Conformal group in minkowsky space. Unitary irreducible representations

1964 ◽  
Vol 32 (2) ◽  
pp. 473-485 ◽  
Author(s):  
A. Esteve ◽  
P. G. Sona
Keyword(s):  
Conformal Group ◽  
Irreducible Representations ◽  
Minkowsky Space

scholarly journals 2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT

2017 ◽  
Vol 2017 (8) ◽  
Author(s):  
Brian Henning ◽  
Xiaochuan Lu ◽  
Tom Melia ◽  
Hitoshi Murayama
Keyword(s):  
Equations Of Motion ◽  
Companion Paper ◽  
Effective Field ◽  
Conformal Group ◽  
Field Theories ◽  
Irreducible Representations ◽  
Higher Dimension ◽  
The Standard Model ◽  
Mass Dimension ◽  
Fermion Generation

Abstract In a companion paper [1], we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)

ALL FREE CONFORMAL REPRESENTATIONS IN ALL DIMENSIONS

1989 ◽  
Vol 04 (08) ◽  
pp. 2015-2020 ◽  
Author(s):  
W. SIEGEL
Keyword(s):  
Space Time ◽  
Conformal Group ◽  
Irreducible Representations ◽  
Spinning Particle ◽  
Finite Dimensional

We find all free, massless, finite-dimensional, irreducible representations of the conformal group SO(D, 2) in all space-time dimensions D. In odd D they are only the scalar and spinor, but in even D they are all those which are (anti-)self-dual (chiral) on all vector indices. These are exactly the ones described by the mechanics of the extended spinning particle.

ALL CONFORMAL INVARIANT REPRESENTATIONS OF d-DIMENSIONAL ANTI-DE SITTER GROUP

1995 ◽  
Vol 10 (23) ◽  
pp. 1719-1731 ◽  
Author(s):  
R.R. METSAEV
Keyword(s):  
Gauge Invariance ◽  
Conformal Group ◽  
Elementary Particles ◽  
Irreducible Representations ◽  
Conformal Invariant ◽  
De Sitter ◽  
Sitter Group ◽  
Invariant Representations

All the irreducible representations of the anti-de Sitter group which are relevant for elementary particles and which can be realized as irreducible representations of the conformal group are found. It is shown that all these representations correspond to massless representations which arise from considerations of gauge invariance. The problem is studied for arbitrary d>2 dimensional anti-de Sitter group.

An Intuitive Method for the Determination of Crystal-Field Parameters in Laser Crystals

1993 ◽  
Vol 329 ◽  
Author(s):  
Frederick G. Anderson ◽  
H. Weidner ◽  
P. L. Summers ◽  
R. E. Peale ◽  
B. H. T. Chai
Keyword(s):  
Crystal Field ◽  
Irreducible Representations ◽  
Laser Crystals ◽  
Intuitive Method ◽  
Crystal Field Parameters ◽  
Intuitive Interpretation

AbstractExpanding the crystal field in terms of operators that transform as the irreducible representations of the Td group leads to an intuitive interpretation of the crystal-field parameters. We apply this method to the crystal field experienced by Nd3+ dopants in the laser crystals YLiF4, YVO4, and KLiYF5.

scholarly journals Fresh perspective on gauging the conformal group

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
M. P. Hobson ◽  
A. N. Lasenby
Keyword(s):  
Conformal Group ◽  
Fresh Perspective

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
Author(s):  
George Kempf
Keyword(s):  
Irreducible Representation ◽  
General Formula ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Reductive Group ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Know How ◽  
Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

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