scholarly journals Errata: Representation of the Inhomogeneous Lorentz Group in Terms of an Angular Momentum Basis: Derivation for the Cases of Nonzero Mass and Zero Mass, Discrete Spin

1965 ◽  
Vol 6 (4) ◽  
pp. 670-670
Author(s):  
J. S. Lomont ◽  
H. E. Moses
Keyword(s):  
Angular Momentum ◽  
Lorentz Group ◽  
Zero Mass ◽  
Inhomogeneous Lorentz Group

Realizations of generators of complex angular momentum

1990 ◽  
Vol 68 (7-8) ◽  
pp. 599-603
Author(s):  
Shuchi Bora ◽  
H. C. Chandola ◽  
B. S. Rajput
Keyword(s):  
Angular Momentum ◽  
Lorentz Group ◽  
Continuous Spin ◽  
Zero Mass ◽  
Complex Angular Momentum ◽  
General Manner ◽  
Homogeneous Lorentz Group ◽  
Real Mass ◽  
Spin Representations ◽  
Spin Contribution

We use the generators of complex angular momentum in complex c3 space and derive the realizations of the homogeneous Lorentz group for nonzero real mass, zero mass, and imaginary mass systems. We use the appropriate little group for different systems to calculate the modifications in the spin contribution to angular momentum and the unphysical continuous spin representations are shown to be eliminated. We diagonalize the helicity operator in c3 space and obtain the generators of complex angular-momentum operators, which are shown to lead, in a general manner, to the standard helicity representations of the Poincare group for timelike and spacelike systems.

Canonical representations for massless particles and zero-mass limits of the helicity representation

1965 ◽  
Vol 285 (1401) ◽  
pp. 287-296 ◽  
Keyword(s):  
Lorentz Group ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Positive Mass ◽  
Continuous Spin ◽  
Massless Particles ◽  
Zero Mass ◽  
Canonical Representations ◽  
Inhomogeneous Lorentz Group

The global forms of the unitary irreducible representations of the inhomogeneous Lorentz group corresponding to zero mass and finite or continuous spin are constructed by means of the little-group technique from those of the two-dimensional Euclidean group, and it is shown that these representations may be derived from the helicity representation for positive mass by taking suitable limits.

Edth-a differential operator on the sphere

1982 ◽  
Vol 92 (2) ◽  
pp. 317-330 ◽  
Author(s):  
Michael Eastwood ◽  
Paul Tod
Keyword(s):  
Angular Momentum ◽  
Differential Operator ◽  
Lorentz Group ◽  
Space Time ◽  
Conformal Group ◽  
Theory Of Relativity ◽  
Asymptotically Flat ◽  
Group 4 ◽  
Lowering Operator ◽  
Inhomogeneous Lorentz Group

Introduction. In (9) Newman and Penrose introduced a differential operator which they denoted ð, the phonetic symboledth. This operator acts onspin weighted, orspinandconformally weightedfunctions on the two-sphere. It turns out to be very useful in the theory of relativity via the isomorphism of the conformal group of the sphere and the proper inhomogeneous Lorentz group (11, 4). In particular, it can be viewed (2) as anangular momentum lowering operatorfor a suitable representation of SO(3) and can be used to investigate the representations of the Lorentz group (4). More recently, edth has appeared in thegood cut equationdescribing Newman'sℋ-spacefor anasymptotically flatspace-time (10). This development is closely related to Penrose's theory oftwistorsand, in particular, toasymptotic twistors(14).

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