Related papers: Nontrivial Quantization of $\phi^4_n$, $n\ge2$
We give a perturbative quantization of space-time $R^4$ in the case where the commutators $C^{{\mu}{\nu}}=[X^{\mu},X^{\nu}]$ of the underlying algebra generators are not central . We argue that this kind of quantum space-times can be used…
We renormalize models with scalar chiral superfields with an odd superpotential to several orders in perturbation theory. These extensions of the cubic Wess-Zumino model are renormalizable in spacetime dimensions which are rational. When…
The autonomous renormalization of the O(N)-symmetric scalar theory is based on an infinite re-scaling of constant fields, whereas finite-momentum modes remain finite. The natural framework for a detailed analysis of this method is a system…
In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable $\phi^4_4$ quantum field theory on the Moyal non commutative ${\mathbb R^4}$ space. This…
Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking…
We announce results about the nonperturbative mathematically rigorous construction of the $:\!\phi^4_4\!:$ quantum field theory in four-dimensional space-time. The complex structure of solutions of the classical nonlinear (real-valued) wave…
Standard quantization using, for example, path integration of field theory models, includes paths of momentum and field reach infinity in the Hamiltonian density, while the Hamiltonian itself remains finite. That fact causes considerable…
We study a renormalized coupling g and mass m in four dimensional phi^4 theory on tori with finite size z=mL. Precise numerical values close to the continuum limit are reported for z=1,2,4, based on Monte Carlo simulations performed in the…
We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner…
Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the…
Mass- and wave-function renormalization is calculated to order $p^4$ in heavy baryon chiral perturbation theory. Two different schemes used in the literature are considered. Several technical issues like field redefinitions,…
Certain higher dimensional operators of the lagrangian may render the vacuum inhomogeneous. A rather rich phase structure of the phi4 scalar model in four dimensions is presented by means of the mean-field approximation. One finds para-…
We give a conjectural way for computing the $S$-matrix and the correlation functions in quantum field theory beyond perturbation theory. The basic idea seems universal and naively simple: to compute the physical quantities one should…
We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle, up to four derivatives in the chiral expansion. The complete off-shell renormalization procedure is implemented, including one…
In recent papers it has been observed that non-Hermitian Hamiltonians, such as those describing $ig\phi^3$ and $-g\phi^4$ field theories, still possess real positive spectra so long as the weaker condition of ${\cal PT}$ symmetry holds.…
Non-commutative Euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is established using regularizations of R^{2n}_\theta…
We consider the O(N)-symmetric phi4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the phi4 continuum theory. The required nonperturbative information is obtained by resumming…
In this paper, we give a rigorous proof of the renormalizability of the massive $\phi_4^4$ theory on a half-space, using the renormalization group flow equations. We find that five counter-terms are needed to make the theory finite, namely…
The simplest non commutative renormalizable field theory, the $\phi_4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V.…
We address the question of whether the quantum scale-invariant theories introduced in [1] are renormalizable or play the role of effective field theories that are valid below the Planck scale $M_P$. We show that starting from two-loop level…