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.