Related papers: On the conjugation action for quantum general line…
A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some…
In this paper, we construct a combinatorial algebra of partial isomorphisms that gives rise to a "projective limit" of the centers of the group algebras C[GL(n,Fq)]. It allows us to prove a GL(n,Fq)-analogue of an old theorem of Farahat and…
Using the general framework of nonequilibrium statistical mechanics for relativistic quantum field systems we derive the basic equations of quantum field kinetics. The main aim of the approach is calculation of observables associated with…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…
We describe explicitly all actions of the quantum permutation groups on classical compact spaces. In particular, we show that the defining action is the only non-trivial ergodic one. We then extend these results to all easy quantum groups…
We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
A recently proposed definition of a linear connection in non-commutative geometry, based on a generalized permutation, is used to construct linear connections on GL_q(n). Restrictions on the generalized permutation arising from the…
We construct quantization of semisimple conjugacy classes of the exceptional group $G=G_2$ along with and by means of their exact representations in highest weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$ of a…
We study linearizability of actions of finite groups on cubic threefolds with non-isolated singularities.
The quantum cohomology of Grassmannians exhibits two symmetries related to the quantum product, namely a \Bbb {Z}/n action and an involution related to complex conjugation. We construct a new ring by dividing out these symmetries in an…
We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum general and special linear groups on tensor products of quantum matrix algebras. More precisely, let m,n,t be arbitrary positive integers,…
Actions of locally compact groups and quantum groups on W*-ternary rings of operators are discussed and related crossed products introduced. The results generalise those for von Neumann algebraic actions with proofs based mostly on passing…
We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns…
We consider the quantum field theoretical formulation of boson field mixing and obtain the exact oscillation formula. This formula does not depend on arbitrary mass parameters. We show that the space for the mixed field states is unitarily…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
A complex conjugation of unitary quantum map is a second-order map (supermap) that maps a unitary operator $U$ to its complex conjugate $U^*$. First, we present a deterministic quantum protocol that universally implements the complex…