Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-03-17
J. Phys. A: Math. Theor. 44 (2011) 475202
Physics
High Energy Physics
High Energy Physics - Theory
7 pages, revtex style; v2: Minor corrections, references added; v3: Typos corrected
Scientific paper
10.1088/1751-8113/44/47/475202
The way to obtain massive non-relativistic states from the Poincare algebra is twofold. First, following Inonu and Wigner the Poincare algebra has to be contracted to the Galilean one. Second, the Galilean algebra is to be extended to include the central mass operator. We show that the central extension might be properly encoded in the non-relativistic contraction. In fact, any Inonu-Wigner contraction of one algebra to another, corresponds to an infinite tower of abelian extensions of the latter. The proposed method is straightforward and holds for both central and non-central extensions. Apart from the Bargmann (non-zero mass) extension of the Galilean algebra, our list of examples includes the Weyl algebra obtained from an extension of the contracted SO(3) algebra, the Carrollian (ultra-relativistic) contraction of the Poincare algebra, the exotic Newton-Hooke algebra and some others. The paper is dedicated to the memory of Laurent Houart (1967-2011).
Khasanov Oleg
Kuperstein Stanislav
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