相关论文: On quantum Jacobi identity
We obtain a finite form of Jacobi's identity and present a combinatorial proof based on the structure of synchronized partitions.
We discover a new version of the celebrated Montgomery identity via quantum integral operators and establish certain quantum integral inequalities of Ostrowski type by using this identity. Relevant connections of the results obtained in…
We prove the noncommutative analogue of Jacobi triple product identity. As an application we organizing the q-characters of circular quiver gauge theories into an infinite product. We conjecture the gauge origami theory interpretation of…
On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is…
We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of arbitrary associative algebra. One is a consequence of other (fundamental identity). From the fundamental identity,…
Recently the second named author discovered a combinatorial identity in the context of vertex representations of quantum Kac-Moody algebras. We give a direct and elementary proof of this identity. Our method is to show a related identity of…
In this paper we define a Grassmann odd analogue of Jacobi structure on a supermanifold. The basic properties are explored. The construction of odd Jacobi manifolds is then used to reexamine the notion of a Jacobi algebroid. It is shown…
Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…
We present several identities involving quasi-minors of noncommutative generic matrices. These identities are specialized to quantum matrices, yielding q-analogues of various classical determinantal formulas.
The main purpose of this article is to discuss a project relating Gopakumar-Vafa invariants to quantum K-invariants on Calabi-Yau threefolds. Results in genus zero, including recent and forthcoming works, are reported.
A quantum Capelli identity is given on the multiparameter quantum general linear group based on the $(p_{ij}, u)$-condition. The multiparameter quantum Pfaffian of the $(p_{ij}, u)$-quantum group is also introduced and the transformation…
In this paper we investigate some divisibility properties of Jacobsthal numbers.
In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.
For any homogeneous identity between $q$-minors, we provide an identity between $P,Q$-minors.
The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and optics. In this paper, we study the Weil…
Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus…
We establish a finiteness property of the quantum K-ring of the complete flag manifold.
We reformulate the notion of a Jacobi algebroid in terms of weighted odd Jacobi brackets. We then show how a Jacobi algebroid can be understood in terms of a kind of curved Q-manifold. In particular the homological condition on the odd…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…