Related papers: A massless quantum field theory over the p-adics
The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner's little group) of the Poincar\'{e} group is re-examined in the massless…
We discuss some properties of noncommutative supersymmetric field theories which do not involve gauge fields. We concentrate on the renormalizability issue of these theories.
We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann-Hilbert problem. Given a loop $\gamma(z), | z |=1$ of elements…
We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The…
I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.
We derive several results concerning non-perturbative renormalization in the spherical field formalism. Using a small set of local counterterms, we are able to remove all ultraviolet divergences in a manner such that the renormalized theory…
We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…
In a recent work arXiv:2008.08601, Halverson, Maiti and Stoner proposed a description of neural networks in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory, while finite $N$ corrections…
These lectures review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of every advanced course on quantum field theory, for effective…
We showed in part I (hep-th/9912092) that the Hopf algebra ${\cal H}$ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group $G$ and that the renormalized theory is obtained from the…
We review here the parametric representation of Feynman amplitudes of renormalizable non-commutative quantum field models.
The aim of this thesis is to analyze part of the results presented by R.E. Borcherds in his article on renormalization and quantum field theories. To facilitate this, the first chapter presents the basic facts on category theory, sheaf…
The usual renormalization procedure for the variational approximation with a trial Gaussian ansatz for the $\lap$ model in 3+1 dimensions is re-analysed as a departing framework for the investigation of the parameters of the model. The…
This is a report of a talk given at the Oberwolfach workshop on "cohomology of finite groups: Interactions and applications" which was held during July 25th - July 31st, 2010. It is an announcement of some of the results (with motivation)…
We discuss here phase transitions in quantum field theory in the context of vacuum realignment through an explicit construction. Vacuum destabilisation may occur through a scalar attaining a nonzero expectation value, or through a…
This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in…
We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.