Related papers: Topologies on Quantum Effects
Quantum effects play an essential role in modern cosmology. Perhaps the most striking example comes from large-scale structures, generally assumed to originate from vacuum quantum fluctuations and stretched by an expansion phase. Inflation…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
We show how an effect algebra $\mathcal{X}$ can be regarded as a category, where the morphisms $x \rightarrow y$ are the elements $f$ such that $x \leq f \leq y$. This gives an embedding $\mathbf{EA} \rightarrow \mathbf{Cat}$. The interval…
Recently, it is shown that, the quantum effects of matter are well described by the conformal degree of freedom of the space-time metric. On the other hand, it is a wellknown fact that according to Einstein's gravity theory, gravity and…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.