The geometric semantics of algebraic quantum mechanics.
نویسندگان
چکیده
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
منابع مشابه
ar X iv : h ep - t h / 98 02 04 6 v 1 7 F eb 1 99 8 Coincidences between M ( atrix ) Theory and Algebraic QFT ?
This is a preliminary account of coincidences between algebraic QFT and some recent observations on " light cone quantization " and applications to " M " theory. The most surprising correspondence is that between the existence of wedge affiliated semiglobal field coordinates without vacuum polarization and those light cone fields (on which " Matrix " theory is based) with analogous properties. ...
متن کاملCoincidences between M(atrix) Theory and Algebraic Qft ?
This is a preliminary account of coincidences between algebraic QFT and some recent observations on \light cone quantization" and applications to \M" theory. The most surprising correspondence is that between the existence of wedge aaliated semiglobal eld coordinates without vacuum polarization and those light cone elds (on which \Matrix" theory is based) with analogous properties. There is als...
متن کاملN ov 2 00 1 Random low rank mixed states are highly entangled Hao
We prove that for many low ranks r ≤ 2m − 3, random rank r mixed states in H A ⊗ H B have realtively high Schmidt numbers based on algebraic-geometric separability criterion proved in [1]. This also means that algebraic-geometric separability criterion can be used to detect all low rank entagled mixed states outside a measure zero set. Quantum entanglement was first noted as a feature of quantu...
متن کاملFunctorial semantics of topological theories
Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce t...
متن کاملAlgebraic geometric construction of a quantum stabilizer code
The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of bina...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
دوره 373 2047 شماره
صفحات -
تاریخ انتشار 2015