The observables of modular quantisation are studied from the point of view of locality. Such a study allows identification of possible Hamiltonians and also enables us to generalize the fundamental bilinear commutation relations of parafield theory. A comparison of modular field theory with a normal U(m) gauge theory, begun in an earlier publication, is completed with the conclusion that the tw...

The violation of the Jacobi identity by the presence of magnetic charge is accomodated by using an explicitly nonassociative theory of octonionic fields. It is found that the dynamics of this theory is simplified if the Lagrangian contains only dyonic charges, but certain problems in the constrained quantisation remain. The extension of these concepts to string theory may however resolve these ...

We show that the relativistic analogue of the two types of time translation in a non-relativistic history theory is the existence of two distinct Poincaré groups. The ‘internal’ Poincaré group is analogous to the one that arises in the standard canonical quantisation scheme; the ‘external’ Poincaré group is similar to the group that arises in a Lagrangian description of the standard theory. In ...

It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger Model that there is nothing wrong with apparently anomalous chiral gauge theory. If quantised correctly, there should be no gauge anomaly and chiral gauge theory should be renormalisable and unitary, even in higher dimensions and with non-abelian gauge groups. Furthermore, mass terms for gauge boso...

The double-slit experiment is the most direct demonstration of interference between individual quantum objects. Since similar experiments with single particles and more slits produce fringes reducible to a combination patterns it usually argued that occurs pairs trajectories, compactly denoted as second-order interference. Here we show mechanics in fact allows for arbitrarily high order. This n...

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol’d determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, t...

Using the algebro-geometric approach, we study structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear waves governed by anisotropic Landau-Lifshitz equation arise as coherent macroscopic low-energy fluctuations ferromagnetic ground state. Special emphasis is devoted to simplest types solutions, describing precessional mo...