相关论文: Scaled Affine Quantization of $\varphi^4_4$ in the…

We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function at small values of the bare coupling…

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…

Realizations of scale invariance are studied in the context of a gravitational theory where the action (in the first order formalism) is of the form $S = \int L_{1} \Phi d^{4}x$ + $\int L_{2}\sqrt{-g}d^{4}x$ where $\Phi$ is a density built…

The renormalization of the two dimensional light-front quantized $\phi^{4}$ theory is discussed. The mass renormalization condition and the renormalized constraint equation are shown to contain all the information to describe the phase…

In this work we consider the 1-component real scalar $\phi^4$ theory in 4 space-time dimensions on the lattice and investigate the finite size scaling of thermodynamic quantities to study whether the thermodynamic limit is attained. The…

Interacting quantum scalar field theories in $dS_D\times M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the…

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…

The differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be based entirely on inductively bounding their…

I present a sequence of non-perturbative approximate solutions for scalar $\phi^4$ theory for arbitrary interaction strength, which contains, but allows to systematically improve on, the familiar mean-field approximation. This sequence of…

Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…

We construct a consistent quantum field theory of a dimensionally reduced self-interacting scalar field. The Kaluza-Klein dimensional reduction on the well-known $\Phi^{4}$ scalar theory, on a certain $(4+n)$ spacetime with an arbitrary…

We discuss a D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d<D. We show that the interacting quantum fields have more regular…

We review and elaborate on some aspects of the classically scale-invariant renormalizable 4-derivative scalar theory $L= \phi\, \partial^4 \phi + g (\partial \phi)^4$. Similar models appear, e.g., in the context of conformal supergravity or…

Traditionally, scalar $\phi^4$ theory in four dimensions is thought to be quantum trivial in the continuum. This tradition is apparently well grounded both in physics arguments and mathematical proofs. Digging into the proofs one finds that…

The quantization of noncommutative scalar field theory is studied from the matrix model point of view, exhibiting the significance of the eigenvalue distribution. This provides a new framework to study renormalization, and predicts a phase…

The issue of the existence and possible triviality of the Euclidean quantum scalar field in dimension 4 is investigated by using some large deviations techniques. As usual, the field $\varphi_{d}^{4}$ is obtained as a limit of regularized…

The four dimensional critical scalar theory at equilibrium with a thermal bath at temperature $T$ is considered. The thermal equilibrium state is labeled by $n$ the winding number of the vacua around the compact imaginary-time direction…

In 1970s, Wilson shown the deep connection of renormalization and scaling of the effective Lagrangian. Polchinski further proved that such connection implied renormalizability of perturbative field theory. We develop the mechanism by an…

Scalar fields coupled to gravity via $\xi R {\Phi}^2$ in arbitrary Friedmann-Robertson-Walker backgrounds can be represented by an effective flat space field theory. We derive an expression for the scalar energy density where the effective…

The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…