therefore do not carry an ab initio contradiction with the present experimental understanding in particle physics. The construction is compared to (extended) SUSY, since SUSY is somewhat analogous to the proposed mechanism. It is pointed out, however, that the proposed mechanism is less irregular in comparison to SUSY, in certain aspects. The only exoticity needed in comparison to a traditional gauge theory setting is that the full group of internal symmetries is not purely compact, but is a semi-direct product of a nilpotent and of a compact part.Comment: 10 pages, contribution to Proceedings of X. International Symposium on Quantum Theory and Symmetries, Springer (2018