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THU: Thursday Contributed Sessions

THU 10: Foundational / Mathematical Aspects – Methods and Approximations

THU 10.2: Talk

Thursday, September 11, 2025, 14:30–14:45, ZHG103

Absolute and relational many-body Green’s function theories — •Ville Härkönen — Tampere University, Tampere, Finland

Quantum mechanics, now a century old, has relied heavily on the Coulomb problem and the Born-Oppenheimer (BO) approximation [1] for describing atoms, molecules, and solids. While the BO approximation is widely used, its limitations are evident in materials like superconducting hydrides.

Wave function methods are impractical for solids due to poor scaling, leading to alternatives like BO-based density functional theory and many-body Green’s function theory. A beyond-BO Green’s function approach was proposed in the 1960s [2], but it contains foundational issues [3].

We have developed an exact many-body Green’s function theory to address these problems [4], revealing that quantum theory may need to be relational rather than absolute [5].

In this talk, we summarize recent developments in beyond-BO Green’s function theory [4,5,6] and explore the implications of relational versus absolute frameworks in quantum mechanics [7].
[1] M. Born and R. Oppenheimer, Ann. Phys. (Leipzig) 389, 457 (1927).
[2] G. Baym, Ann. Phys. 14, 1 (1961).
[3] B. Sutcliffe, Adv. Chem. Phys. 114, 1 (2000).
[4] V. J. Härkönen, R. van Leeuwen, and E. K. U. Gross, Phys. Rev. B 101, 235153 (2020).
[5] V. J. Härkönen, arXiv:2503.01417 .
[6] V. J. Härkönen, Phys. Rev. B 106, 205137 (2022).
[7] J. B. Barbour, Br. J. Philos. Sci. 33, 251 (1982); L. Smolin, arXiv:1805.12.

Keywords: Relational quantum theory; Many-body Green's functions; Absolute quantum theory; Born-Oppenheimer approximation