相关论文: Quantum differential operators on K[x]
We consider algebras of quantum differential operators, for appropriate bicharacters on a polynomial algebra in one indeterminate and for the coordinate algebra of quantum $n$-space for $n\geq 3$. In the former case a set of generators for…
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that…
For ring of differential operators on smooth affine algebraic variety over perfect field of prime characteristic a set of algebra generators and a set of defining relations are found explicitly.
We describe the center of the ring $\Diff(n)$ of $\h$-deformed differential operators of type A. We establish an isomorphism between certain localizations of $\Diff(n)$ and the Weyl algebra $\text{W}_n$ extended by $n$ indeterminates.
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
By reading a standard formula for the ring of Grothendieck differential operators in a derived way, we construct a derived (sheaf of) ring of Grothendieck differential operators for Noetherian schemes $X$ separated and finite-type over a…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
In contrast with differential operators on modules over commutative and graded commutative rings, there is no satisfactory notion of a differential operator in noncommutative geometry.
We introduce the notion of a coordinate $\mathbf{k}$-algebra scheme and the corresponding notion of a $\mathcal{B}$-operator. This class of operators includes endomorphisms and derivations of the Frobenius map, and it also generalizes the…
Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional…
We consider the Noetherian properties of the ring of differential operators of an affine semigroup algebra. First we show that it is always right Noetherian. Next we give a condition, based on the data of the difference between the…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
We define and analyze Toeplitz operators whose symbols are the elements of the complex quantum plane, a non-commutative, infinite dimensional algebra. In particular, the symbols do not come from an algebra of functions. The process of…
For the ring of differential operators on a smooth affine algebraic variety $X$ over a field of characteristic zero a finite set of algebra generators and a finite set of defining relations are found explicitly. As a consequence, a finite…
We describe a generalization of Drinfeld's description of the center of a quantum group to the case of quantum affine algebras. We use the obtained central elements to construct the affine analogue of Macdonald's difference operators.
Let $k$ be an algebraically closed field of characteristic zero, let $X$ and $Y$ be smooth irreducible algebraic curves over $k$, and let $D(X)$ and $D(Y)$ denote respectively the quotient division rings of the ring of differential…
Quantum differential operators on Reflection Equation Algebras, corresponding to Hecke symmetries R were introduced in previous publications. In the present paper we are mainly interested in quantum analogs of the Laplace and Casimir…