Wick-Voros和Moyal乘积的扭曲非对易场论

Moyal和Wick-Voros平面上的扭曲量子场的不等价性

Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent

Moyal平面和Wick-Voros平面A^{M，V}_θ是 *-同构的。在每一个平面上的庞加莱群作为一个霍普夫代数对称，如果它的余积被扭曲因子变形。证明了T：A^M_θ到A^V_θ的 *-同构也不映射Poincaré群代数的相应twists.因此，在这些具有扭曲庞加莱-霍普夫对称性的平面上的量子场论是不等价的。我们明确验证了这一结果表明，一个非平凡的依赖于非对易参数是存在的威克-沃洛斯平面的自能图，而它是已知的缺席Moyal平面（在没有规范场）。我们的结果不同于（arXiv：0810.2095 [hep-th]）的结果，这是因为量子场论的处理方法不同。

Thermal effective potential in two- and three- dimensional non-commutative spaces

Thermal correlation functions and the associated effective statistical potential are computed in two- and three-dimensional non-commutative space using an operator formulation that makes no reference to a star product. The corresponding results for the Moyal and Voros star products are then easily obtained by taking the corresponding overlap with Moyal and Voros bases. The forms of the correlation function and the effective potential are found to be the same, except that in the Voros case the thermal length undergoes a non-commutative deformation, ensuring that it has a lower bound of the orde…

Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros

In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is of physical importance. Thus it is well known that the commutation relations among spacetime coordinates, which define a noncommutative spacetime, do not constrain the deformation induced on the algebra of functions uniquely. Such deformations are all mathematically equivalent in a very precise sense. Here we show how this freedom at the level of deformations of the algebra of functions can …

Moyal平面是谱三元组

Moyal Planes are Spectral Triples

公理nonunital谱三元组，扩展那些在单位的情况下，Connes，提出。作为一个指导，并由于其在非对易量子场论的重要性，空间$\R^{2N}$赋予Moyal产品进行了深入的研究。给出了这些非对易超平面的一些物理应用，如非对易Wick单项式的构造和Connes-Lott泛函作用量的计算。

Voros product and the Pauli principle at low energies

Using the Voros star product, we investigate the status of the two particle correlation function to study the possible extent to which the previously proposed violation of the Pauli principle may impact at low energies. The results show interesting features which are not present in the computations made using the Moyal star product.

扭曲Poincare对称性综述

Review of Twisted Poincare Symmetry

本文综述了Moyal平面上扭曲Poincare协变量子场的构造与应用，将Drinfeld twist用于量子引力的geons，通过CMB各向异性限制时空非交换性，并探讨了Moyal与Voros量子场的差异及泛函积分的反射正定性问题。

Matrix Bases for Star Products: a Review

We review the matrix bases for a family of noncommutative $\star$ products based on a Weyl map. These products include the Moyal product, as well as the Wick-Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for field theory, fuzzy spaces and emergent gravity.

Non-commutative Field Theory, Translational Invariant Products and Ultraviolet/Infrared Mixing

We review the Moyal and Wick-Voros products, and more in general the translation invariant non-commutative products, and apply them to classical and quantum field theory. We investigate phi^4 field theories calculating their Green's functions up to one-loop for the two- and four-point cases. We also review the connections of these theories with Drinfeld twists.

Curing the UV/IR mixing for field theories with translation-invariant $\star$ products

The ultraviolet/infrared (UV/IR) mixing of noncommutative field theories has been recently shown to be a generic feature of translation- invariant associative products. In this paper we propose to take into account the quantum corrections of the model to modify in this way the noncommutative action. This idea was already used to cure the UV/IR mixing for theories on Moyal space. We show that in the present framework also, this proposal proves successful for curing the mixing. We achieve this task by explicit calculations of one and higher loops Feynman amplitudes. For the sake of completeness,…

Covariant Quantum Fields on Noncommutative Spacetimes

A spinless covariant field $ϕ$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,Λ)ϕ(x)U(a,Λ)^{-1}=ϕ(Λx+a)$ where $(a,Λ)$ is an element of the Poincaré group $\Pg$ and $U:(a,Λ)\to U(a,Λ)$ is its unitary representation on quantum vector states. It expresses the fact that Poincaré transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincaré transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covaria…

Noncommutative deformations of quantum field theories, locality, and causality

We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the basic structural features of the vacuum expectation values of star-modified products of fields and field commutators. As an alternative to microcausality, we introduce a notion of $θ$-locality, where $θ$ is the noncommutativity parameter. We also analyze the conditions for the convergence and continuity of star products and define the function algebra that …

Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology

In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories on Moyal and Wick-Voros planes; the duality between deformations of the multiplication map on the algebra of functions on spacetime $\mathscr{F}(\mathbb{R}^4)$ and coproduct deformations of the Poincaré-…

Causal Poisson bracket via deformation quantization

Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced star-product is naturally related to the standard Moyal product through an appropriate causal Green's functions connecting points in the space of classical solutions to the equations of motion. Our results resemble the Peierls-DeWitt bracket analyzed in the multisymplectic context. Once our star-product is defined we are able to apply the Wigner-Weyl map in order to in…