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It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains…

Systematic approaches to building up gauge invariant descriptions of charged fields, such as electrons or quarks, are described. Physically relevant descriptions must then be singled out from a multiplicity of possibilities and to this end…

The role of implicit assumptions in current decoherence theory is pointed out and clarified.

A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument…

We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…

In this conference summary talk at Hadron03, questions and challenges for Hadron physics of light flavours are outlined. Precision data and recent discoveries are at last exposing the limitations of the naive constituent quark model and…

In this contribution I will try to give an overview of what has been achieved in constituent quark models of mesons and baryons by a comparison of some selected results from various ansaetze with experimental data. In particular I will…

Contrary to the central claim (Hsu, 2026) published in Physics Letters B, the Tomonaga--Schwinger equation remains covariant despite the nonlinear modification of it. The proof of covariance becomes simple after the loopholes and mistakes…

It is proved that symmetry structure of the parity-viol. (p.v.) amplitudes of weak radiative hyperon decays in the VMD approach, and the violation of Hara's theorem in particular, are also obtained when direct coupling e_q…

With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some insights on the nature of the tetraquark and pentaquark candidates, a constituent…

We review some selected recent results on hadron spectroscopy and related theoretical studies based on constituent quark models.

A selfcontained proof of the KAM theorem in the Thirring model is discussed, completely relaxing the ``strong diophantine property'' hypothesis used in previous papers. Keywords: \it KAM, invariant tori, classical mechanics, perturbation…

I elaborate on the argument that the violation of Hara's theorem for conserved current requires that the current is not sufficiently well localized. It is also stressed that whatever sign of asymmetry is measured in the $\Xi ^0 \to \Lambda…

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$…

It is shown that the conclusion of the paper "Hidden assumptions in decoherence theory" (quant-ph/0001021) is the result of a misunderstanding of the concept of pointer states. It is argued that pointer states are selected by the…

We show the inconsistency of the argument linking the integral quantum Hall effect to gauge invariance. The inconsistency mainly consists of equating gauge and real vector potential transformations for a particular system geometry. Correct…

We extend to any maximally entangled state of a bipartite system whose constituents are arbitrarily (but finite) dimensional the result, recently derived for two-dimensional constituents, that hidden variable theories cannot have local…

We reconsider the Constituent Chiral Quark Model of Manohar and Georgi in the presence of $SU(3)_{L}\times SU(3)_{R}$ external sources. As recently emphasized by Weinberg, the corresponding effective Lagrangian is renormalizable in the…

Chiral loop corrections for hadronic properties are considered in a constituent quark model. It is emphasized that the correct implementation of such corrections requires a sum over intermediate hadronic states. The leading non-analytic…