Related papers: The $\Phi^3_4$ and $\Phi^3_6$ matricial QFT models…

We apply a recently developed method to exactly solve the $\Phi^3$ matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a…

In previous work we have shown that the (\theta->\infty)-limit of \phi^4_4-quantum field theory on noncommutative Moyal space is an exactly solvable matrix model. In this paper we translate these results to position space. We show that the…

We review our recent construction of the $\phi^4$-model on four-dimensional Moyal space. A milestone is the exact solution of the quartic matrix model $Z[E,J]=\int d\Phi \exp(tr(J\Phi- E\Phi^2 -(\lambda/4) \Phi^4))$ in terms of the solution…

We consider the quartic analogue of the Kontsevich model, which is defined by a measure $\exp(-{N}\,\mathrm{Tr}(E\Phi^2+(\lambda/4)\Phi^4)) d\Phi$ on Hermitian ${N}\times{N}$-matrices, where $E$ is any positive matrix and $\lambda$ a…

We provide further analytical and first numerical results on the solvable $\lambda\phi^4_4$-NCQFT model. We prove that for $\lambda<0$ the singular integral equation has a unique solution, whereas for $\lambda>0$ there is considerable…

Previously the exact solution of the planar sector of the self-dual $\Phi^4$-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant…

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling…

There is a matrix model corresponding to a scalar field theory called Grosse-Wulkenhaar model, which is renormalizable by adding a harmonic oscillator potential to scalar $\Phi^{4}$ theory on Moyal spaces. There are more unknowns in…

Theories with generalised conformal structure contain a dimensionful parameter, which appears as an overall multiplicative factor in the action. Examples of such theories are gauge theories coupled to massless scalars and fermions with…

We study the quantization of the noncommutative selfdual \phi^3 model in 4 dimensions, by mapping it to a Kontsevich model. The model is shown to be renormalizable, provided one additional counterterm is included compared to the…

We study the noncommutative \phi^4_4-quantum field theory at the self-duality point. This model is renormalisable to all orders as shown in earlier work of us and does not have a Landau ghost problem. Using the Ward identity of Disertori,…

As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…

The regularisation of the $\lambda\phi^4_4$-model on noncommutative Moyal space gives rise to a solvable QFT model in which all correlation functions are expressed in terms of the solution of a fixed point problem. We prove that the…

We study a quartic matrix model with partition function $Z=\int d\ M\exp{\rm Tr}\ (-\Delta M^2-\frac{\lambda}{4}M^4)$. The integral is over the space of Hermitian $(\Lambda+1)\times(\Lambda+1)$ matrices, the matrix $\Delta$, which is not a…

The quaternion Fourier transform (QFT), a generalization of the classical 2D Fourier transform, plays an increasingly active role in particular signal and colour image processing. There tends to be an inordinate degree of interest placed on…

We study various correlation functions (two and three point functions) in a large $N$ matrix model of six commuting matrices with a numerical Monte Carlo algorithm. This is equivalent to a model of a gas of particles in six dimensions with…

A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. Discrete sampling and bisection algorithm are applied for finding numerical…

This is a sequel to [SIGMA 9 (2013), 007, 23 pages, arXiv:1210.1177], in which there is a construction of a $2\times2$ positive-definite matrix function $K (x)$ on $\mathbb{R}^{2}$. The entries of $K(x)$ are expressed in terms of…

We study real-time holographic four point Wightman functions involving scalars, photons, gluons and gravitons in the Poincare patch of AdS$_4$. We show that when the momenta of the middle two operators are spacelike, four-point exchange…

We find the exact solutions of the $\Phi_{2}^{3}$ finite matrix model (Grosse-Wulkenhaar model). In the $\Phi_{2}^{3}$ finite matrix model, multipoint correlation functions are expressed as $G_{|a_{1}^{1}\ldots…