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Study of bound states in a thermal gas using the S-matrix formalism

We have studied the formation of bound states in a thermal gas in the context of quantum field theory (QFT). We have considered a scalar QFT with $φ^4$ interaction, where $φ$ is a scalar particle with mass $m$. We have observed the formation of a bound state of $φ$-$φ$ type when the coupling constant is negative and its modulus is larger than a certain critical value. We have calculated the contribution of the bound state to the pressure of the thermal gas of the system by using the S-matrix formalism. Our analysis is based on a unitarized one-loop resumed approach in which the theory is finite and well defined for each value of the coupling constant. We have observed that the total pressure as a function of the coupling constant is continuous also at the critical coupling: the jump in pressure due to the sudden appearance of the bound state is exactly cancelled by an analogous jump (but with opposite sign) of the interaction contribution to the pressure.