scholarly journals On the non-neutral component of outer forms of the orthogonal group

2021 ◽  
Vol 225 (1) ◽  
pp. 106477
Author(s):  
Uriya A. First
Keyword(s):  
Orthogonal Group ◽  
Neutral Component

First H+ Charge-Exchange Images in the Stim.

1976 ◽  
Vol 34 ◽  
pp. 504-505
Author(s):  
Wm. H. Escovitz ◽  
T. R. Fox ◽  
R. Levi-Setti
Keyword(s):  
Charge Exchange ◽  
Neutral Component ◽  
Channel Electron Multiplier ◽  
Electron Multiplier ◽  
Neutral Particles ◽  
Charged Beam ◽  
Scanning Transmission ◽  
Contrast Mechanism ◽  
Ion Microscopy ◽  
Beam Component

Charge exchange, the neutralization of ions by electron capture as the ions traverse matter, is a well-known phenomenon of atomic physics which is relevant to ion microscopy. In conventional transmission ion microscopes, the neutral component of the beam after it emerges from the specimen cannot be focused. The scanning transmission ion microscope (STIM) enables the detection of this signal to make images. Experiments with a low-resolution 55 kV STIM indicate that the charge-exchange signal provides a new contrast mechanism to detect extremely small amounts of matter. In an early version of charge-exchange detection (fig. 1), a permanent magnet installed between the specimen and the detector (a channel electron multiplier) sweeps the charged beam component away from the detector and allows only the neutrals to reach it. When the magnet is removed, both charged and neutral particles reach the detector.

scholarly journals ON 3-DIMENSIONAL HOMOTOPY QUANTUM FIELD THEORY, I

2012 ◽  
Vol 23 (09) ◽  
pp. 1250094 ◽  
Author(s):  
VLADIMIR TURAEV ◽  
ALEXIS VIRELIZIER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Discrete Group ◽  
The State ◽  
Fusion Category ◽  
Quantum Field ◽  
Neutral Component ◽  
3 Dimensional

Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory with target the Eilenberg–MacLane space K(G, 1).

scholarly journals Canonical transformations for fermions in superanalysis

2014 ◽  
Vol 26 (06) ◽  
pp. 1450009
Author(s):  
Joachim Kupsch
Keyword(s):  
Infinite Number ◽  
Orthogonal Group ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Continuous Representation ◽  
Canonical Transformations ◽  
Module Extension ◽  
Bogoliubov Transformations

Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

scholarly journals THE INVARIANTS FIELD OF SOME FINITE PROJECTIVE LINEAR GROUP ACTIONS

2011 ◽  
Vol 85 (1) ◽  
pp. 19-25
Author(s):  
YIN CHEN
Keyword(s):  
Finite Field ◽  
Projective Space ◽  
Vector Space ◽  
Orthogonal Group ◽  
Homogeneous Polynomial ◽  
Classical Group ◽  
Projective Group ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Projective Linear Group

AbstractLet Fq be a finite field with q elements, V an n-dimensional vector space over Fq and 𝒱 the projective space associated to V. Let G≤GLn(Fq) be a classical group and PG be the corresponding projective group. In this note we prove that if Fq (V )G is purely transcendental over Fq with homogeneous polynomial generators, then Fq (𝒱)PG is also purely transcendental over Fq. We compute explicitly the generators of Fq (𝒱)PG when G is the symplectic, unitary or orthogonal group.

Vertex Subgroups of Irreducible Representations of Solvable Groups

1971 ◽  
Vol 23 (1) ◽  
pp. 12-21
Author(s):  
J. Malzan
Keyword(s):  
Vector Space ◽  
Unit Sphere ◽  
Convex Subset ◽  
Orthogonal Group ◽  
Solvable Groups ◽  
Fundamental Region ◽  
Irreducible Representations ◽  
Theoretical Problem ◽  
Real Vector ◽  
The Real

If ρ(G) is a finite, real, orthogonal group of matrices acting on the real vector space V, then there is defined [5], by the action of ρ(G), a convex subset of the unit sphere in V called a fundamental region. When the unit sphere is covered by the images under ρ(G) of a fundamental region, we obtain a semi-regular figure.The group-theoretical problem in this kind of geometry is to find when the fundamental region is unique. In this paper we examine the subgroups, ρ(H), of ρ(G) with a view of finding what subspace, W of V consists of vectors held fixed by all the matrices of ρ(H). Any such subspace lies between two copies of a fundamental region and so contributes to a boundary of both. If enough of these boundaries might be found, the fundamental region would be completely described.

The orthogonal group over a local ring is 4-reflectional

1994 ◽  
Vol 49 (3) ◽  
pp. 369-373 ◽  
Author(s):  
Hans R�pcke
Keyword(s):  
Local Ring ◽  
Orthogonal Group

scholarly journals Chirality in Geometric Algebra

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1521
Author(s):  
Michel Petitjean
Keyword(s):  
Geometric Algebra ◽  
Orthogonal Group ◽  
Matrix Representation ◽  
Quadratic Space ◽  
Complex Numbers ◽  
Chiral Algebra

We define chirality in the context of chiral algebra. We show that it coincides with the more general chirality definition that appears in the literature, which does not require the existence of a quadratic space. Neither matrix representation of the orthogonal group nor complex numbers are used.

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