Wigner quantization of some one-dimensional Hamiltonians

Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown. Among those we have the ubiquitous relation with Lie superalgebras and their representations. In this paper, we study two one-dimensional Hamiltonians for which the Wigner quantization is related with the orthosymplectic Lie superalgebra osp(1|2). One of them, the Hamiltonian H = xp, is popular due to its connection with the Riemann zeros, discovered by Berry and Keating on the one hand and Connes on the other. The Hamiltonian of the free particle, H_f = p^2/2, is the second Hamiltonian we will examine. Wigner quantization introduces an extra representation parameter for both of these Hamiltonians. Canonical quantization is recovered by restricting to a specific representation of the Lie superalgebra osp(1|2)

Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $\epsilon$-away below the two-boson threshold) spectrum of Fr\"ohlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{(0)}$, where $G^{(0)}\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated

Evidence of American Martens Populating the Turtle Mountains of North Dakota

American martens (Martes americana) were native to northeastern North Dakota but were considered extirpated by the early 1800s. Although there is no historic evidence of martens occurring beyond the northeast, forested habitat potentially suitable for martens exists in the Turtle Mountains region of northcentral North Dakota and southwestern Manitoba. From 1989– 1991, the Turtle Mountain Trappers Association translocated 59 martens into the Canadian portion of the Turtle Mountains. During summer 2007, we used covered track-plates and/or remotely-triggered cameras placed at 123 survey sites distributed among 41 1-km2 grid cells (a GIS-generated layer imposed on electronic maps of the study region) to determine if martens occupied the Turtle Mountains in North Dakota. Martens were detected at 26 (21%) sites, representing 20 of the 41 sample cells (49%) widely dispersed throughout the study area. Our study provided the first evidence of martens occurring in North Dakota since the early 1800s

On metric-connection compatibility and the signature change of space-time

We discuss and investigate the problem of existence of metric-compatible linear connections for a given space-time metric which is, generally, assumed to be semi-pseudo-Riemannian. We prove that under sufficiently general conditions such connections exist iff the rank and signature of the metric are constant. On this base we analyze possible changes of the space-time signature.Comment: 18 standard LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are require

Evidence of American Martens Populating the Turtle Mountains of North Dakota

American martens (Martes americana) were native to northeastern North Dakota but were considered extirpated by the early 1800s. Although there is no historic evidence of martens occurring beyond the northeast, forested habitat potentially suitable for martens exists in the Turtle Mountains region of northcentral North Dakota and southwestern Manitoba. From 1989– 1991, the Turtle Mountain Trappers Association translocated 59 martens into the Canadian portion of the Turtle Mountains. During summer 2007, we used covered track-plates and/or remotely-triggered cameras placed at 123 survey sites distributed among 41 1-km2 grid cells (a GIS-generated layer imposed on electronic maps of the study region) to determine if martens occupied the Turtle Mountains in North Dakota. Martens were detected at 26 (21%) sites, representing 20 of the 41 sample cells (49%) widely dispersed throughout the study area. Our study provided the first evidence of martens occurring in North Dakota since the early 1800s