1,004 research outputs found
Generalisations of the Laplace-Runge-Lenz vector in classical mechanics
Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 199
Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference
Information geometric techniques and inductive inference methods hold great
promise for solving computational problems of interest in classical and quantum
physics, especially with regard to complexity characterization of dynamical
systems in terms of their probabilistic description on curved statistical
manifolds. In this article, we investigate the possibility of describing the
macroscopic behavior of complex systems in terms of the underlying statistical
structure of their microscopic degrees of freedom by use of statistical
inductive inference and information geometry. We review the Maximum Relative
Entropy (MrE) formalism and the theoretical structure of the information
geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special
focus is devoted to the description of the roles played by the sectional
curvature, the Jacobi field intensity and the information geometrodynamical
entropy (IGE). These quantities serve as powerful information geometric
complexity measures of information-constrained dynamics associated with
arbitrary chaotic and regular systems defined on the statistical manifold.
Finally, the application of such information geometric techniques to several
theoretical models are presented.Comment: 29 page
Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
We study the entanglement entropy between (possibly distinct) topological
phases across an interface using an Abelian Chern-Simons description with
topological boundary conditions (TBCs) at the interface. From a microscopic
point of view, these TBCs correspond to turning on particular gapping
interactions between the edge modes across the interface. However, in studying
entanglement in the continuum Chern-Simons description, we must confront the
problem of non-factorization of the Hilbert space, which is a standard property
of gauge theories. We carefully define the entanglement entropy by using an
extended Hilbert space construction directly in the continuum theory. We show
how a given TBC isolates a corresponding gauge invariant state in the extended
Hilbert space, and hence compute the resulting entanglement entropy. We find
that the sub-leading correction to the area law remains universal, but depends
on the choice of topological boundary conditions. This agrees with the
microscopic calculation of \cite{Cano:2014pya}. Additionally, we provide a
replica path integral calculation for the entropy. In the case when the
topological phases across the interface are taken to be identical, our
construction gives a novel explanation of the equivalence between the
left-right entanglement of (1+1)d Ishibashi states and the spatial entanglement
of (2+1)d topological phases.Comment: 36 pages, 7 figures, two appendice
Holography of Gravitational Action Functionals
Einstein-Hilbert (EH) action can be separated into a bulk and a surface term,
with a specific ("holographic") relationship between the two, so that either
can be used to extract information about the other. The surface term can also
be interpreted as the entropy of the horizon in a wide class of spacetimes.
Since EH action is likely to just the first term in the derivative expansion of
an effective theory, it is interesting to ask whether these features continue
to hold for more general gravitational actions. We provide a comprehensive
analysis of lagrangians of the form L=Q_a^{bcd}R^a_{bcd}, in which Q_a^{bcd} is
a tensor with the symmetries of the curvature tensor, made from metric and
curvature tensor and satisfies the condition \nabla_cQ^{abcd}=0, and show that
they share these features. The Lanczos-Lovelock lagrangians are a subset of
these in which Q^{abcd} is a homogeneous function of the curvature tensor. They
are all holographic, in a specific sense of the term, and -- in all these cases
-- the surface term can be interpreted as the horizon entropy. The
thermodynamics route to gravity, in which the field equations are interpreted
as TdS=dE+pdV, seems to have greater degree of validity than the field
equations of Einstein gravity itself. The results suggest that the holographic
feature of EH action could also serve as a new symmetry principle in
constraining the semiclassical corrections to Einstein gravity. The
implications are discussed.Comment: revtex 4; 17 pages; no figure
Gravity and the Thermodynamics of Horizons
Spacetimes with horizons show a resemblance to thermodynamic systems and it
is possible to associate the notions of temperature and entropy with them.
Several aspects of this connection are reviewed in a manner appropriate for
broad readership. The approach uses two essential principles: (a) the physical
theories must be formulated for each observer entirely in terms of variables
any given observer can access and (b) consistent formulation of quantum field
theory requires analytic continuation to the complex plane. These two
principles, when used together in spacetimes with horizons, are powerful enough
to provide several results in a unified manner. Since spacetimes with horizons
have a generic behaviour under analytic continuation, standard results of
quantum field theory in curved spacetimes with horizons can be obtained
directly (Sections III to VII). The requirements (a) and (b) also put strong
constraints on the action principle describing the gravity and, in fact, one
can obtain the Einstein-Hilbert action from the thermodynamic considerations.
The latter part of the review (Sections VIII to X) investigates this deeper
connection between gravity, spacetime microstructure and thermodynamics of
horizons. This approach leads to several interesting results in the
semiclassical limit of quantum gravity, which are described.Comment: published version; references update
Perfect Fluid Theory and its Extensions
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian
formulations. The theory is related to a description of extended structures in
higher dimensions. Internal symmetry and supersymmetry degrees of freedom are
incorporated. Additional miscellaneous subjects that are covered include
physical topics concerning quantization, as well as mathematical issues of
volume preserving diffeomorphisms and representations of Chern-Simons terms (=
vortex or magnetic helicity).Comment: 3 figure
The Ongoing Impact of Modular Localization on Particle Theory
Modular localization is the concise conceptual formulation of causal
localization in the setting of local quantum physics. Unlike QM it does not
refer to individual operators but rather to ensembles of observables which
share the same localization region, as a result it explains the probabilistic
aspects of QFT in terms of the impure KMS nature arising from the local
restriction of the pure vacuum. Whereas it played no important role in the
perturbation theory of low spin particles, it becomes indispensible for
interactions which involve higher spin fields, where is leads to the
replacement of the operator (BRST) gauge theory setting in Krein space by a new
formulation in terms of stringlocal fields in Hilbert space. The main purpose
of this paper is to present new results which lead to a rethinking of important
issues of the Standard Model concerning massive gauge theories and the Higgs
mechanism. We place these new findings into the broader context of ongoing
conceptual changes within QFT which already led to new nonperturbative
constructions of models of integrable QFTs. It is also pointed out that modular
localization does not support ideas coming from string theory, as extra
dimensions and Kaluza-Klein dimensional reductions outside quasiclassical
approximations. Apart from hologarphic projections on null-surfaces, holograhic
relations between QFT in different spacetime dimensions violate the causal
completeness property, this includes in particular the Maldacena conjecture.
Last not least, modular localization sheds light onto unsolved problems from
QFT's distant past since it reveals that the Einstein-Jordan conundrum is
really an early harbinger of the Unruh effect.Comment: a small text overlap with unpublished arXiv:1201.632
D-branes and BCFT in Hpp-wave backgrounds
In this paper we study two classes of symmetric D-branes in the Nappi-Witten
gravitational wave, namely D2 and branes. We solve the sewing constraints
and determine the bulk-boundary couplings and the boundary three-point
couplings. For the D2 brane our solution gives the first explicit results for
the structure constants of the twisted symmetric branes in a WZW model. We also
compute the boundary four-point functions, providing examples of open string
four-point amplitudes in a curved background. We finally discuss the annulus
amplitudes, the relation with branes in and in and the analogy
between the open string couplings in the model and the couplings for
magnetized and intersecting branes.Comment: 83 pages, 1 figur
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