236 research outputs found
Effective actions with fixed points, (error in derivation of coefficient corrected)
The specific form of the constant term in the asymptotic expansion of the
heat-kernel on an axially-symmetric space with a codimension two fixed-point
set of conical singularities is used to determine the associated conformal
change of the effective action in four dimensions. Another derivation of the
relevant coefficient is presented.Comment: 10p,uses JyTeX,MUTP/94/1
Causality in Time-Neutral Cosmologies
Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological
models in which the initial and final conditions are independently specified,
and several authors have investigated experimental tests of such models.
We point out here that GMH time-neutral models can allow superluminal
signalling, in the sense that it can be possible for observers in those
cosmologies, by detecting and exploiting regularities in the final state, to
construct devices which send and receive signals between space-like separated
points. In suitable cosmologies, any single superluminal message can be
transmitted with probability arbitrarily close to one by the use of redundant
signals. However, the outcome probabilities of quantum measurements generally
depend on precisely which past {\it and future} measurements take place. As the
transmission of any signal relies on quantum measurements, its transmission
probability is similarly context-dependent. As a result, the standard
superluminal signalling paradoxes do not apply. Despite their unusual features,
the models are internally consistent.
These results illustrate an interesting conceptual point. The standard view
of Minkowski causality is not an absolutely indispensable part of the
mathematical formalism of relativistic quantum theory. It is contingent on the
empirical observation that naturally occurring ensembles can be naturally
pre-selected but not post-selected.Comment: 5 pages, RevTeX. Published version -- minor typos correcte
Effective actions on the squashed three-sphere
The effective actions of a scalar and massless spin-half field are determined
as functions of the deformation of a symmetrically squashed three-sphere. The
extreme oblate case is particularly examined as pertinant to a high temperature
statistical mechanical interpretation that may be relevant for the holographic
principle. Interpreting the squashing parameter as a temperature, we find that
the effective `free energies' on the three-sphere are mixtures of thermal
two-sphere scalars and spinors which, in the case of the spinor on the
three-sphere, have the `wrong' thermal periodicities. However the free energies
do have the same leading high temperature forms as the standard free energies
on the two-sphere. The next few terms in the high-temperature expansion are
also explicitly calculated and briefly compared with the Taub-Bolt-AdS bulk
result.Comment: 23 pages, JyTeX. Conclusion slightly amended, one equation and minor
misprints correcte
Aspects of classical and quantum motion on a flux cone
Motion of a non-relativistic particle on a cone with a magnetic flux running
through the cone axis (a ``flux cone'') is studied. It is expressed as the
motion of a particle moving on the Euclidean plane under the action of a
velocity-dependent force. Probability fluid (``quantum flow'') associated with
a particular stationary state is studied close to the singularity,
demonstrating non trivial Aharonov-Bohm effects. For example, it is shown that
near the singularity quantum flow departs from classical flow. In the context
of the hydrodynamical approach to quantum mechanics, quantum potential due to
the conical singularity is determined and the way it affects quantum flow is
analysed. It is shown that the winding number of classical orbits plays a role
in the description of the quantum flow. Connectivity of the configuration space
is also discussed.Comment: LaTeX file, 21 pages, 8 figure
Zeta functions, renormalization group equations, and the effective action
We demonstrate how to extract all the one-loop renormalization group
equations for arbitrary quantum field theories from knowledge of an appropriate
Seeley--DeWitt coefficient. By formally solving the renormalization group
equations to one loop, we renormalization group improve the classical action,
and use this to derive the leading-logarithms in the one-loop effective action
for arbitrary quantum field theories.Comment: 4 pages, ReV-TeX 3.
Quantum Dynamics without the Wave Function
When suitably generalized and interpreted, the path-integral offers an
alternative to the more familiar quantal formalism based on state-vectors,
selfadjoint operators, and external observers. Mathematically one generalizes
the path-integral-as-propagator to a {\it quantal measure} on the space
of all ``conceivable worlds'', and this generalized measure expresses
the dynamics or law of motion of the theory, much as Wiener measure expresses
the dynamics of Brownian motion. Within such ``histories-based'' schemes new,
and more ``realistic'' possibilities open up for resolving the philosophical
problems of the state-vector formalism. In particular, one can dispense with
the need for external agents by locating the predictive content of in its
sets of measure zero: such sets are to be ``precluded''. But unrestricted
application of this rule engenders contradictions. One possible response would
remove the contradictions by circumscribing the application of the preclusion
concept. Another response, more in the tradition of ``quantum logic'', would
accommodate the contradictions by dualizing to a space of
``co-events'' and effectively identifying reality with an element of this dual
space.Comment: plainTeX, 24 pages, no figures. To appear in a special volume of {\it
Journal of Physics A: Mathematical and General} entitled ``The Quantum
Universe'' and dedicated to Giancarlo Ghirardi on the occasion of his 70th
birthday. Most current version is available at
http://www.physics.syr.edu/~sorkin/some.papers/ (or wherever my home-page may
be
Fuzzy Rings in D6-Branes and Magnetic Field Background
We use the Myers T-dual nonabelin Born-Infeld action to find some new
nontrivial solutions for the branes in the background of D6-branes and Melvin
magnetic tube field. In the D6-Branes background we can find both of the fuzzy
sphere and fuzzy ring solutions, which are formed by the gravitational
dielectric effect. We see that the fuzzy ring solution has less energy then
that of the fuzzy sphere. Therefore the fuzzy sphere will decay to the fuzzy
ring configuration. In the Melvin magnetic tube field background there does not
exist fuzzy sphere while the fuzzy ring configuration may be formed by the
magnetic dielectric effect. The new solution shows that propagating in
the D6-branes and magnetic tube field background may expand into a rotating
fuzzy ring. We also use the Dirac-Born-Infeld action to construct the ring
configuration from the D-branes.Comment: Latex, 15 pages, detailed comments in section 2, typos correcte
Dirac fields in the background of a magnetic flux string and spectral boundary conditions
We study the problem of a Dirac field in the background of an Aharonov-Bohm
flux string. We exclude the origin by imposing spectral boundary conditions at
a finite radius then shrinked to zero. Thus, we obtain a behaviour of
eigenfunctions which is compatible with the self-adjointness of the radial
Hamiltonian and the invariance under integer translations of the reduced flux.
After confining the theory to a finite region, we check the consistency with
the index theorem, and evaluate its vacuum fermionic number and Casimir energy.Comment: 9 pages, 1 figure Two references added To be published in
International Journal of Modern Physics
Choice of Consistent Family, and Quantum Incompatibility
In consistent history quantum theory, a description of the time development
of a quantum system requires choosing a framework or consistent family, and
then calculating probabilities for the different histories which it contains.
It is argued that the framework is chosen by the physicist constructing a
description of a quantum system on the basis of questions he wishes to address,
in a manner analogous to choosing a coarse graining of the phase space in
classical statistical mechanics. The choice of framework is not determined by
some law of nature, though it is limited by quantum incompatibility, a concept
which is discussed using a two-dimensional Hilbert space (spin half particle).
Thus certain questions of physical interest can only be addressed using
frameworks in which they make (quantum mechanical) sense. The physicist's
choice does not influence reality, nor does the presence of choices render the
theory subjective. On the contrary, predictions of the theory can, in
principle, be verified by experimental measurements. These considerations are
used to address various criticisms and possible misunderstandings of the
consistent history approach, including its predictive power, whether it
requires a new logic, whether it can be interpreted realistically, the nature
of ``quasiclassicality'', and the possibility of ``contrary'' inferences.Comment: Minor revisions to bring into conformity with published version.
Revtex 29 pages including 1 page with figure
Compactification, topology change and surgery theory
We study the process of compactification as a topology change. It is shown
how the mediating spacetime topology, or cobordism, may be simplified through
surgery. Within the causal Lorentzian approach to quantum gravity, it is shown
that any topology change in dimensions may be achieved via a causally
continuous cobordism. This extends the known result for 4 dimensions.
Therefore, there is no selection rule for compactification at the level of
causal continuity. Theorems from surgery theory and handle theory are seen to
be very relevant for understanding topology change in higher dimensions.
Compactification via parallelisable cobordisms is particularly amenable to
study with these tools.Comment: 1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected
case adde
- …