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A universal theory of chaos is presented which postulates the self-organized ordered growth of self-similar, scale invariant, eddy energy structures by space-time integration of inherent microscale energy generation mechanisms in the medium…
The treatment of fields as operator valued distributions (OPVD) is recalled with the emphasis on the importance of causality following the work of Epstein and Glaser. Gauge invariant theories demand the extension of the usual translation…
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed unity, and the unitarity principle as the requirement that…
We consider gauge theories on Poisson manifolds emerging as semiclassical approximations of noncommutative spacetime with Lie algebra type noncommutativity. We prove an important identity, which allows to obtain simple and manifestly…
The observed baryon asymmetry of the universe (BAU) cannot be explained by the known sources of charge-parity (CP)-violation in the Standard Model (SM). A non-zero permanent electric-dipole-moment (EDM) for fundamental particles, nuclei or…
We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor…
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…
In this paper, we investigate the physical basis behind the molecular biochirality from the computation of a parity violation energy difference (PVED) in enantiomers of organic molecules (e.g., amino acids, which occur as levogyrous-type in…
We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence…
Disordered solids, straddling the solid-fluid boundary, lack a comprehensive continuum mechanical description. They exhibit a complex microstructure wherein multiple meta-stable states exist. Deforming disordered solids induces particles…
It is shown that in non-linear electrodynamics (in particular, Born-Infeld one) in the framework of general relativity there exist "weakly singular" configurations such that (i) the proper mass M is finite in spite of divergences of the…
We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of…
We show that the connection between certain integrable perturbations of $N=2$ superconformal theories and graphs found by Lerche and Warner extends to a broader class. These perturbations are such that the generators of the perturbed chiral…
Variational analysis techniques in lattice QCD are powerful tools that give access to the excited state spectrum of QCD. At zero momentum, these techniques are well established and can cleanly isolate energy eigenstates of either positive…
In the non-relativistic limit, helimagnetic order is always associated with odd-parity magnetism. That is, for single-particle states the expectation value of the electronic spin is odd in crystal momentum, which implies direct control of…
We find general non-linear lagrangians of a U(1) field invariant under electric-magnetic duality. They are characterized by an arbitrary function and go to the Maxwell theory in the weak field limit. We give some explicit examples which are…
Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics. In this paper we undertake these problems and…
In this paper we present a generalization of the Radon-Nikodym theorem proved by Pedersen and Takesaki. Given a normal, semifinite and faithful (n.s.f.) weight $\phi$ on a von Neumann algebra M and a strictly positive operator $\delta$,…
Given a sequence $\vec d=(d_1,\dots,d_k)$ of natural numbers, we consider the Lie subalgebra $\mathfrak{h}$ of $\mathfrak{gl}(d,\mathbb{F})$, where $d=d_1+\cdots +d_k$ and $\mathbb{F}$ is a field of characteristic 0, generated by two block…
Near full-null degenerate singular points of analytic vector fields, asymptotic behaviors of orbits are not given by eigenvectors but totally decided by nonlinearities. Especially, in the case of high full-null degeneracy, i.e., the lowest…