121 research outputs found
Reissner Nordstr\"{o}m Background Metric in Dynamical Co-ordinates: Exceptional Behaviour of Hadamard States
We cast the Reissner Nordstrom solution in a particular co-ordinate system
which shows dynamical evolution from initial data. The initial data for the
case is regular. This procedure enables us to treat the metric as a
collapse to a singularity. It also implies that one may assume Wald axioms to
be valid globally in the Cauchy development, especially when Hadamard states
are chosen. We can thus compare the semiclassical behaviour with spherical dust
case, looking upon the metric as well as state specific information as
evolution from initial data. We first recover the divergence on the Cauchy
horizon obtained earlier. We point out that the semiclassical domain extends
right upto the Cauchy horizon. This is different from the spherical dust case
where the quantum gravity domain sets in before. We also find that the
backreaction is not negligible near the central singularity, unlike the dust
case. Apart from these differences, the Reissner Nordstrom solution has a
similarity with dust in that it is stable over a considerable period of time.
The features appearing dust collapse mentioned above were suggested to be
generally applicable within spherical symmetry. Reissner Nordstrom background
(along with the quantum state) generated from initial data, is shown not to
reproduce them
Effect of Bacterial Adsorption on Low Frequency Electrical Properties of Clean Quartz Sands and Iron-Oxide Coated Sands
Low frequency electrical measurements (0.1-1000 Hz) were conducted to investigate the adsorption effect of Pseudomonas aeruginosa cells onto clean quartz sands and iron-oxide coated sands. The clean quartz sands showed a gradual increase in the microbial adsorption to mineral grains, concurrent with an increase of 13% in the imaginary conductivity component (σ″). However, iron-oxide coated sands (20-100% by weight) showed a rapid increase in microbial adsorption with σ″ reaching a maximum of 37% for the 80-100% iron coated sands. No significant changes were observed in the real conductivity component (σ′) due to microbial adsorption. A power law dependency was observed between the adsorbed cells and σ″. We suggest that the polarization results from the increase in the surface roughness and surface area of the grain due to bacteria sorption. These results suggest that low frequency electrical measurements can play an important role in assessing microbial transport in subsurface environments
Supersymmetric Field-Theoretic Models on a Supermanifold
We propose the extension of some structural aspects that have successfully
been applied in the development of the theory of quantum fields propagating on
a general spacetime manifold so as to include superfield models on a
supermanifold. We only deal with the limited class of supermanifolds which
admit the existence of a smooth body manifold structure. Our considerations are
based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In
particular, we show that the class of supermanifolds constructed by
Bonora-Pasti-Tonin satisfies the criterions which guarantee that a
supermanifold admits a Hausdorff body manifold. This construction is the
closest to the physicist's intuitive view of superspace as a manifold with some
anticommuting coordinates, where the odd sector is topologically trivial. The
paper also contains a new construction of superdistributions and useful results
on the wavefront set of such objects. Moreover, a generalization of the
spectral condition is formulated using the notion of the wavefront set of
superdistributions, which is equivalent to the requirement that all of the
component fields satisfy, on the body manifold, a microlocal spectral condition
proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy
Hadamard states from null infinity
Free field theories on a four dimensional, globally hyperbolic spacetime,
whose dynamics is ruled by a Green hyperbolic partial differential operator,
can be quantized following the algebraic approach. It consists of a two-step
procedure: In the first part one identifies the observables of the underlying
physical system collecting them in a *-algebra which encodes their relational
and structural properties. In the second step one must identify a quantum
state, that is a positive, normalized linear functional on the *-algebra out of
which one recovers the interpretation proper of quantum mechanical theories via
the so-called Gelfand-Naimark-Segal theorem. In between the plethora of
possible states, only few of them are considered physically acceptable and they
are all characterized by the so-called Hadamard condition, a constraint on the
singular structure of the associated two-point function. Goal of this paper is
to outline a construction scheme for these states which can be applied whenever
the underlying background possesses a null (conformal) boundary. We discuss in
particular the examples of a real, massless conformally coupled scalar field
and of linearized gravity on a globally hyperbolic and asymptotically flat
spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum
Mathematical Physics", held in Regensburg from the 29th of September to the
02nd of October 201
Infrared problem for the Nelson model on static space-times
We consider the Nelson model with variable coefficients and investigate the
problem of existence of a ground state and the removal of the ultraviolet
cutoff. Nelson models with variable coefficients arise when one replaces in the
usual Nelson model the flat Minkowski metric by a static metric, allowing also
the boson mass to depend on position. A physical example is obtained by
quantizing the Klein-Gordon equation on a static space-time coupled with a
non-relativistic particle. We investigate the existence of a ground state of
the Hamiltonian in the presence of the infrared problem, i.e. assuming that the
boson mass tends to 0 at infinity
Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime
We prove that the singularity structure of all n-point distributions of a
state of a generalised real free scalar field in curved spacetime can be
estimated if the two-point distribution is of Hadamard form. In particular this
applies to the real free scalar field and the result has applications in
perturbative quantum field theory, showing that the class of all Hadamard
states is the state space of interest. In our proof we assume that the field is
a generalised free field, i.e. that it satisies scalar (c-number) commutation
relations, but it need not satisfy an equation of motion. The same argument
also works for anti-commutation relations and it can be generalised to
vector-valued fields. To indicate the strengths and limitations of our
assumption we also prove the analogues of a theorem by Borchers and Zimmermann
on the self-adjointness of field operators and of a very weak form of the
Jost-Schroer theorem. The original proofs of these results in the Wightman
framework make use of analytic continuation arguments. In our case no
analyticity is assumed, but to some extent the scalar commutation relations can
take its place.Comment: 18 page
A general worldline quantum inequality
Worldline quantum inequalities provide lower bounds on weighted averages of
the renormalised energy density of a quantum field along the worldline of an
observer. In the context of real, linear scalar field theory on an arbitrary
globally hyperbolic spacetime, we establish a worldline quantum inequality on
the normal ordered energy density, valid for arbitrary smooth timelike
trajectories of the observer, arbitrary smooth compactly supported weight
functions and arbitrary Hadamard quantum states. Normal ordering is performed
relative to an arbitrary choice of Hadamard reference state. The inequality
obtained generalises a previous result derived for static trajectories in a
static spacetime. The underlying argument is straightforward and is made
rigorous using the techniques of microlocal analysis. In particular, an
important role is played by the characterisation of Hadamard states in terms of
the microlocal spectral condition. We also give a compact form of our result
for stationary trajectories in a stationary spacetime.Comment: 19pp, LaTeX2e. The statement of the main result is changed slightly.
Several typos fixed, references added. To appear in Class Quantum Gra
Focusing and the Holographic Hypothesis
The ``screen mapping" introduced by Susskind to implement 't Hooft's
holographic hypothesis is studied. For a single screen time, there are an
infinite number of images of a black hole event horizon, almost all of which
have smaller area on the screen than the horizon area. This is consistent with
the focusing equation because of the existence of focal points. However, the
{\it boundary} of the past (or future) of the screen obeys the area theorem,
and so always gives an expanding map to the screen, as required by the
holographic hypothesis. These considerations are illustrated with several
axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi
Bounds on negative energy densities in flat spacetime
We generalise results of Ford and Roman which place lower bounds -- known as
quantum inequalities -- on the renormalised energy density of a quantum field
averaged against a choice of sampling function. Ford and Roman derived their
results for a specific non-compactly supported sampling function; here we use a
different argument to obtain quantum inequalities for a class of smooth, even
and non-negative sampling functions which are either compactly supported or
decay rapidly at infinity. Our results hold in -dimensional Minkowski space
() for the free real scalar field of mass . We discuss various
features of our bounds in 2 and 4 dimensions. In particular, for massless field
theory in 2-dimensional Minkowski space, we show that our quantum inequality is
weaker than Flanagan's optimal bound by a factor of 3/2.Comment: REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference
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