Related papers: The light-front vacuum
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.
We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenberg's uncertainty relation for position and modular momentum. We apply our…
We study reaction-diffusion equations in one spatial dimension and with general (space- or time-) inhomogeneous mixed bistable-ignition reactions. For those satisfying a simple quantitative hypothesis, we prove existence and uniqueness of…
The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.
We show, e.g., that a holomorphic Banach vector bundle over a pseudoconvex open subset of, say, Hilbert space is holomorphically trivial if it is continuously trivial. Some applications are also given.
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
This paper is a survey aimed on the introduction of non-Abelian Hodge theory that gives the correspondence between flat bundles and Higgs bundles. We will also introduce some topics arising from this theory, especially some recent…
We describe several recent results obtained in collaboration with P. Gravejat, C. Hainzl, E. S\'er\'e and J.P. Solovej, concerning a nonlinear model for the relativistic quantum vacuum in interaction with a classical electromagnetic field.
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
We study the question of generalizing light-front field theories to finite temperature. We show that the naive generalization has serious problems and we identify the source of the difficulty. We provide a proper generalization of these…
We study homology and cohomology of triassociative algebras with non-trivial coefficients.
The relationship (both classical and quantum mechanical) between the discrete Liouville equation and Teichm\"uller theory is reviewed.
Helicity is a property of light which is familiar from particle physics but less well-known in optics. In this paper we recall the explicit form taken by the helicity of light within classical electromagnetic theory and reflect upon some of…
Here we present ZFC theorems yielding the Halpern-L\a"uchli theorem and avoiding metamathematical notions in their formulations.
Observational evidence along with theoretical arguments which call for non-baryonic dark matter are reviewed. A brief summary of the dark matter session is included.
In this talk, we describe our present understanding of thermal field theories on the light-front with an application to Schwinger model.
We test the opacity of a void Universe to TeV energy gamma rays having obtained the extra-galactic background light in that Universe using a simple model and the observed constraints on the star formation rate history. We find that the void…
I review a new treatment of an old idea for light-front quantization of lattice gauge theories and give new results from some illustrative calculations: [I] transverse lattice gauge theory; [II] pure glue; [III] heavy sources and winding…
We provide a partial answer to a question of Ekholm, Honda, and K\'alm\'an about the relationship between Khovanov homology and decomposable Lagrangian cobordisms. We also utilize previously defined filtered invariants to give obstructions…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…