10 citations · 31 across the 13 of their papers we have counts for
13 papers
The bulk spectral gap is certifiable from above but uncomputable from below
Xiangling Xu, Matthias Schötz, Jie Wang +4
Determining spectral gaps in the thermodynamic limit is a central challenge in quantum many-body physics. When a fixed boundary condition is imposed, this problem is undecidable: n…
Real Nullstellensatz for 2-step nilpotent Lie algebras
Philipp Schmitt, Matthias Schötz
We prove a noncommutative real Nullstellensatz for 2-step nilpotent Lie algebras that extends the classical, commutative real Nullstellensatz as follows: Instead of the real polyno…
Associativity and Commutativity of Partially Ordered Rings
Matthias Schötz
Consider a commutative monoid and a biadditive binary operation . We will show that under some additional general assumptions, the operation …
Positivstellensätze for Semirings
Konrad Schmüdgen, Matthias Schötz
In this paper we develop a number of results and notions concerning Positivstellensätze for semirings (preprimes) of commutative unital real algebras. First we reduce the Archimede…
Symmetry Reduction of States II: A non-commutative Positivstellensatz for CPn
Philipp Schmitt, Matthias Schötz
We give a non-commutative Positivstellensatz for CP^n: The (commutative) *-algebra of polynomials on the real algebraic set CP^n with the pointwise product can be realized by phase…
Symmetry Reduction of States I
Philipp Schmitt, Matthias Schötz
We develop a general theory of symmetry reduction of states on (possibly non-commutative) *-algebras that are equipped with a Poisson bracket and a Hamiltonian action of a commutat…
Wick Rotations in Deformation Quantization
Philipp Schmitt, Matthias Schötz
We study formal and non-formal deformation quantizations of a family of manifolds that can be obtained by phase space reduction from with the Wick star product i…
Gelfand-Naimark Theorems for Ordered *-Algebras
Matthias Schötz
The classical Gelfand--Naimark theorems provide important insight into the structure of general and of commutative C*-algebras. It is shown that these can be generalized to certain…
Stone-Weierstraß Theorems for Riesz Ideals of Continuous Functions
Matthias Schötz
Notions of convergence and continuity specifically adapted to Riesz ideals I of the space of continuous real-valued functions on a Lindelöf locally compact Hausdorff space are give…
Equivalence of Order and Algebraic Properties in Ordered *-Algebras
Matthias Schötz
The aim of this article is to describe a class of *-algebras that allows to treat well-behaved algebras of unbounded operators independently of a representation. To this end, Archi…
A Convergent Star Product on the Poincaré Disc
Daniela Kraus, Oliver Roth, Matthias Schötz +1
On the Poincaré disc and its higher-dimensional analogs one has a canonical formal star product of Wick type. We define a locally convex topology on a certain class of real-analyti…
On Characters and Pure States of *-Algebras
Matthias Schötz
It is easy to see that every character (i.e. unital *-homomorphism to the complex numbers) of a commutative unital associative *-algebra is a pure state (i.e. extreme point in the…
Convergent Star Products for Projective Limits of Hilbert Spaces
Matthias Schötz, Stefan Waldmann
Given a locally convex vector space with a topology induced by Hilbert seminorms and a continuous bilinear form on it we construct a topology on its symmetric algebra such that the…