Related papers: Gaussian-Perturbative Calculations with a Homogene…
Basing on new regularization-renormalization method, the $\lambda\phi^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is…
We consider $\phi^4$ theory with $\phi(x)\in\mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\hat{\lambda}$ the (negative) critical bare mass $\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$ where the…
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We re-examine some technical aspects of the subtractive renormalization, in particular, the mass…
There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the…
We obtain the renormalized equations of motion for matter and semi-classical gravity in an inhomogeneous space-time. We use the functional Schrodinger picture and a simple Gaussian approximation to analyze the time evolution of the…
Very recently, the Large Hadron Collider was turned on. There, the experiments are aiming to test different scenarios for elementary particles interactions from SUSY, Extra dimensions to others. In fact, SUSY was invented to kill the…
We give a general $SU(2)_L\times SU(2)_R$ $\times U(1)_{EM}$ sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking, and present the general formulation of the model. It is found that $\sigma $ and…
Using a four fermion interaction Lagrangian, we demonstrate that the spontaneous breaking of vector symmetries requires the existence of a light (comparing with the heavy fermion mass) scalar particle and the low energy effective theory…
We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $\phi^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the…
The Standard Model (SM) is usually considered to be unnatural because the scalar Higgs mass receives a quadratic divergent correction. We suggest a new way to solve the naturalness problem from point of view of renormalization group method.…
The Euclidean $(\phi^{4})_{3,\epsilon$ model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le…
We argue that massless (lambda Phi^4)_4 is "trivial" without being entirely trivial. It has a non-trivial effective potential which leads to spontaneous symmetry breaking, but the particle excitations above the broken vacuum are…
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…
Given a square box $\Lambda_n\subseteq\mathbb Z^2$ of side length $L^n$ with $L,n>1$, we study hierarchical random fields $\{\phi_x\colon x\in\Lambda_n\}$ with law proportional to ${\rm…
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…
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…
A non-perturbative effective model is derived for the Higgs sector of the standard model, described by a simple scalar theory. The renormalized couplings are determined by the derivatives of the Gaussian Effective Potential that are known…
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…
The non-perturbative autonomous renormalization of the scalar $\Phi^4$-model is applied in the framework of stochastic quantization. I show that this requires a selective, momentum-dependent renormalization of the Onsager coefficient…
The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…