Related papers: New features of FORM
A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
This book provides an introduction to the emerging field of quantum thermodynamics, with particular focus on its relation to quantum information and its implications for quantum computers and next generation quantum technologies. The text,…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
GENESIS3 is the new version of the GENESIS software environment for musical creation by means of mass-interaction physics network modeling. It was designed, and developed from scratch, in hindsight of more than 10 years working on and using…
We report on recent results on the Quantum Field Theory of mixed particles. The quantization procedure is discussed in detail, both for fermions and for bosons and the unitary inequivalence of the flavor and mass representations is proved.…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.
General methods of quantitative and qualitative continuity analysis of characteristics of composite quantum systems are described. Several modifications of the Alicki-Fannes-Winter method are considered, which make it applicable to a wide…
3D promises a new dimension in composing systems by aggregating chips. Literally. While the most common uses are still tightly connected with its early forms as a packaging technology, new application domains have been emerging. As the…
The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
The draft paper defines a system, which is capable of maintaining bases of test cases for logical specifications. The specifications, which are subject to this system are transformed from their original shape in first-order logic to…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
We introduce a formalism that exploits the many-input many-output nature of nodes in quantum circuits. There is a diagrammatic and an algebraic version, the latter similar to the spinor formalism of general relativity. This allows us to…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
Quantum learning paradigms address the question of how best to harness conceptual elements of quantum mechanics and information processing to improve operability and functionality of a computing system for specific tasks through experience.…