Related papers: A new mathematical problem related to quantization…
We give a rigorous description of a model of the quantized electromagnetic field interacting with quantized current fields. In the special case of classical currents our results agree with common knowledge about the problem. A toy model of…
The purpose of this review is to give the most popular description of the scheme of quantization of relativistic fields that was named relativistic canonical quantization (RCQ). I do not give here the full exact account of this scheme. But…
I review some open problems on the ever-growing field of non-equilibrium phase transitions, paying special attention to the formulation of such problems in terms of Langevin equations or, equivalently, field-theoretical descriptions, and…
A brief report on recent work on the sphere-packing problem.
This is the current form of lecture notes on my approach to field quantization. I explain on a simple scalar-field model the physical motivation and show some preliminary applications (field produced by a pointlike charge, the…
In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…
This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and,…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure…
A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.
We analyze on the formalism of probability measures -functional integrals on function spaces , the problem of infinities on Euclidean field theories
Simple classical mechanical systems and solution spaces of classical field theories involve singularities. In certain situations these singularities can be understood in terms of stratified Kaehler spaces. We give an overview of a research…
In this paper, we give a brief survey of recent developments on Noether's problem and rationality problem for multiplicative invariant fields including author's recent papers Hoshi [Hos15] about Noether's problem over Q, Hoshi, Kang and…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…
In near-field optics and optical tunneling theory, photon wave mechanics, i.e., the first quantized theory of the photon, allows us to address the spatial field localization problem in a flexible manner which links smoothly to classical…
There are several mathematical and physical reasons why Dirac's quantization must hold. How far one can go without it remains an open problem. The present work outlines a few steps in this direction.
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
The development of nonabelian gauge fields for last 60 years is reviewed. The new method of quantization of gauge fields applicable beyond perturbation theory is proposed.