Related papers: Two-parameter quantum groups and quantum planes
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
We formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible to fulfill the requirements of locality, unitarity and…
Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…
A natural counterpart to the Lie-Trotter product formula for norm-continuous one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic operator cocycles whose expectation semigroup is norm continuous. Compared…
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…
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…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where…
A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in…
We construct twisting elements for module algebras of restricted two-parameter quantum groups from factors of their R-matrices. We generalize the theory of Giaquinto and Zhang to universal deformation formulas for categories of module…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally extended planar absolute time Lie groups. Through these…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
In this note we give explicit isomorphisms of 2-categories between various versions of the categorified quantum group associated to a simply-laced Kac-Moody algebra. These isomorphisms are convenient when working with the categorified…
A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated…
Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an…
(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum…
A model of joint random walk of two agents on an infinite plane is considered. The agents possess no means of mutual classical communication, but have access to quantum entanglement resource which is used according to a pre-arranged…