An algebraic condition for the Bisognano-Wichmann Property

The Bisognano-Wichmann property for local, Poincar\'e covariant nets of standard subspaces is discussed. We present a sufficient algebraic condition on the covariant representation ensuring Bisognano-Wichmann and Duality properties without further assumptions on the net. Our modularity condition holds for direct integrals of scalar massive and massless representations. We conclude that in these cases the Bisognano-Wichmann property is much weaker than the Split property. Furthermore, we present a class of massive modular covariant nets not satisfying the Bisognano-Wichmann property.Comment: Invited contribution to the Proceedings of the 14th Marcel Grossmann Meeting - MG14 (Rome, 2015

The Bisognano-Wichmann property on nets of standard subspaces, some sufficient conditions

We discuss the Bisognano-Wichmann property for local Poincar\'e covariant nets of standard subspaces. We give a sufficient algebraic condition on the covariant representation ensuring the Bisognano-Wichmann and Duality properties without further assumptions on the net called modularity condition. It holds for direct integrals of scalar massive and massless representations. We present a class of massive modular covariant nets not satisfying the Bisognano-Wichmann property. Furthermore, we give an outlook in the standard subspace setting on the relation between the Bisognano-Wichmann property and the Split property.Comment: Final version. To appear in Annales Henri Poincar\'

Spin, Statistics, and Reflections, I. Rotation Invariance

The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry, which is referred to as "modular P_1CT-symmetry (Bisognano, Wichmann, 1975, 1976, and Guido, Longo, [funct-an/9406005]). This symmetry is used to construct a representation of G_R by pairs of modular P_1CT-operators. The representation thus obtained satisfies Pauli's spin-statistics relation.Comment: Accepted for publication in Ann. H. Poincare, (annoying) misprints correcte

Modular Theory and Eyvind Wichmann's Contributions to modern Particle Physics Theory

Some of the consequences of Eyvind Wichmann's contributions to modular theory and the QFT phase-space structure are presented. In order to show the power of those ideas in contemporary problems, I selected the issue of algebraic holography as well as a new nonperturbative constructive approach (based on the modular structur of wedge-localized algebras and modular inclusions) and show that these ideas are recent consequences of the pathbreaking work which Wichmann together with his collaborator Bisognano initiated in the mid 70$^{ies}.Comment: A rogue address which entered chapter 2 has since been omitted. 21 pages, tcilatex, to be published in a special Festschrift volume, dedicated to Prof. E. Wichmann on the occasion of his seventieth birthda

Split property for free massless finite helicity fields

We prove the split property for any finite helicity free quantum fields. Finite helicity Poincar\'e representations extend to the conformal group and the conformal covariance plays an essential role in the argument. The split property is ensured by the trace class condition: Tr (exp(-s L_0)) is finite for all s>0 where L_0 is the conformal Hamiltonian of the M\"obius covariant restriction of the net on the time axis. We extend the argument for the scalar case presented in [7]. We provide the direct sum decomposition into irreducible representations of the conformal extension of any helicity-h representation to the subgroup of transformations fixing the time axis. Our analysis provides new relations among finite helicity representations and suggests a new construction for representations and free quantum fields with non-zero helicity.Comment: v2: Minor corrections, comments and references added, as to appear in Ann. H. Poin

The Bisognano-Wichmann Theorem for Massive Theories

The geometric action of modular groups for wedge regions (Bisognano-Wichmann property) is derived from the principles of local quantum physics for a large class of Poincare covariant models in d=4. As a consequence, the CPT theorem holds for this class. The models must have a complete interpretation in terms of massive particles. The corresponding charges need not be localizable in compact regions: The most general case is admitted, namely localization in spacelike cones.Comment: 16 pages; improved and corrected formulation

Modular Covariance, PCT, Spin and Statistics

The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.Comment: 15 pages, plain TeX, talk presented to the Colloquium "New Problems in the General Theory of Fields and Particles", Paris 1994. To appear in the special issue of the Ann. Inst. H. Poincar\'e devoted to the Colloquiu

Ground-state hyperfine structure of H-, Li-, and B-like ions in middle-Z region

The hyperfine splitting of the ground state of H-, Li-, and B-like ions is investigated in details within the range of nuclear numbers Z = 7-28. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in 1/Z. The screened QED corrections are evaluated to all orders in (\alpha Z) utilizing an effective potential approach. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model. The specific differences between the hyperfine-structure level shifts of H- and Li-like ions, where the uncertainties associated with the nuclear structure corrections are significantly reduced, are also calculated.Comment: 22 pages, 11 tables, 2 figure

Influence of perturbations on the electron wave function inside the nucleus

A variation of the valence electron wave function inside a nucleus induced by a perturbative potential is expressed in terms of the potential momenta. As an application we consider QED vacuum polarization corrections due to the Uehling and Wichmann-Kroll potentials to the weak interaction matrix elements.Comment: 16 pages, Latex, IOP stil