Related papers: A note on a quantization via the Ran space

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…

We prove sharp remainder bounds for the Berezin-Toeplitz quantization and present applications to semiclassical quantum measurements.

This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.

This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

Very recently we present a theory [Wei-long She, Chin. Phys. 14, 2514(2005); Online: http://www.jop.org/journals/cp; http://arxiv.org/abs/quant-ph/0512097] to show that the quantization of light energy in vacuum can be derived directly from…

Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three…

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface…

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…

A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…

In this note we give a detailed proof of a theorem of Aubin.

We give a new proof of the Kat\v{e}tov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredient is how the ring of bounded continuous real-valued…

The non-perturbative, lattice field theory approach towards the quantization of Euclidean gravity is reviewed. Included is a tentative summary of the most significant results and a presentation of the current state of art.

Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is…

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…