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

Approximation Bounds For Minimum Degree Matching

We consider the MINGREEDY strategy for Maximum Cardinality Matching. MINGREEDY repeatedly selects an edge incident with a node of minimum degree. For graphs of degree at most $\Delta$ we show that MINGREEDY achieves approximation ratio at least $\frac{\Delta-1}{2\Delta-3}$ in the worst case and that this performance is optimal among adaptive priority algorithms in the vertex model, which include many prominent greedy matching heuristics. Even when considering expected approximation ratios of randomized greedy strategies, no better worst case bounds are known for graphs of small degrees.Comment: % CHANGELOG % rev 1 2014-12-02 % - Show that the class APV contains many prominent greedy matching algorithms. % - Adapt inapproximability bound for APV-algorithms to a priori knowledge on |V|. % rev 2 2015-10-31 % - improve performance guarantee of MINGREEDY to be tigh

Wigner's infinite spin representations and inert matter

Positive energy ray representations of the Poincar\'e group are naturally subdivided into three classes according to their mass and spin content: m>0, m=0 finite helicity and m=0 infinite helicity. For a long time the localization properties of the massless infinite spin class remained unknown before it became clear that such matter does not permit compact spactime localization and its generating covariant fields are localized on semi-infinite spacelike strings. Using a new perturbation theory for higher spin fields we show that infinite spin matter cannot interact with normal matter and we formulate condition under which this also could happen for finite spin s>1 fields. This raises the question of a possible connection between inert matter and dark matter.Comment: 27 page

Peculiarities of massive vectormesons and their zero mass limits

Massive QED, in contrast with its massless counterpart, possesses two conserved charges; one is a screened (vanishing) Maxwell charge which is directly associated with the massive vector mesons through the identically conserved Maxwell current. A somewhat peculiar situation arises for couplings of Hermitian matter fields to massive vector potentials; in that case the only current is the screened Maxwell current and the coupling disappears in the massless limit. In case of selfinteracting massive vector mesons the situation becomes even more peculiar in that the usually renormalizability guaranteeing validity of the first order power-counting criterion breaks down in second order and requires the compensatory presence of additional Hermitian H-fields. Some aspect of these observation have already been noticed in the BRST gauge theoretic formulation, but here we use a new setting based on string-local vector mesons which is required by Hilbert space positivity. The coupling to H-fields induces Mexican hat like selfinteractions; they are not imposed and bear no relation with spontaneous symmetry breaking; they are rather consequences of the foundational causal localization properties realized in a Hilbert space setting. In case of selfinteracting massive vectormesons their presence is required in order to maintain the first order power-counting restriction of renormalizability also in second order. The presentation of the new Hilbert space setting for vector mesons which replaces gauge theory and extends on-shell unitarity to its off-shell counterpart is the main motivation for this work. The new Hilbert space setting also shows that the second order Lie-algebra structure of selfinteracting vector mesons is a consequence of the principles of QFT and promises a deeper understanding of the origin of confinement.Comment: 34 pages Latex, several additional remarks and citations, improved formulations, same as published versio

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 $s\geq1$ 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