scholarly journals Holonomy operator and quantization ambiguities on spinor space

2013 ◽  
Vol 87 (10) ◽  
Author(s):  
Etera R. Livine ◽  
Johannes Tambornino
Keyword(s):  
Spinor Space

The geometry and algebra of the representations of the Lorentz group

1968 ◽  
Vol 303 (1474) ◽  
pp. 381-396 ◽  
Keyword(s):  
Projective Space ◽  
Lorentz Group ◽  
Point Of View ◽  
Normal Curve ◽  
Geometrical Representation ◽  
Spinor Space ◽  
Dimensional Projective Space ◽  
And Algebra ◽  
Rational Normal Curve ◽  
Formal Point

In this paper a (2j + l)-spinor analysis is developed along the lines of the 2-spinor and 3-spinor ones. We define generalized connecting quantities A μv (j) which transform like (j, 0) ⊗ (j -1, 0) in spinor space and like second rank tensors under transformations in space-time. The general properties of the A uv are investigated together with algebraic relations involving the Lorentz group generators, J μv . The connexion with 3j symbols is discussed. From a purely formal point of view we introduce a geometrical representation of a (2j +1)-spinor as a point in a 2j dimensional projective space. Then, for example, the charge con­jugate of a (2j + l)-spinor is just the polar of the corresponding point with respect to a certain rational, normal curve in the projective space. It is suggested that this representation will prove useful.

Algebraic expressions for symmetry-adapted functions of the icosahedral group in spinor space

1999 ◽  
Vol 55 (6) ◽  
pp. 1049-1060 ◽  
Author(s):  
Peng-Dong Fan ◽  
Jin-Quan Chen ◽  
J. P. Draayer
Keyword(s):  
Angular Momentum ◽  
Projection Operators ◽  
Icosahedral Group ◽  
Quantum Numbers ◽  
Algebraic Expressions ◽  
Group I ◽  
Spinor Space ◽  
Symmetry Adapted Functions ◽  
Eigenfunction Method

Algebraic expressions for projection operators and symmetry-adapted functions (SAFs) of the icosahedral group for spinor (double-valued) representations are found by using the double-induced technique and eigenfunction method. The SAFs are functions of the angular momentum j, the quantum numbers \lambda, \nu, \mu of the group chain I \supset D_5 \supset C_5, and the multiplicity label \bar m. By this procedure, SAFs for the group I are provided once for all instead of one j value at a time.

EXPLANATION OF THE DATA ON $\Gamma (Z^0\to b\bar b) /\Gamma (Z^0\to {\rm hadrons})$ AND THE INCLUSIVE b→sγ BRANCHING RATIO

1996 ◽  
Vol 11 (12) ◽  
pp. 1011-1022 ◽  
Author(s):  
E.H. LEMKE
Keyword(s):  
Cross Section ◽  
Transverse Energy ◽  
Branching Ratio ◽  
Diboson Production ◽  
Spinor Space ◽  
200 Gev ◽  
Inclusive Jet ◽  
Basic Spinor ◽  
Spinor Symmetry

Calculations show that the data on the Z0 hadronic branching ratio fraction to [Formula: see text] at the Z0 pole as well as the inclusive b→sγ branching ratio can be explained by an anomalous (γ-Z0)WW coupling having ∆κ=−1 and λ=0. Such a vertex was derived from a representation in spinor space some time ago. The agreement is analyzed and possible implication of that basic spinor symmetry are described. Finally, the recent data on diboson production and their interpretation are examined critically. The used and shortly presented electroweak unification scheme of “structureless compositeness” provides two natural explanations of the increase of the inclusive jet cross-section above 200 GeV jet transverse energy observed at FNAL recently.

scholarly journals On projections to the pure spinor space

2011 ◽  
Vol 2011 (12) ◽  
Author(s):  
P. A. Grassi ◽  
S. Guttenberg
Keyword(s):  
Pure Spinor ◽  
Spinor Space

Augmented Spinor Space*

2007 ◽  
Vol 28 (2) ◽  
pp. 225-234 ◽  
Author(s):  
Xiuhong Feng ◽  
Lin Zhu ◽  
Yanlin Yu
Keyword(s):  
Spinor Space

Spinor Space and Line Geometry

1951 ◽  
Vol 3 ◽  
pp. 442-459
Author(s):  
Václav Hlavatý
Keyword(s):  
Line Geometry ◽  
Spinor Space

Synopsis. This is the first of two papers dealing with the projective theory of spinors. It contains the algebraic introduction to the projective spinor analysis which will be dealt with in the second paper.

scholarly journals "MINIMAL GEOMETRIC DATA" APPROACH TO DIRAC ALGEBRA, SPINOR GROUPS AND FIELD THEORIES

2007 ◽  
Vol 04 (06) ◽  
pp. 1005-1040 ◽  
Author(s):  
DANIEL CANARUTTO
Keyword(s):  
Vector Bundle ◽  
Momentum Space ◽  
Field Theories ◽  
Dimensional Manifold ◽  
Short Account ◽  
Dirac Algebra ◽  
Spinor Space ◽  
Spinor Geometry ◽  
Original Approach ◽  
Bundle Structure

The first three sections contain an updated, not-so-short account of a partly original approach to spinor geometry and field theories introduced by Jadczyk and myself [3–5]; it is based on an intrinsic treatment of 2-spinor geometry in which the needed background structures do not need to be assumed, but rather arise naturally from a unique geometric datum: a vector bundle with complex 2-dimensional fibers over a real 4-dimensional manifold. The following two sections deal with Dirac algebra and 4-spinor groups in terms of two spinors, showing various aspects of spinor geometry from a different perspective. The last section examines particle momenta in 2-spinor terms and the bundle structure of 4-spinor space over momentum space.

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