2023/07/21 by H. Kawai, Kiyoharu Kawana, Kawai, Hikaru +5
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2307.11420
openalex publication_date 2023/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In ordinary thermodynamics, around first-order phase transitions, the intensive parameters such as temperature and pressure are automatically fixed to the phase transition point when one controls the extensive parameters such as total volume and total energy. From the microscopic point of view, the extensive parameters are more fundamental than the intensive parameters. Analogously, in conventional quantum field theory (QFT), coupling constants (including masses) in the path integral correspond to intensive parameters in the partition function of the canonical formulation. Therefore, it is natural to expect that in a more fundamental formulation of QFT, coupling constants are dynamically fixed a posteriori, just as the intensive parameter in the micro-canonical formulation. Here, we demonstrate that the automatic tuning of the coupling constants is realized at a quantum-phase-transition point at zero temperature, even when the transition is of higher order, due to the Lorentzian nature of the path integral. This naturally provides a basic foundation for the multi-critical point principle. As a concrete toy model for solving the Higgs hierarchy problem, we study how the mass parameter is fixed in the ϕ4 theory at the one-loop level in the micro-canonical or further generalized formulation of QFT. We find that there are two critical points for the renormalized mass: zero and of the order of ultraviolet-cutoff. In the former, the Higgs mass is automatically tuned to be zero and thus its fine-tuning problem is solved. We also show that the quadratic divergence is absent in a more realistic two-scalar model that realizes the dimensional transmutation. Additionally, we explore the possibility of fixing quartic coupling in ϕ4 theory and find that it can be fixed to a finite value.