Analyse harmonique sur les groupes de Lie: seminaire, by P. Eymard, J. Faraut, G. Schiffmann, R. Takahashi PDF

By P. Eymard, J. Faraut, G. Schiffmann, R. Takahashi

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Extra info for Analyse harmonique sur les groupes de Lie: seminaire, Nancy-Strasbourg

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We incorporate these spinors into a four-component column YJ = (;-). 8) This double spinor is called a ‘Dirac spinor’ (here and later, four-component Copyright © 1998 IOP Publishing Ltd spinor objects are denoted by boldface letters). 12) so ;'a are the usual Dirac matrices (in the special representation). 11) is the standard transformation law of Dirac spinors. Q we conjugate IC/, to obtain $& and conjugate j* to obtain x'. Let us combine the resulting two-component spinors in a four-component row q =(x5(, $d.

To clarify this assertion, we introduce one auxiliary notion which will be useful also when constructing irreducible representations of the (super) Poincare group. 4. Stubility subgroup In a Hilbert space of one-particle states with a given mass m, we consider the substance V, of particle states having a given four-momentum qa, pa 14) = q a 14) for any state 14) E V,. 17) in momentum space. We define the set H, of group elements (A, b) such that the corresponding operators U(A,b) transform V, onto itself.

6+66) + (pb)&a(8cd)8';} c( + )abed. 7. 1. Conformal Killing vectors Let M be a space-time manifold with local coordinates X" and metric ds2=gmn(x)dx" dx"(of Lorentzian signature). 1) which changes the metric as follows 6gmn(x)=g6n(x)-gg,n(x)= - Vmtn- V n t m . 2) A vector field <"(x) is called a 'conformal Killing' vector if it satisfies the equation 1 Vmtn +Vn

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