Constructing interacting-boson dynamics and equilibrium states by representation-free path integrals

Construct automorphism groups and equilibrium states for interacting bosons on the abstract Buchholz algebra by means of path integrals without passing to a bosonic Fock representation.

Background

The paper develops finite-mode traces, Gibbs states, trace-norm product formulas, and closed-path expansions intrinsically, without using a Fock representation. These constructions are presented as a starting point for extending path-integral methods to the full abstract Buchholz algebra. The unresolved issue is whether these finite-mode and closed-path techniques suffice to construct dynamics and equilibrium states for interacting bosonic systems at the representation-independent level, rather than only after choosing the Fock realization.

References

Whether automorphism groups and equilibrium states of interacting bosons can actually be constructed by path integrals without passing to the Fock representation is the subject of our next study.

— The Buchholz Algebra from the Universal Resolvent Algebra--Particle Structure, Gibbs States, and Closed-Path Expansions without Fock Representations  (2610.01622 - Sekine, 1 Oct 2026) in Conclusion, final paragraph