Related papers: Kurt Symanzik - a stable fixed point beyond trivia…
We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic $\psi^4_d$ model in $d=1,2,3$ with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the…
A general framework of non-perturbative quantum field theory on a curved background is presented. A quantum field theory is in this setting characterised by an embedding of a space of field configurations into a Hilbert space over…
A mathematically rigorous relativistic quantum Yang-Mills theory with an arbitrary semisimple compact gauge Lie group is set up in the Hamiltonian canonical formalism. The theory is non-perturbative, without cut-offs, and agrees with the…
For an anisotropic euclidean $\phi^4$-theory with two interactions $[u (\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4]$ the $\beta$-functions are calculated from five-loop perturbation expansions in $d=4-\varepsilon$ dimensions, using…
The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. All presently known…
We investigate some issues concerning the zero-momentum four-point renormalized coupling constant g in the symmetric phase of O(N) models, and the corresponding Callan-Symanzik beta-function. In the framework of the 1/N expansion we show…
We consider a classical equation known as the $\phi^4$ model in one space dimension. The kink, defined by $H(x)=\tanh(x/{\sqrt{2}})$, is an explicit stationary solution of this model. From a result of Henry, Perez and Wreszinski it is known…
A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…
Quantum long-range models at zero temperature can be described by fractional Lifshitz field theories, that is, anisotropic models whose actions are short-range in time and long-range in space. In this paper we study the renormalization of…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
Horndeski gravity is a popular contender for a phenomenological model of dynamical dark energy, and as such subject to observational constraints. In this work, we ask whether Horndeski gravity can be more than a phenomenological model and…
The Phi4 theory in 4-epsilon dimensions has two fixed points, which coincide in the limit epsilon->0. One is a Gaussian UV fixed point, and the other a non-trivial IR fixed point. They lead to two different continuum field theories. The…
The classic composite fermion field theory (Ref. 1) builds up an excellent framework to uniformly study important physical objects and globally explain anomalous experimental phenomena in fractional quantum Hall physics while there are also…
We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical critical exponent. This model is different from the one introduced in [Hartmann et al., SciPost…
Few natural basic principles allow to extend Feynman integral over the paths to an integral over the surfaces so, that they coincide at long time scale, that is when the surface degenerates into a single particle world line. In the first…
We discuss the approach to asymptotic dynamics due to Kulish and Faddeev. We show that there are problems in applying this method to theories with four point interactions. The source of the difficulties is identified and a more general…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
In Weinberg's asymptotic safety approach, a finite dimensional critical surface for a UV stable fixed point generates a theory of quantum gravity with a finite number of physical parameters. We argue that, in an extension of Feynman's…
The strong evidence for the `triviality' of (lambda Phi^4)_4 theory is not incompatible with spontaneous symmetry breaking. Indeed, for a `trivial' theory the effective potential should be given exactly by the classical potential plus the…
The spontaneous symmetry breaking in (1+1)-dimensional $\phi^{4}$ theory is studied with discretized light-front quantization, that is, by solving the zero-mode constraint equation. The symmetric ordering is assumed for the operator-valued…