27 research outputs found
A Note on the correspondence between Qubit Quantum Operations and Special Relativity
We exploit a well-known isomorphism between complex hermitian
matrices and , which yields a convenient real vector
representation of qubit states. Because these do not need to be normalized we
find that they map onto a Minkowskian future cone in , whose
vertical cross-sections are nothing but Bloch spheres. Pure states are
represented by light-like vectors, unitary operations correspond to special
orthogonal transforms about the axis of the cone, positive operations
correspond to pure Lorentz boosts. We formalize the equivalence between the
generalized measurement formalism on qubit states and the Lorentz
transformations of special relativity, or more precisely elements of the
restricted Lorentz group together with future-directed null boosts. The note
ends with a discussion of the equivalence and some of its possible
consequences.Comment: 6 pages, revtex, v3: revised discussio
Penrose Limits and Spacetime Singularities
We give a covariant characterisation of the Penrose plane wave limit: the
plane wave profile matrix is the restriction of the null geodesic
deviation matrix (curvature tensor) of the original spacetime metric to the
null geodesic, evaluated in a comoving frame. We also consider the Penrose
limits of spacetime singularities and show that for a large class of black
hole, cosmological and null singularities (of Szekeres-Iyer ``power-law
type''), including those of the FRW and Schwarzschild metrics, the result is a
singular homogeneous plane wave with profile , the scale
invariance of the latter reflecting the power-law behaviour of the
singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction
Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves
We prove that M-theory plane waves with extra supersymmetries are necessarily
homogeneous (but possibly time-dependent), and we show by explicit construction
that such time-dependent plane waves can admit extra supersymmetries. To that
end we study the Penrose limits of Goedel-like metrics, show that the Penrose
limit of the M-theory Goedel metric (with 20 supercharges) is generically a
time-dependent homogeneous plane wave of the anti-Mach type, and display the
four extra Killings spinors in that case. We conclude with some general remarks
on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2
Kaigorodov spaces and their Penrose limits
Kaigorodov spaces arise, after spherical compactification, as near horizon
limits of M2, M5, and D3-branes with a particular pp-wave propagating in a
world volume direction. We show that the uncompactified near horizon
configurations K\times S are solutions of D=11 or D=10 IIB supergravity which
correspond to perturbed versions of their AdS \times S analogues. We derive the
Penrose-Gueven limits of the Kaigorodov space and the total spaces and analyse
their symmetries. An Inonu-Wigner contraction of the Lie algebra is shown to
occur, although there is a symmetry enhancement. We compare the results to the
maximally supersymmetric CW spaces found as limits of AdS\times S spacetimes:
the initial gravitational perturbation on the brane and its near horizon
geometry remains after taking non-trivial Penrose limits, but seems to
decouple. One particuliar limit yields a time-dependent homogeneous plane-wave
background whose string theory is solvable, while in the other cases we find
inhomogeneous backgrounds.Comment: latex2e, 24 page
Homogeneity and plane-wave limits
We explore the plane-wave limit of homogeneous spacetimes. For plane-wave
limits along homogeneous geodesics the limit is known to be homogeneous and we
exhibit the limiting metric in terms of Lie algebraic data. This simplifies
many calculations and we illustrate this with several examples. We also
investigate the behaviour of (reductive) homogeneous structures under the
plane-wave limit.Comment: In memory of Stanley Hobert, 33 pages. Minor corrections and some
simplification of Section 4.3.
Newton-Hooke spacetimes, Hpp-waves and the cosmological constant
We show explicitly how the Newton-Hooke groups act as symmetries of the
equations of motion of non-relativistic cosmological models with a cosmological
constant. We give the action on the associated non-relativistic spacetimes and
show how these may be obtained from a null reduction of 5-dimensional
homogeneous pp-wave Lorentzian spacetimes. This allows us to realize the
Newton-Hooke groups and their Bargmann type central extensions as subgroups of
the isometry groups of the pp-wave spacetimes. The extended Schrodinger type
conformal group is identified and its action on the equations of motion given.
The non-relativistic conformal symmetries also have applications to
time-dependent harmonic oscillators. Finally we comment on a possible
application to Gao's generalization of the matrix model.Comment: 21 page
Supersymmetry and homogeneity of M-theory backgrounds
We describe the construction of a Lie superalgebra associated to an arbitrary
supersymmetric M-theory background, and discuss some examples. We prove that
for backgrounds with more than 24 supercharges, the bosonic subalgebra acts
locally transitively. In particular, we prove that backgrounds with more than
24 supersymmetries are necessarily (locally) homogeneous.Comment: 19 pages (Erroneous Section 6.3 removed from the paper.
Power-law singularities in string theory and M-theory
We extend the definition of the Szekeres-Iyer power-law singularities to
supergravity, string and M-theory backgrounds, and find that are characterized
by Kasner type exponents. The near singularity geometries of brane and some
intersecting brane backgrounds are investigated and the exponents are computed.
The Penrose limits of some of these power-law singularities have profiles
for . We find the range of the
exponents for which and the frequency squares are bounded by 1/4. We
propose some qualitative tests for deciding whether a null or timelike
spacetime singularity can be resolved within string theory and M-theory based
on the near singularity geometry and its Penrose limits.Comment: 32 page
Causal structures and causal boundaries
We give an up-to-date perspective with a general overview of the theory of
causal properties, the derived causal structures, their classification and
applications, and the definition and construction of causal boundaries and of
causal symmetries, mostly for Lorentzian manifolds but also in more abstract
settings.Comment: Final version. To appear in Classical and Quantum Gravit