16,039 research outputs found
The Oil Man and the Sea: Navigating the Northern Gateway by Arno Kopecky
Review of Arno Kopecky\u27s The Oil Man and the Sea: Navigating the Northern Gateway
Nets of Subfactors
A subtheory of a quantum field theory specifies von~Neumann subalgebras
\aa(\oo) (the `observables' in the space-time region \oo) of the
von~Neumann algebras \bb(\oo) (the `fields' localized in \oo). Every local
algebra being a (type \III_1) factor, the inclusion \aa(\oo) \subset
\bb(\oo) is a subfactor. The assignment of these local subfactors to the
space-time regions is called a `net of subfactors'. The theory of subfactors is
applied to such nets. In order to characterize the `relative position' of the
subtheory, and in particular to control the restriction and induction of
superselection sectors, the canonical endomorphism is studied. The crucial
observation is this: the canonical endomorphism of a local subfactor extends to
an endomorphism of the field net, which in turn restricts to a localized
endomorphism of the observable net. The method allows to characterize, and
reconstruct, local extensions \bb of a given theory in terms of the
observables. Various non-trivial examples are given.Comment: Plain TeX, 32 pages. Several unnecessarily restrictive assumptions
have been relaxed. Proposition 4.10. has been reformulated in a more natural
way. Sect. 3 has been rearranged and a too general statement has been
adjusted. Some further minor change
Tailoring superradiance to design artificial quantum systems
Cooperative phenomena arising due to the coupling of individual atoms via the
radiation field are a cornerstone of modern quantum and optical physics. Recent
experiments on x-ray quantum optics added a new twist to this line of research
by exploiting superradiance in order to construct artificial quantum systems.
However, so far, systematic approaches to deliberately design superradiance
properties are lacking, impeding the desired implementation of more advanced
quantum optical schemes. Here, we develop an analytical framework for the
engineering of single-photon superradiance in extended media applicable across
the entire electromagnetic spectrum, and show how it can be used to tailor the
properties of an artificial quantum system. This "reverse engineering" of
superradiance not only provides an avenue towards non-linear and quantum
mechanical phenomena at x-ray energies, but also leads to a unified view on and
a better understanding of superradiance across different physical systems.Comment: 6 pages + supplemental materia
On local boundary CFT and non-local CFT on the boundary
The holographic relation between local boundary conformal quantum field
theories (BCFT) and their non-local boundary restrictions is reviewed, and
non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium
in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067
with R. Long
How to remove the boundary in CFT - an operator algebraic procedure
The relation between two-dimensional conformal quantum field theories with
and without a timelike boundary is explored.Comment: 18 pages, 2 figures. v2: more precise title, reference correcte
Mapping the invisible hand: a body model of a phantom limb
After amputation, individuals often have vivid experiences of their absent limb (i.e., a phantom limb). Therefore, one’s conscious image of one’s body cannot depend on peripheral input only (Ramachandran & Hirstein, 1998). However, the origin of phantom sensations is hotly debated. Reports of vivid phantoms in the case of congenital absence of the limb show that memory of former body state is not necessary (Brugger et al., 2000). According to one view, phantoms may reflect innate organization of sensorimotor cortices (Melzack, 1990). Alternatively, phantoms could reflect generalization from viewing other people’s bodies (Brugger et al., 2000), a sensorimotor example of the classic theory that understanding oneself follows from understanding the “generalized other” (Mead, 1934, p. 154). Because phantom limbs cannot be stimulated, sensory testing cannot directly compare visual and somatosensory influences on representations of phantom limbs. Consequently, empirical investigation of phantoms is limited
Geometric modular action for disjoint intervals and boundary conformal field theory
In suitable states, the modular group of local algebras associated with
unions of disjoint intervals in chiral conformal quantum field theory acts
geometrically. We translate this result into the setting of boundary conformal
QFT and interpret it as a relation between temperature and acceleration. We
also discuss aspects ("mixing" and "charge splitting") of geometric modular
action for unions of disjoint intervals in the vacuum state.Comment: Dedicated to John E. Roberts on the occasion of his 70th birthday; 24
pages, 3 figure
Thermal States in Conformal QFT. II
We continue the analysis of the set of locally normal KMS states w.r.t. the
translation group for a local conformal net A of von Neumann algebras on the
real line. In the first part we have proved the uniqueness of KMS state on
every completely rational net. In this second part, we exhibit several
(non-rational) conformal nets which admit continuously many primary KMS states.
We give a complete classification of the KMS states on the U(1)-current net and
on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro
net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many
primary KMS states. To this end, we provide a variation of the
Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework:
if there is an inclusion of split nets A in B and A is the fixed point of B
w.r.t. a compact gauge group, then any locally normal, primary KMS state on A
extends to a locally normal, primary state on B, KMS w.r.t. a perturbed
translation. Concerning the non-local case, we show that the free Fermi model
admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his
90th birthday. The final version is available under Open Access. This paper
contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a
proof of the same theorem in the book by Bratteli-Robinson). v3: a reference
correcte
Infinite index extensions of local nets and defects
Subfactor theory provides a tool to analyze and construct extensions of
Quantum Field Theories, once the latter are formulated as local nets of von
Neumann algebras. We generalize some of the results of [LR95] to the case of
extensions with infinite Jones index. This case naturally arises in physics,
the canonical examples are given by global gauge theories with respect to a
compact (non-finite) group of internal symmetries. Building on the works of
Izumi, Longo, Popa [ILP98] and Fidaleo, Isola [FI99], we consider generalized
Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite
von Neumann algebras, which generalize ordinary Q-systems introduced by Longo
[Lon94] to the infinite index case. We characterize inclusions which admit
generalized Q-systems of intertwiners and define a braided product among the
latter, hence we construct examples of QFTs with defects (phase boundaries) of
infinite index, extending the family of boundaries in the grasp of [BKLR16].Comment: 50 page
Charged sectors, spin and statistics in quantum field theory on curved spacetimes
The first part of this paper extends the Doplicher-Haag-Roberts theory of
superselection sectors to quantum field theory on arbitrary globally hyperbolic
spacetimes. The statistics of a superselection sector may be defined as in flat
spacetime and each charge has a conjugate charge when the spacetime possesses
non-compact Cauchy surfaces. In this case, the field net and the gauge group
can be constructed as in Minkowski spacetime.
The second part of this paper derives spin-statistics theorems on spacetimes
with appropriate symmetries. Two situations are considered: First, if the
spacetime has a bifurcate Killing horizon, as is the case in the presence of
black holes, then restricting the observables to the Killing horizon together
with "modular covariance" for the Killing flow yields a conformally covariant
quantum field theory on the circle and a conformal spin-statistics theorem for
charged sectors localizable on the Killing horizon. Secondly, if the spacetime
has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes,
"geometric modular action" of the rotational symmetry leads to a
spin-statistics theorem for charged covariant sectors where the spin is defined
via the SU(2)-covering of the spatial rotation group SO(3).Comment: latex2e, 73 page
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