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arXiv:hep-th/0208134

Bosonic String at Finite Temperature

de Souza, W. P.

Published Aug 19, 2002• 1 citation
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Abstract

The Thermo Field Dynamics formalism is presented. In particular, it is applied to the two-dimensional field theory that describes a open bosonic string. The value of entropy operator is computed in various Dirichlet and Neumann boundary states. The Thermal Bogoliubov transformations, the thermal vacuum and the thermal Fock space are computed explicitely for the case of SU(1,1) thermal algebra.

DOI
10.48550/arxiv.hep-th/0208134

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The Thermo Field Dynamics formalism is presented. In particular, it is applied to the two-dimensional field theory that describes a open bosonic string. The value of entropy operator is computed in various Dirichlet and Neumann boundary states. The Thermal Bogoliubov transformations, the thermal vacuum and the thermal Fock space are computed explicitely for the case of SU(1,1) thermal algebra.
In this work we explain the construction of the thermal vacuum for the bosonic string, as well that of the thermal boundary state interpreted as a Dp-brane at finite temperature. In both case we calculate the respective entropy using the entropy operator of the Thermo Field Dynamics theory. We show that the contribution of the thermal string entropy is explicitly present in the Dp-brane entropy. Furthermore, we show that the Thermo Field approach is suitable to introduce temperature in boundary states.
All possible Bogoliubov operators that generate the thermal transformations in thermo field dynamics form an SU(1,1)\mathrm{SU}(1,1)SU(1,1) group. We discuss this construction in the bosonic string theory. In particular, the transformation of the Fock space and string operators generated by the most general SU(1,1)\mathrm{SU}(1,1)SU(1,1) unitary Bogoliubov transformation and the entropy of the corresponding thermal string are computed. Also, we construct the thermal D-brane generated by the SU(1,1)\mathrm{SU}(1,1)SU(1,1) transformation in a constant Kalb-Ramond field and compute its entropy.
In this paper we review the construction of the thermal bosonic string and DDD-brane in the framework of the Thermo Field Dynamics (TFD). We briefly recall the well-known light-cone quantization of the bosonic string in the conformal gauge in flat space-time. Then we give a bird's eye view of the fundamental concepts of the TFD. Also, we present the thermalization of the bosonic string and the construction of the thermal D-brane boundary state. Finally, we show the calculation of the entropy of the thermal open string states with all boundary conditions and the entropy of the thermal D-brane state.
Perturbation theory in thermofield dynamics (a real time finite temperature quantum field theory) is formulated in the interaction representation and a diagrammatic expansion for the expectation value of time ordered products is derived solely on the basis of the thermal state condition and the algebraic properties of the operators. This new formulation has a much wider domain of applicability than those presented previously. The method is applicable even in the case of purely quantum mechanical systems. When certain bosonic operators, which commute with the unperturbed Hamiltonian, contribute to the renormalization of the thermal state vacuum the vacuum diagrams do not cancel in the usual way. It will be shown how these diagrams arise and how they may be computed.