Related papers: On 't Hooft's representation of the \beta-function
The perturbative $\beta$-function is known exactly in a number of supersymmetric theories and in the 't Hooft renormalization scheme in the $\phi_4^4$ model. It is shown how this allows one to compute the effective action exactly for…
We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't~Hooft's one-loop result. The method can also be used for theories with…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
The ambiguities inherent in renormalization are considered when using mass-independent renormalization in massless theories that involve two coupling coupling constants. We review how there is no renormalization scheme in which the…
Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa…
We show that even $\zeta$-functions may be removed from the $\beta$-functions of general multi-coupling theories up to high loop order by means of coupling redefinitions. For theories whose $\beta$-function is determined by the anomalous…
We show that even $\zeta$-functions may be removed from the $\beta$-functions of general multi-coupling theories up to high loop order by means of coupling redefinitions. For theories whose $\beta$-function is determined by the anomalous…
By construction, gauge theories require gauge fixing. In conventional approaches to spontaneously broken gauge theories, the choice of the Unitary ('t Hooft) gauge involves the sacrifice of manifest renormalizability (unitarity). It is…
We investigate a possibility of scale invariant but non-conformal supersymmetric field theories from a perturbative approach. The explicit existence of monotonically decreasing a-function that generates beta-functions as a gradient flow…
The possibility is discussed that existence of renormalon singularities is not the internal property of the specific field theory but depends on the renormalization scheme.
In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to…
In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model.…
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the…
In a series of recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the…
The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for…
We construct the field theory which describes the universal properties of the quasi-static isotropic depinning transition for interfaces and elastic periodic systems at zero temperature, taking properly into account the non-analytic form of…
The complete set of two-loop renormalization group equations in general gauge field theories is presented. This includes the \beta functions of parameters with and without a mass dimension.
We consider perturbation of a conformal field theory by a pair of relevant logarithmic operators and calculate the beta function up to two loops. We observe that the beta function can not be derived from a potential. Thus the…
In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we…
We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra…