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All possible Bogoliubov operators that generate the thermal transformationsin the Thermo Field Dynamics (TFD) form a SU(1,1) group. We discuss thiscontruction in the bosonic string theory. In particular, the transformation ofthe Fock space and string operators generated by the most general SU(1,1)unitary Bogoliubov transformation and the entropy of the corresponding thermalstring are computed. Also, we construct the thermal $D$-brane solutiongenerated by the SU(1,1) transformation in a constant Kalb-Ramond field andcompute its entropy.Comment: misprints correcte

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>thermal group of bosonic strings and<i>D</i>-branes

SU(1,1)thermal group of bosonic strings andD-branes