A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity

We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is \Phi_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j=1}^m A_j^p)^{q/p}))^{1/q} for m positive definite operators A_j. In part I we only considered the case q=1 and proved the concavity of \Phi_{p,1} for 0 < p \leq 1 and the convexity for p=2. We conjectured the convexity of \Phi_{p,1} for 1< p < 2. Here we not only settle the unresolved case of joint convexity for 1 \leq p \leq 2, we are also able to include the parameter q\geq 1 and still retain the convexity. Among other things this leads to a definition of an L^q(L^p) norm for operators when 1 \leq p \leq 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces -- which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.Comment: Proof of a conjecture in math/0701352. Revised version replaces earlier draft. 18 pages, late

A sharpened nuclearity condition for massless fields

A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the momentum transfer of local operators in this model.Comment: 13 pages, LaTeX. As appeared in Letters in Mathematical Physic

Solitons in Affine and Permutation Orbifolds

We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the twisted representations of the fixed point subnet. This allows us to prove a number of conjectures: in the affine orbifold case we clarify the issue of ``fixed point resolutions''; in the permutation orbifold case we determine all irreducible representations of the orbifold, and we also determine the fusion rules in a nontrivial case, which imply an integral property of chiral data for any completely rational conformal net.Comment: Latex, 48 pages, minor style correction

Lightfront holography and area density of entropy associated with localization on wedge-horizons

It is shown that a suitably formulated algebraic lightfront holography, in which the lightfront is viewed as the linear extension of the upper causal horizon of a wedge region, is capable of overcoming the shortcomings of the old lightfront quantization. The absence of transverse vacuum fluctuations which this formalism reveals, is responsible for an area (edge of the wedge) -rearrangement of degrees of freedom which in turn leads to the notion of area density of entropy for a ``split localization''. This area proportionality of horizon associated entropy has to be compared to the volume dependence of ordinary heat bath entropy. The desired limit, in which the split distance vanishes and the localization on the horizon becomes sharp, can at most yield a relative area density which measures the ratio of area densities for different quantum matter. In order to obtain a normalized area density one needs the unknown analog of a second fundamental law of thermodynamics for thermalization caused by vacuum fluctuation through localization on causal horizons. This is similar to the role of the classical Gibbs form of that law which relates Bekenstein's classical area formula with the Hawking quantum mechanism for thermalization from black holes. PACS: 11.10.-z, 11.30.-j, 11.55.-mComment: The last two sections have been modified. This is the form in which the paper will be published in IJP

Joint system quantum descriptions arising from local quantumness

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely

New Concepts in Particle Physics from Solution of an Old Problem

Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein causality. Among the collateral results of this new nonperturbative approach are profound relations between crossing symmetry of particle physics and Hawking-Unruh like thermal aspects (KMS property, entropy attached to horizons) of quantum matter behind causal horizons, aspects which hitherto were exclusively related with Killing horizons in curved spacetime rather than with localization aspects in Minkowski space particle physics. The scope of this modular framework is amazingly wide and ranges from providing a conceptual basis for the d=1+1 bootstrap-formfactor program for factorizable d=1+1 models to a decomposition theory of QFT's in terms of a finite collection of unitarily equivalent chiral conformal theories placed a specified relative position within a common Hilbert space (in d=1+1 a holographic relation and in higher dimensions more like a scanning). The new framework gives a spacetime interpretation to the Zamolodchikov-Faddeev algebra and explains its thermal aspects.Comment: In this form it will appear in JPA Math Gen, 47 pages tcilate

The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.454

Review of genetic factors in intestinal malrotation

Intestinal malrotation is well covered in the surgical literature from the point of view of operative management, but few reviews to date have attempted to provide a comprehensive examination of the topic from the point of view of aetiology, in particular genetic aetiology. Following a brief overview of molecular embryology of midgut rotation, we present in this article instances of and case reports and case series of intestinal malrotation in which a genetic aetiology is likely. Autosomal dominant, autosomal recessive, X-linked and chromosomal forms of the disorder are represented. Most occur in syndromic form, that is to say, in association with other malformations. In many instances, recognition of a specific syndrome is possible, one of several examples discussed being the recently described association of intestinal malrotation with alveolar capillary dysplasia, due to mutations in the forkhead box transcription factor FOXF1. New advances in sequencing technology mean that the identification of the genes mutated in these disorders is more accessible than ever, and paediatric surgeons are encouraged to refer to their colleagues in clinical genetics where a genetic aetiology seems likely