Pionic Modes Studied by Quasielastic (\vec{p}, \vec{n}) Reactions

It has long been expected that the pionic modes show some collective phenomena such as the pion condensation in the high density nuclear matter and its precursor phenomena in the ordinary nuclei. Here we show an evidence of the precursor observed in the isovector spin longitudinal cross sections ID_q of the quasielastic 12C, 40Ca (\vec{p}, \vec{n}) reactions at T_p = 346 and 494MeV with the momentum transfer q = 1.7fm-1. Another aim of this report is to evaluate the Landau-Migdal parameters g'_{NN}, g'_{N\Delta} and g'_{\Delta\Delta} at the large momentum region from the above reactions. We obtained g'_{NN} \approx 0.6-0.7, g'_{N\Delta} \approx 0.3-0.4. The results are consistent with those at the small momentum region, which are obtained from the Gamov-Teller strength distribution.Comment: 6 pages, 4 figures, proceedings for 7th International Spring Seminar on Nuclear Physics "Challenges of Nuclear Structure" at Maiori, Ital

How to add a boundary condition

Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to B_2: we provide a procedure to construct a Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of B_2 to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S^1.Comment: 20 page

Classification of Subfactors with the Principal Graph D1n

AbstractWe show that the number of the conjugacy classes of the AFD type II1 subfactors with the principal graph D1n is n − 2. This gives the last missing number in the complete classfication list of subfactors with index 4 by S. Popa. This also disproves an announcement of A. Ocneanu that such a subfactor is unique for each n. We give two different proofs. One is by an application of an idea of an orbifold model in solvable lattice model theory to Ocneanu′s paragroup theory and the other is by reduction to classification of dihedral group actions. The latter also shows that the AFD type III1 subfactors with the principal graph D1n split as type II1 subfactors tensored with the common AFD type III1 factor. We also discuss a relation between these proofs and a construction of subfactors using Cuntz algebra endomorphisms

Representations of Conformal Nets, Universal C*-Algebras and K-Theory

We study the representation theory of a conformal net A on the circle from a K-theoretical point of view using its universal C*-algebra C*(A). We prove that if A satisfies the split property then, for every representation \pi of A with finite statistical dimension, \pi(C*(A)) is weakly closed and hence a finite direct sum of type I_\infty factors. We define the more manageable locally normal universal C*-algebra C*_ln(A) as the quotient of C*(A) by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if A is completely rational with n sectors, then C*_ln(A) is a direct sum of n type I_\infty factors. Its ideal K_A of compact operators has nontrivial K-theory, and we prove that the DHR endomorphisms of C*(A) with finite statistical dimension act on K_A, giving rise to an action of the fusion semiring of DHR sectors on K_0(K_A)$. Moreover, we show that this action corresponds to the regular representation of the associated fusion algebra.Comment: v2: we added some comments in the introduction and new references. v3: new authors' addresses, minor corrections. To appear in Commun. Math. Phys. v4: minor corrections, updated reference

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

Algebraic conformal quantum field theory in perspective

Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.Comment: Review paper, 40 pages. v2: minor changes and references added, so as to match published versio

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

Two-step contribution to the spin-longitudinal and spin-transverse cross sections of the quasielastic (p,n) reactions

The two-step contribution to the spin-longitudinal and the spin-transverse cross sections of ^{12}C,^{40}Ca(p,n) reactions at 494 MeV and 346 MeV is calculated. We use a plane-wave approximation and evaluate the relative contributions from the one-step and the two-step processes. We found that the ratios of the two-step to the one-step processes are larger in the spin-transverse cross sections than in the spin-longitudinal ones. Combining these results with the distorted-wave impulse approximation (DWIA) results we obtained considerable two-step contributions to the spin-longitudinal and the spin-transverse cross sections. The two-step processes are important in accounting for the underestimation of the DWIA results for the spin-longitudinal and the spin-transverse cross sections.Comment: LaTeX 11 pages, 10 figure

Noninteraction of waves in two-dimensional conformal field theory

In higher dimensional quantum field theory, irreducible representations of the Poincare group are associated with particles. Their counterpart in two-dimensional massless models are "waves" introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Moebius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Moebius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness (with respect to waves) imply Moebius symmetry. Under natural assumptions, we observe that the maps which give asymptotic fields in Poincare covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Moebius covariant theory.Comment: 28 pages, no figur

Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete