Real-time thermal self-energies: in the variational bases and spaces

• Main Authors: Ahmed, M.A.A., Zainuddin, H., Shah, N.M.
• Format: Article
• Published: Elsevier 2022
• Online Access: http://psasir.upm.edu.my/id/eprint/102995/; https://linkinghub.elsevier.com/retrieve/pii/S2211379722003783

In this work, we introduce a systematic study for studying the scalar propagator and tadpole self-energy by considering an arbitrary parameter σ that allows for a path integral description in real-time formalism (RTF). The closed time path formalism (CTP) and Thermofield Dynamics (TFD) are two popular choices for the parameter σ in the Feynman rules. We have constructed a scalar propagator and a tadpole self-energy in two different bases in the momentum space as well as the mixed space. The results show that the diagonal components of self-energy in both spaces for the 1/2 basis are the same in both approaches within RTF, whereas the other off-diagonal components of self-energy are different because they depend on the path parameter. On the other hand, the diagonal components of self-energy in both spaces for the new basis are not the same in both approaches within RTF, whereas the off-diagonal components of self-energy are vanishing. That means the new basis allows one to reduce the components for the quantities studied, like self-energy or other.