[en] We consider Deutsch's computational model of a quantum system evolving in a spacetime containing closed timelike curves. Although it is known that this model predicts nonlinear and nonunitary evolutions of the system, we demonstrate that it also gives rise to evolutions which are a discontinuous function of the input state. These discontinuities persist for the most natural modifications of Deutsch's approach.

[en] For any pair of bounded observables A and B with pure point spectra, we construct an associated ‘joint observable’ which gives rise to a notion of a joint (projective) measurement of A and B, and which conforms to the intuition that one can measure non-commuting observables simultaneously, provided one is willing to give up arbitrary precision. As an application, we show how our notion of a joint observable naturally allows for a construction of a ‘functional calculus,’ so that for any pair of observables A and B as above, and any (Borel measurable) function $f:{\mathbb{R}}^2\to <!--\; ???\; -->\mathbb{R}$, a new ‘generalized observable’ $f(A,B)$ is obtained. Moreover, we show that this new functional calculus has some rather remarkable properties. (paper)

[en] Symmetry breaking can produce 'Alice' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. Alice behavior arises algebraically, when strings obstruct unbroken symmetries--a fragile criterion. We give a topological criterion, compelling Alice behavior or deforming it away. Our criterion, that π₀(H) acts nontrivially on π₁(H), links topologically Alice strings to topological monopoles. We twist topologically Alice loops to form monopoles. We show that Alice strings of condensed matter systems (nematic liquid crystals, ³He-A, and related non-chiral Bose condensates and amorphous chiral superconductors) are topologically Alice, and support fundamental monopole charge when twisted into loops. Thus they might be observed indirectly, not as strings, but as loop-like point defects. We describe other models, showing Alice strings failing our topological criterion; and twisted Alice loops supporting deposited, but not fundamental, monopole number

[en] We compute the chiral symmetries of the Lagrangian for confining “vector-like” gauge theories with massless fermions in d-dimensional Minkowski space and, under a few reasonable assumptions, determine the form of the quadratic fermion condensates which arise through spontaneous breaking of these symmetries. We find that for each type (complex, real, or pseudoreal) of representation of the gauge group carried by the fermions, the chiral symmetries of the Lagrangian, as well as the residual symmetries after dynamical breaking, exactly follow the pattern of Bott periodicity as the dimension changes. The consequences of this for the topological features of the low-energy effective theory are considered.