相关论文: The Non-Commutative \lambda \phi^{4} Model
Noncommutative spacetimes lead to nonlocal quantum field theories (qft's) where spin-statistics theorems cannot be proved. For this reason, and also backed by detailed arguments, it has been suggested that they get corrected on such…
We study numerically classical collisions of waves in $\lambda\phi^4$ theory. These processes correspond to multiparticle scattering in the semiclassical regime. Parametrizing initial and final wavepackets by energy $E$ and particle numbers…
In this note we investigate a new type of non-commutative field theory based on a constant skew-symmetric three-form parameter. In 3+1 dimensions such a three-form parameter can be viewed as a short-distance regulator which nevertheless…
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
We propose a new non-perturbative technique for calculating the field-theory S-matrix directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert…
Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
We consider the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a foliation of $\mathbb{R}^3$ into fuzzy spheres. We first review the construction of a natural matrix…
We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a…
A redesigned starting point for covariant \phi^4_n, n\ge 4, models is suggested that takes the form of an alternative lattice action and which may have the virtue of leading to a nontrivial quantum field theory in the continuum limit. The…
We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar field theory…
We study the Separability of the noncommutative (NC) space coordinate degrees of freedom with the generalized Peres-Horodecki separability criterion (Simon's condition) for a bipartite Gaussian state. Non-symplectic nature of the…
The time-convolutionless master equation provides a general framework to model non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative…
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…
The two parameter model is reduced to a one parameter model by using simple transformations. Because the separation between different phase regions for a one parameter model is just a point, the equivalence between the two models leads to…
We study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field…
The polarized Gowdy ${\bf T}^3$ vacuum spacetimes are characterized, modulo gauge, by a ``point particle'' degree of freedom and a function $\phi$ that satisfies a linear field equation and a non-linear constraint. The quantum Gowdy model…
We consider a generalised non-commutative space-time in which non-commutativity is extended to all phase space variables. If strong enough, non-commutativity can affect stability of the system. We perform stability analysis on a couple of…
Noncommutative phase space of an arbitrary dimension is considered. The both of operators coordinates and momenta in noncommutative phase space may be noncommutative. In this paper, we introduce momentum-momentum noncommutativity in…
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…