Related papers: Obstructions to Deformation Quantization of Bundles

Obstructions to Deformation Quantization of Bundles

URL: http://arxiv.org/abs/2607.12910v1
Date: Tue, 14 Jul 2026 15:43:48 GMT
Title: Obstructions to Deformation Quantization of Bundles
Abstract summary: Let $left(M, mathcalO_M right)$ be a smooth algebraic variety over field $$ of characteristic $0$.<n>Let $E$ be a vector bundle over $left(M, mathcalO_M right)$ and $mathcalO_hbar$ a deformation quantization of $mathcalO_M$ compatible with $$.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Let $\left(M, \mathcal{O}_M \right)$ be a smooth algebraic variety over field $κ$ of characteristic $0$ with an algebraic symplectic form $ω$, or a complex manifold with a holomorphic form $ω$. Furthermore, let $E$ be a vector bundle over $\left(M, \mathcal{O}_M \right)$ and $\mathcal{O}_{\hbar}$ a deformation quantization of $\mathcal{O}_M$ compatible with $ω$. Assuming that $E$ possesses a deformation quantization to order $\hbar^k$ we consider the problem of extending it to order $\hbar^\ell$ for $\ell > k$, and establish triviality of an obstruction class as a necessary condition for this extension to exist. Furthermore, in the case $\ell \le 2k+1$, we prove that this condition is also sufficient.

Related papers

Self-testing of exact entanglement embezzlement [0.0]
We consider exact entanglement embezzlement with a catalyst state vector $$ in a Hilbert space $mathcalH$ using unitaries.<n>We show that any such protocol must arise from a unique state on the tensor product $mathcalO_d otimes mathcalO_d$ of the Cuntz algebra with itself.
arXiv Detail & Related papers (2026-05-21T16:50:39Z)
Approximating the operator norm of local Hamiltonians via few quantum states [53.16156504455106]
Consider a Hermitian operator $A$ acting on a complex Hilbert space of $2n$.<n>We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a local $n$-qubit Hamiltonian.<n>We show that whenever $A$ is $d$-local, textiti.e., $deg(A)le d$, we have the following discretization-type inequality.
arXiv Detail & Related papers (2025-09-15T14:26:11Z)
Non-representable quantum measures [55.2480439325792]
Grade-$d$ measures on a $sigma$-algebra $mathcalAsubseteq 2X$ over a set $X$ are generalizations of measures satisfying one of a hierarchy of weak additivity-type conditions.<n>Every signed polymeasure $lambda$ on $(X,mathcalA)d$ produces a grade-$d$ measure as its diagonal $widetildelambda(A):=lambda(A,cdots,A)$.
arXiv Detail & Related papers (2025-08-20T00:47:24Z)
A New $q$-Heisenberg Algebra [0.0]
We introduce a novel $q$-$hbar$ deformation of the Heisenberg algebra, designed to unify and extend several existing $q$-deformed formulations.<n>The resulting structures are shown to align with quantum planes citeYuri-Manin2010 and enveloping algebras associated with Lie algebra homomorphisms citeReyes2014a.
arXiv Detail & Related papers (2025-05-31T20:16:42Z)
Monge-Kantorovich Fitting With Sobolev Budgets [6.748324975906262]
We show that when $rho$ is concentrated near an $mtext-d$ set we may interpret this as a manifold learning problem with noisy data.<n>We quantify $nu$'s performance in approximating $rho$ via the Monge-Kantorovich $p$-cost $mathbbW_pp(rho, nu)$, and constrain the complexity by requiring $mathrmsupp nu$ to be coverable by an $f : mathbbRm
arXiv Detail & Related papers (2024-09-25T01:30:16Z)
Subspace Controllability and Clebsch-Gordan Decomposition of Symmetric Quantum Networks [0.0]
We describe a framework for the controllability analysis of networks of $n$ quantum systems of an arbitrary dimension $d$, it qudits Because of the symmetry, the underlying Hilbert space, $cal H=(mathbbCd)otimes n$, splits into invariant subspaces for the Lie algebra of $S_n$-invariant elements in $u(dn)$, denoted here by $uS_n(dn)$.
arXiv Detail & Related papers (2023-07-24T16:06:01Z)
$\ell_p$-Regression in the Arbitrary Partition Model of Communication [59.89387020011663]
We consider the randomized communication complexity of the distributed $ell_p$-regression problem in the coordinator model. For $p = 2$, i.e., least squares regression, we give the first optimal bound of $tildeTheta(sd2 + sd/epsilon)$ bits. For $p in (1,2)$,we obtain an $tildeO(sd2/epsilon + sd/mathrmpoly(epsilon)$ upper bound.
arXiv Detail & Related papers (2023-07-11T08:51:53Z)
Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model [77.34726150561087]
We provide a systematic treatment of boundaries based on subgroups $Ksubseteq G$ with the Kitaev quantum double $D(G)$ model in the bulk. The boundary sites are representations of a $*$-subalgebra $Xisubseteq D(G)$ and we explicate its structure as a strong $*$-quasi-Hopf algebra. As an application of our treatment, we study patches with boundaries based on $K=G$ horizontally and $K=e$ vertically and show how these could be used in a quantum computer
arXiv Detail & Related papers (2022-08-12T15:05:07Z)
Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann. We show how our results have immediate applications to the modern theory of polarization.
arXiv Detail & Related papers (2022-05-30T18:01:34Z)
Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$. It is assumed that a density matrix $rho$ can be determined from the expectation values of observables. Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
arXiv Detail & Related papers (2021-12-14T16:29:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.