Related papers: Quantum Structure of Field Theory and Standard Mod…
We introduce tropical scalar field theory as a model for renormalizable quantum field theory, and examine in detail the case of quartic self-interaction and internal $O(N)$ symmetry. This model arises in a formally zero-dimensional limit of…
We investigate the entanglement structure of the continuous multi-scale entanglement renormalization ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett., 110, 100402 (2013)] for ground states of quantum field theories (QFTs). The cMERA,…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
We demonstrate our simple strategy for renormalization with QED at one-loop level, basing on an elaboration of the effective field theory philosophy. No artificial regularization or deformation of the original theory is introduced here and…
We present an improved action for Pionless Effective Field Theory (EFT). Previous formulations of renormalizable nuclear EFTs have encountered instabilities in systems with more than four nucleons. We resolve this issue by introducing a…
Lattice regularizations are pivotal in the non-perturbative quantization of gauge field theories. Wilson's proposal to employ group-valued link fields simplifies the regularization of gauge fields in principal fiber bundles, preserving…
The local limit of a quantum field theory on the loop space is studied. It is proved that the invariance of the theory with respect to the group of diffeomorphisms leads to Feynman diagrams convergence in the local limit.
Standard perturbation theory (SPT) for large-scale matter inhomogeneities is unsatisfactory for at least three reasons: there is no clear expansion parameter since the density contrast is not small on all scales; it does not fully account…
Following a Four Dimensional Renormalization approach to ultraviolet divergences (FDR), we extend the concept of predictivity to non-renormalizable quantum field theories at arbitrarily large perturbative orders. The idea of topological…
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
Radiative corrections in quantum field theories with small departures from Lorentz symmetry alter structural aspects of the theory, in particular the definition of asymptotic single-particle states. Specifically, the mass-shell condition,…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams…
Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
The main difficulty of quantum field theory is the problem of divergences and renormalization. However, realistic models of quantum field theory are renormalized within the perturbative framework only. It is important to investigate…
In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation techniques applied to families of CQFT's labelled by finite…
I suggest that the current situation in quantum field theory (QFT) provides some reason to question the universal validity of ontological reductionism. I argue that the renormalization group flow is reversible except at fixed points, which…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…