Perturbation theory without diagrams: the polaron case

Area of Science:

• Quantum Field Theory
• Many-Body Physics
• Theoretical Physics

Background:

• Higher-order perturbative calculations in quantum (field) theory face challenges due to the factorial growth of individual diagrams.
• Accurate computation of these terms is crucial for understanding fundamental physical systems.

Purpose of the Study:

• To present a numerical approach for evaluating higher-order perturbative contributions.
• To apply this method to calculate coefficients for the polaron ground-state energy.

Main Methods:

• Utilizes the cumulant expansion of observables for numerical evaluation at finite temperature.
• Employs extrapolation to zero temperature.
• Leverages state-of-the-art multidimensional integration routines.
• Incorporates analytical and numerical procedures for result reliability.

Main Results:

• Successfully calculated two new coefficients for the polaron ground-state energy.
• These coefficients correspond to four- and five-loop calculations.
• The implemented procedures ensured the reliability of the obtained results.

Conclusions:

• The cumulant expansion method offers an effective way to manage complexity in higher-order quantum calculations.
• This approach provides accurate numerical results for polaron energy, advancing theoretical physics.
• The study demonstrates the viability of numerical integration for complex perturbative problems.