P. Bieliavsky, R. Gurau, V. Rivasseau
Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is taken to extend such theories to non-flat backgrounds such as solvable symmetric spaces.
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In a non-commutative field theory, the energy-momentum tensor obtained from the Noether method needs not be symmetric; in a massless theory, it needs not be traceless either. In a non-commutative scalar field theory, the method yields a locally conserved yet non-symmetric energy-momentum tensor whose trace does not vanish for massless fields. A non-symmetric tensor also governs the response of the action to a general coordinate transformation. In non-commutative gauge theory, if translations are suitably combined with gauge transformations, the method yields a covariantly constant tensor which…
We study non Hermitian quantum systems in noncommutative space as well as a \cal{PT}-symmetric deformation of this space. Specifically, a \mathcal{PT}-symmetric harmonic oscillator together with iC(x_1+x_2) interaction is discussed in this space and solutions are obtained. It is shown that in the \cal{PT} deformed noncommutative space the Hamiltonian may or may not possess real eigenvalues depending on the choice of the noncommutative parameters. However, it is shown that in standard noncommutative space, the iC(x_1+x_2) interaction generates only real eigenvalues despite the fact that the Ham…
Non-commutative creation operators for symmetric polynomials
本文重新审视了Kirillov和Noumi提出的非交换创造算子，用于描述Schur、Jack和Macdonald多项式，通过在Young图中按规则添加方块而非随意位置来实现Pieri规则。
An exact GH membrane matrix model solution is given that corresponds to the world volume swept out by a fast moving axially symmetric drop with a sharp tip.
Conformally symmetric wormhole solutions supported by non-commutative geometries in the context of $f(Q,T)$ gravity
本文在 $f(Q,T)$ 引力与非对易分布背景下，利用共形对称性系统求解了可穿越虫洞的精确解析解，发现喉部附近 NEC 和 SEC 被违反，并证明其可由极少量物质构建，还分析了平衡力与复杂度因子。
Recent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity parameter theta. The present paper studies the asymptotic behaviour of solutions of the zero-rest-mass scalar wave equation in such a modified Schwarzschild space-time in a neighbourhood of spatial infinity. The analysis is eventually reduced to finding solutions of an inhomogeneous Euler--Poisson--Darboux equation, where the parameter theta affects explicitly the …
Comment on "Thermodynamic properties of Schwarzschild black hole in non-commutative gauge theory of gravity"
该评论指出，非交换引力理论中Schwarzschild黑洞热力学分析存在计算错误，导致事件视界和表面重力定义不当，所有结果需重新检验。
Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SU_q(2), the Green function and the Kernel on the q-homogeneous space M=SU(2)_q/U(1) are derived. A path integration is formulated. Green function for the free massive scalar field on the non-commutative Einstein space R^1xM is presented.
We study the generalization of S-duality to non-commutative gauge theories. For rank one theories, we obtain the leading terms of the dual theory by Legendre transforming the Lagrangian of the non-commutative theory expressed in terms of a commutative gauge field. The dual description is weakly coupled when the original theory is strongly coupled if we appropriately scale the non-commutativity parameter. However, the dual theory appears to be non-commutative in space-time when the original theory is non-commutative in space. This suggests that locality in time for non-commutative theories is a…
We consider Yukawa couplings generated by a configuration of intersecting seven-branes in F-theory. In configurations with a single interaction point and no fluxes turned on, the Yukawa matrices have rank one. This is no longer true when the three-form H-flux is turned on, which is generically the case for F-theory compactifications on Calabi-Yau fourfolds. In the presence of H-fluxes, the Yukawa coupling is computed using a non-commutative deformation of holomorphic Chern-Simons theory (and its reduction to seven-branes) and subsequently the rank of the Yukawa matrix changes. Such fluxes give…
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
We propose a new approach to field theory on $κ$-Minkowski non-commutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical non-commutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the $κ$-Poincare' coproduct should lead to interaction vertices that a…
The specific nonlinear vector $σ$-model coupled to Einstein gravity is investigated. The model arises in the studies of the gravitating matter in non-commutative geometry. The static spherically symmetric spacetimes are identified by direct solving of the field equations. The asymptotically flat black hole with the ``non-commutative'' vector hair appears for the special choice of the integration constants, giving thus another counterexample to the famous ``no-hair'' theorem.
Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson-Thomas invariants of Calabi-Yau threefolds. For the special case when A is the non-commutative crepant resolution of the threefold ordinary double point, it is proved using torus localization that the invariants count certain pyramid-shaped partition-like configurations, or equivalently infinite dimer configurations in the square dimer model with a fixed boundary condition. The resulting partition function admits an inf…
This article is based on the study of wormhole geometries in the context of symmetric teleparallel gravity or $f(Q)$ gravity, where $Q$ is the non-metricity scalar, and it is responsible for the gravitational interaction. To discuss the wormhole solutions, we consider spherically symmetric static spacetime metric with anisotropic matter contents under well-known non-commutative distributions known as Gaussian and Lorentzian distributions with an extra condition of permitting conformal killing vectors (CKV). This work aims to obtain wormhole solutions under these distributions, and through we f…
It is pointed out that the usual $θ$-algebra assumed for non-commuting coordinates is not $P$- and $T$-invariant, unless one {\it formally} transforms the non-commutativity parameter $θ^{μν}$ in an appropriate way. On the other hand, the Lorentz-covariant DFR algebra, which `relativitizes' the $θ$-algebra by replacing $θ^{μν}$ with a second-rank antisymmetric tensor operator $\htheta^{μν}$, is $C$-, $ P$- and $T$-invariant. It is then proved that $C, P$ and $T$ are separately conserved in Lorentz-invariant Non-Commutative QED.
Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane
采用不依赖表象的方法研究非对易平面上的量子霍尔与简谐振子系统，修正了非对易空间对称规范的错误形式，得到霍尔系统谱、电导率等静态性质及非平衡动力学，还发现非对易简谐振子动力学呈准周期行为。
We study the shadow and energy emission rate of a spherically symmetric non-commutative black hole in Rastall gravity. Depending on the model parameters, the non-commutative black hole can reduce to the Schwarzschild black hole. Since the non-vanishing non-commutative parameter affects the formation of event horizon, the visibility of the resulting shadow depends on the non-commutative parameter in Rastall gravity. The obtained sectional shadows respect the unstable circular orbit condition, which is crucial for physical validity of the black hole image model.
The consistency equations of patch inflation are considered in a next-to-leading-order slow-roll (SR) expansion. Some general aspects of braneworld degeneracy are pointed out, both with an ordinary scalar field and a Born-Infeld tachyon. The discussion is then extended to the maximally symmetric noncommutative case.
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