Towards Local Temperature States in QFT (Mathematical Aspects of Quantum Information and Quantum Chaos)
Izumi Ojima · Institutional Repositories DataBase (IRDB) · 2000
Simple example of local temperature stateAiming at a general formulation of non-equilibrium states in the framework of QFT, we start from a simple model-example of local temperature state: Let $\varphi(x)$ be a massless free scalar field (in four dimensions) characterized by(Given a two-point function $\omega^{(2)}(\varphi(x)\varphi(y))$ , we can define a quasi-free state $\omega$ of $\varphi$ through the Wick formula:When a two-point function $\omega^{(2)}$ is chosen consistently with Eqs.$(1, 2)$ asthe corresponding quasi-free state $\omega=\omega_{\beta}$ describes a global thermal equi- librium satisfying the KMS condition for any pair of polynomial fields $A=$ $\varphi(x_{1})\cdots\varphi(x_{r})$ and $B=\varphi(y_{1})\cdots\varphi(y_{s})$ , $\omega_{\beta}(A\alpha_{(i\beta,\mathrm{O})}(B))=\omega_{\beta}(BA)$ , (5) *Talk based on a joint work of D.Buchholz, H.Roos and $\mathrm{I}.\mathrm{O}$ . in progress