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Noncommutativity of observables is a central feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the laws of thermodynamics for systems…

We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group. Most importantly, we depart from the common…

Contrary to what Lambare [arXiv:2008.00369] assumes, in non-Newtonian calculus (a calculus based on non-Diophantine arithmetic) an integral is typically given by a nonlinear map. This is the technical reason why all the standard proofs of…

It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity…

We present a class of solvable models that resemble string theories in many respects but have a strikingly different non-perturbative sector. In particular, there are no exponentially small contributions to perturbation theory in the string…

As is well established, several gauge theories admit vortices whose mean life time is very large. In some cases, this stability is a consequence of the topology of the symmetry group of the underlying theory. The main focus of the present…

Asymptotically nonlocal field theories approximate ghost-free nonlocal theories at low energies, yet are theories of finite order in the number of derivatives. These theories have an emergent nonlocal scale that regulates loop diagrams and…

Characterising the propagation of particles in an external non-Abelian field only in terms of invariants constructed from its field tensor is not always sufficient, especially, in many analytically tractable and phenomenologically…

Takens Theorem for a partially hyperbolic dynamics provides a normal linearization along the center manifold. In this paper, we give the nonautonomous version of Takens Theorem under non-resonance conditions formulated in terms of the…

We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.

The paper argues that far from challenging - or even refuting - Bohm's quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to…

We consider a quantum field theory on a spherically symmetric quantum space time described by loop quantum gravity. The spin network description of space time in such a theory leads to equations for the quantum field that are discrete. We…

We extend the soft theorems for scattering amplitudes of scalar effective field theories to one-loop order. Our analysis requires carefully accounting for the fact that the soft limit is not guaranteed to commute with evaluating…

Chain total double complexes with reductive differentials for non-abelian simplexes with associated spaces are considered. It is conjectured that corresponding relative cohomology is equivalent to the coset space of vanishing over…

Noncommutative gauge fields (similar to the type that arises in string theory with background B-fields) are constructed for arbitrary nonabelian gauge groups with the help of a map that relates ordinary nonabelian and noncommutative gauge…

We discuss general properties and possible types of magnetic vortices in non-Abelian gauge theories (we consider here $G= SU(N), SO(N), USp(2N)$) in the Higgs phase. The sources of such vortices carry "fractional" quantum numbers such as…

The loop variable approach used earlier to obtain free equations of motion for the massive modes of the open string, is generalized to include interaction terms. These terms, which are polynomial, involve only modes of strictly lower mass.…

In this paper we study general properties of noncommutative field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. We analyze the extension of the Wightman axioms to this context and…

Analytic methods for Abelian projection are developed. A number of results are obtained related to string tension measurements. It is proven that even without gauge fixing, abelian projection yields string tensions of the underlying…

In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary…