Related papers: On quantum Jacobi identity
Making use of the theory of infinitesimal canonical transformations, a concise proof is given of Jacobi's identity for Poisson brackets.
We survey various origins and expressions for the quantum potential with some new observations.
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
This is a research announcement of the theory of orbifold quantum cohomology.
The quantal algebra combines classical and quantum mechanics into an abstract structurally unified structure. The structure uses two products: one symmetric and one anti-symmetric. The local structure of spacetime is contained in the…
We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the…
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
A quantum integrable model related to $U_q(\hat{sl}(N))$ is considered. A reduced model is introduced which allows interpretation in terms of quantized affine Jacobi variety. Closed commutation relations for observables of reduced model are…
We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the K\"all\'en-Lehmann representation of products of two Anti-de Sitter two-point functions. A rich mathematical…
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…
We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by Wang. More precisely, the resulting quantum groups…
Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…
The Jacobian algebras are introduced and their various properties are studied.
We investigate some forms of quantum logic arising from the standard and the unsharp approach.
In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…
In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.
In this paper we discuss the unitary inequivalentness in quantum physics. Then based on some of the current outstanding problems in theoretical physics, we will show the important role of this concept to better understand the physical…
This paper introduces and analyzes symmetric and anti-symmetric quantum binary functions. Generally, such functions uniquely convert a given computational basis state into a different basis state, but with either a plus or a minus sign.…
In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.