Related papers: The Non-Commutative \lambda \phi^{4} Model
The renormalized trajectory of massless $\phi^4$-theory on four dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the…
We examine the nonequilibrium dynamics of a self-interacting $\lambda\phi^4$ scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and $O(\lambda^2)$, the effective equation of…
We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar $\phi^4$ model with an additional oscillator potential. This model is known to…
The quantum discrete $\phi ^4$ model at finite temperature is studied in the mean-field approximation. The phase diagrams are obtained for a wide range of the model parameters. The domains of applicability for the classical, quantum, and…
We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing…
During the '70, several relativistic quantum field theory models in $D=1+1$ and also in $D=2+1$ have been constructed in a non-perturbative way. That was done in the so-called {\it constructive quantum field theory} approach, whose main…
As argued previously, amplitudes of quantum field theories on noncommutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann--Low formula with time-ordering applied…
We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $\lambda\phi^4$ theory in $d=4-\epsilon$, we obtain the full spectrum of…
The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up the opportunity to investigate probabilistic machine learning within quantum field theory. Here, we will discuss…
We consider the massive vector $N$-component $(\lambda\phi^{4})_{D}$ theory in Euclidian space and, using an extended Matsubara formalism we perform a compactification on a $d$-dimensional subspace, $d\leq D$. This allows us to treat…
We apply the quartic exponential variational approximation to the symmetry breaking phenomena of scalar field in three and four dimensions. We calculate effective potential and effective action for the time-dependent system by separating…
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting…
We study the thermal phase transitions of a generic real scalar field, without a $Z_2$-symmetry, referred to variously as an inert, sterile or singlet scalar, or $\phi^3+\phi^4$ theory. Such a scalar field arises in a wide range of models,…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
In this paper we find non-trivial vacuum states for the renormalizable non-commutative $\phi^4$ model. An associated linear sigma model is then considered. We further investigate the corresponding spontaneous symmetry breaking.
In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al.. Here we extend it to certain noncommutative versions of the cylinder, $\mathbb{R}^{3}$ and…
We discuss the formulation of classical field theoretical models on $n$-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
For lambda phi^4 models, the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem. We show that…