Non-perturbative constraints on perturbation theory at finite temperature

Abstract

It has long been understood that the inclusion of temperature in the perturbative treatment of quantum field theories leads to complications that are not present at zero temperature. In these proceedings we report on the non-perturbative obstructions that arise, and how these lead to deviations in the predictions of lattice scalar correlation functions in massive ${\varphi }^4$ theory. Using the known non-perturbative spectral constraints satisfied by finite-temperature correlation functions we outline why the presence of distinct particle-like excitations could provide a resolution to these issues.

8 pages, 3 figures; talk presented at the EMMI Workshop: "Aspects of Criticality II", 2-4 July 2024, Wroclaw, Poland; v2: matches published version

References in corpus (20)

• The pressure of hot QCD up to g^6 ln(1/g)
• Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density
• Basics of thermal field theory -- a tutorial on perturbative computations
• Screened Perturbation Theory
• Optimized Perturbation Theory at Finite Temperature
• Resummation in Hot Field Theories
• Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries
• Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram
• Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories
• Screened Perturbation Theory to Three Loops
• Four-loop pressure of massless O(N) scalar field theory
• Four-loop screened perturbation theory
• Axiomatic Analyticity Properties and Representations of Particles in Thermal Quantum Field Theory
• Pion spectral properties above the chiral crossover of QCD
• Asymptotic dynamics of thermal quantum fields
• Pseudo-scalar meson spectral properties in the chiral crossover region of QCD
• Analytic Properties of Finite-Temperature Self-Energies
• Branch Cuts Due to Finite-Temperature Quasiparticles
• Quasiparticles in Finite-Temperature Field Theory
• On the (in)consistency of perturbation theory at finite temperature