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The Feynman demonstration that electromagnetic field momentum is real-even for static fields-can be made more pedagogically useful by simplifying its geometry. Instead of Feynman's disk with charged balls on its surface, this article uses…
We give obstructions for a noncompact manifold to admit a complete Riemannian metric with (nonuniformly) positive scalar curvature. We treat both the finite volume and infinite volume cases.
Quantum cosmology based on Lorentzian path integrals is a promising avenue. However, many previous works allow non-Lorentzian configurations by integrating the squared scale factor over the whole real line. Here we show that restricting the…
Objects composed of lattice defects exist within a one-dimensional tight-binding model whose electron reflection coefficient in the low-energy case is equal to zero. Localized states are absent as well. The effective mass concept explains…
In this paper we calculate the analytic expression of the phase time for the scattering of an electron off a complex square barrier. As is well known the (negative) imaginary part of the potential takes into account, phenomenologically, the…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
Gell-Mann's quarks are coherent particles confined within a hadron at rest, but Feynman's partons are incoherent particles which constitute a hadron moving with a velocity close to that of light. It is widely believed that the quark model…
Let $(M_{n},S_{n})_{n\ge 0}$ be a Markov random walk with positive recurrent driving chain $(M_{n})_{n\ge 0}$ having countable state space $\mathcal{S}$ and stationary distribution $\pi$. It is shown in this note that, if the dual sequence…
A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of $\R^N$. Under the assumption that the obstacle $\K$ is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed…
Fermion systems with flat bands can boost superconductivity by enhancing the density of states at the Fermi level. We use quasiexact numerical methods to show that repulsive interactions between spinless fermions in a one-dimensional (1D)…
It has recently been shown within a formal axiomatic framework using a definition of four-momentum based on the St\"uckelberg-Feynman-Sudarshan-Recami "switching principle" that Einstein's relativistic dynamics is logically consistent with…
We answer three questions posed by Bubeck and Linial on the limit densities of subtrees in trees. We prove there exist positive $\varepsilon_1$ and $\varepsilon_2$ such that every tree that is neither a path nor a star has inducibility at…
We investigate the passivity constraints on the relations between transmission, reflection, and absorption eigenvalues in linear time-invariant systems. Using techniques from matrix analysis, we derive necessary and sufficient conditions…
Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent hypergeometric functions of two variables $F_4$. These are defined for…
If textbook Lorentz invariance is actually a property of the equations describing a sector of the excitations of vacuum above some critical distance scale, several sectors of matter with different critical speeds in vacuum can coexist and…
A calculation is presented which quantitatively accounts for the terminal velocity of a cylindrical magnet falling through a long copper or aluminum pipe. The experiment and the theory are a dramatic illustration of the Faraday's and Lenz's…
We derive a path-integral expression for the effective action in the continuum limit of an AFM Heisenberg spin ladder with an arbitrary number of legs. The map is onto an $O(3)$ nonlinear $\sigma$-model (NL$\sigma$M) with the addition of a…
We show that supersymmetry Ward identities contain an anomalous term which takes the form of a surface term in Hilbert space. In the one-instanton sector the anomalous term is the integral of a total rho-derivative where rho is the…
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast,…
A power counting rule is provided that allows us to obtain upper bounds for the absolute values of Feynman parametric integrands. The rule reflects both the ultraviolet and infrared behavior taking into account that the external momenta are…