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Efficiently bounding large determinants is an essential step innon-relativistic fermionic constructive quantum field theory to prove theabsolute convergence of the perturbation expansion of correlation functions interms of powers of the strength $u\in \mathbb{R}$ of the interparticleinteraction. We provide, for large determinants of fermionic convariances,sharp bounds which hold for all (bounded and unbounded, the latter not beinglimited to semibounded) one-particle Hamiltonians. We find the smallestuniversal determinant bound to be exactly $1$. In particular, the convergenceof perturbation series at $u=0$ of any fermionic quantum field theory isensured if the matrix entries, with respect to some fixed orthonormal basis, ofthe covariance and the interparticle interaction decay sufficiently fast. Ourproofs use H\"older inequalities for general non-commutative $L^{p}$-spacesderived by Araki and Masuda.

Universal Bounds for Large Determinants from Non-Commutative H\"older Inequalities in Fermionic Constructive Quantum Field Theory