相关论文: Why Professor Richard Feynman was upset solving th…

The existence of singularities of the solution for a class of Lax equations is investigated using a development of the fac- torization method first proposed by Semenov-Tian-Shansky and Reymann [11], [9]. It is shown that the existence of a…

We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…

I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…

We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem…

Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…

The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…

Geometric frustration in quantum magnetism refers to that magnetic interactions on different bonds cannot be simultaneously minimized. The usual Cooper pairing systems favor the uniform distribution of the pairing phase among lattice sites…

Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not…

By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory…

I provide the backstory on how a historical error in the Feynman Lectures on Physics was corrected.

A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…

In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the…

Entanglement in Quantum Field Theory is restricted to spacelike separations to the order of the Compton wavelength $\hbar/mc$ (e.g., S. J. Summers and R. Werner, {\it J. Math. Phys.}, {\bf 28}, 10,2440-2447, (1987)). Yet spin entanglement…

It is believed that classical behavior emerges in a quantum system due to decoherence. It has also been proposed that gravity can be a source of this decoherence. We examine this in detail by studying a number of quantum systems, including…

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…

A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter…

We show that, contrary to the statements made by many authors, the backflow is not a nonclassical effect. The backflow is a characteristic feature of solutions of the wave equations: quantum and classical. We present simple solutions of the…

Newton famously showed that a gravitational force inversely proportional to the square of the distance, $F \sim 1/r^2$, formally explains Kepler's three laws of planetary motion. But what happens to the familiar elliptical orbits if the…

We present an approximate model of Wheeler-Feynman electrodynamics for which uniqueness of solutions is proved. It is simple enough to be instructive but close enough to Wheeler-Feynman electrodynamics such that we can discuss its natural…

In this paper we explore some surprising consequences of the retardation effects of Maxwell's electrodynamics to a system of charged particles. The specific cases of three interacting particles are considered in the framework of classical…