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Volume 8,     Number 1,     Spring 2000

 

LIE ALGEBRAS AND THE DOUBLING
IN THERMO FIELD DYNAMICS
M. DE MONTIGNY, F.C. KHANNA AND A.E. SANTANA

Abstract. The structure of thermo field dynamics (TFD) is basedon an algebraic doubling. This gives rise to the standard representation of C-algebras, and here we use its Hilbert space as the representation space of Lie algebras. From the group-theoretical point of view, our construction amounts to a simple application of the semi-direct product. In particular, we study these representations for su(2) symmetry. Our main results include the construction of new representations of the Duffin-Kemmer-Petiau (DKP) algebra, in particular, a four-dimensional representation for spin 0 particles in 2+1 space-time. We establish a connection among the doublings that appear in TFD, C-algebras, Hopf algebras, and adjoint representations of Lie algebras.

 

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