SUMMARY
The thermal state of a scalar field in Quantum Field Theory (QFT) is defined by allowing the time variable to take on complex values. To evaluate the expectation value of any operator in this thermal state at temperature T, one integrates over the complex time variable from 0 to 1/T along the imaginary axis. This process involves propagating the operator for an amount of 1/T in the direction of imaginary time, with the condition that the 'in' state at t=0 and the 'out' state at t=i/T are identical, necessitating periodicity of correlators with respect to the translation t --> t + i/T. For fermions, antiperiodicity is required.
PREREQUISITES
- Understanding of Quantum Field Theory (QFT)
- Familiarity with complex analysis in the context of time variables
- Knowledge of operator expectation values
- Concept of periodicity and antiperiodicity in quantum states
NEXT STEPS
- Study the concept of complex time variables in QFT
- Learn about the calculation of expectation values in thermal states
- Research periodicity and antiperiodicity in quantum mechanics
- Consult advanced texts on Quantum Field Theory for deeper insights
USEFUL FOR
Researchers, physicists, and students in theoretical physics, particularly those focusing on Quantum Field Theory and statistical mechanics.