相关论文: Hamiltonian Renormalization III. Renormalisation F…
In the companion paper we motivated a renormalisation flow on Osterwalder-Schrader data (OS-data) consisting of 1. a Hilbert space, 2. a cyclic vacuum and 3. a Hamiltonian annihilating that vacuum. As the name suggests, the motivation was…
In this article we extend the test of Hamiltonian Renormalisation proposed in this series of articles to the D-dimensional case using a massive free scalar field. The concepts we introduce are explicitly computed for the D=2 case but…
In previous works in this series we focussed on Hamiltonian renormalisation of free field theories in all spacetime dimensions or interacting theories in spacetime dimensions lower than four. In this paper we address the Hamiltonian…
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
Hamiltonian Renormalisation, as defined within this series of works, was derived from covariant Wilson renormalisation via Osterwalder-Schrader reconstruction. As such it directly applies to QFT with a true (physical) Hamiltonian bounded…
We investigate the renormalization group flow of a gravity--matter system in which a scalar field is minimally coupled to Einstein gravity and its kinetic term is given by a scale-dependent form factor $f_\Lambda(-\Box)$. Employing the…
A possible avenue towards a non-perturbative Quantum Field Theory (QFT) on Minkowski space is the constructive approach which employs the Euclidian path integral formulation, in the presence of both ultraviolet (UV) and infrared (IR)…
A general framework is presented for the renormalization of Hamiltonians via a similarity transformation. Divergences in the similarity flow equations may be handled with dimensional regularization in this approach, and the resulting…
Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and…
We construct novel conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use Wilsonian renormalization group equation method to find the fixed points.…
Using the local potential approximation of the exact renormalization group (RG) equation, we show the various domains of values of the parameters of the O(1)-symmetric scalar Hamiltonian. In three dimensions, in addition to the usual…
We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are…
The Hamiltonian renormalisation programme motivated by constructive QFT and Osterwalder-Schrader reconstruction which was recently launched for bosonic field theories is extended to fermions. As fermion quantisation is not in terms of…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a…
We develop a novel approach to the Wilsonian renormalisation of Hamiltonians for 2-dimensional quantum field theories on the cylinder described in the UV by marginally relevant deformations of conformal field theories. To introduce a…
We construct a qubit regularization of the $O(3)$ non-linear sigma model in two and three spatial dimensions using a quantum Hamiltonian with two qubits per lattice site. Using a worldline formulation and worm algorithms, we show that in…
We construct supersymmetric conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use the Wilsonian renormalization group equation method, which is one of the…
A metric is introduced on the space of parameters (couplings) describing the large N limit of the O(N) model in Euclidean space. The geometry associated with this metric is analysed in the particular case of the infinite volume limit in 3…
We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson--Fisher fixed point. Arguing that the parameter…