Related papers: Unitarity Bound of the Wave Function Renormalizati…
In Quantum Field Theory models of electro-weak interactions with spontaneously broken gauge invariance, renormalizability limits to four the degree of the Higgs potential, whose minima determine the possible vacuum states in tree…
We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has…
The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective the renormalization prescriptions not only imply the renormalization of the couplings of the theory in…
A plausible physical interpretation of the renormalizability condition is given. It is shown that renormalizable quantum field theories describe such systems wherein the tendency to collapse associated with vacuum fluctuations of attractive…
We construct an ultraviolet-complete, local, and unitary quantum field theory in 2+1 dimensions that exhibits spontaneous breaking of space-time parity, persisting to arbitrarily high temperatures. The theory is defined by a renormalization…
The Wilsonian renormalization group (WRG) equation is used to derive a new class of scale invariant field theories with nonvanishing anomalous dimensions in 2-dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. When the…
In this paper, we develop a wave function renormalization scheme for models of non-relativistic quantum particles interacting with a quantized relativistic field, in the Hamiltonian formalism of quantum field theory. We construct the…
The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function…
Through introducing a notion of renormalization of particle-number density, a simple perturbation scheme of nonequilibrium quantum-field theory is proposed. In terms of the renormalized particle-distribution functions, which characterize…
The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a…
We set up a bootstrap problem for renormalization. Working in the massless four-dimensional O$(N)$ model and the $\lambda \phi^4$ theory, we prove that unitarity leads to all-loop recursion relations between coefficients of scattering…
We discuss the field independent additive constant in Wilson actions carefully within the exact renormalization group formalism. The additive constant does not affect the correlation functions of fields normalized by the partition function,…
The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. Generically for the conformal sector, complete…
We discuss the quantum mechanics of a particle restricted to the half-line $x > 0$ with potential energy $V = \alpha/x^2$ for $-1/4 < \alpha < 0$. It is known that two scale-invariant theories may be defined. By regularizing the near-origin…
The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance.…
The Wilsonian renormalization group properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. If couplings are chosen so that the quantum field theory exists on…
In this paper we introduce a perturbatively super-renormalizable and unitary theory of quantum gravity in any dimension D. The theory presents two entire functions, a.k.a. "form factors", and a finite number of local operators required by…
We consider the general supersymmetric one-dimensional quantum system with boundary, critical in the bulk but not at the boundary. The renormalization group flow on the space of boundary conditions is generated by the boundary beta…
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…
Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree…