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The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
A perturbative approach for non renormalizable theories is developed. It is shown that the introduction of an extra expansion parameter allows one to get rid of divergences and express physical quantities as series with finite coefficients.…
I review some open questions relating to the large transverse momentum divergences in transverse moments of transverse momentum dependent (TMD) parton correlation func- tions. I also explain, in an abbreviated and summarized form, recent…
I review recent results on conformal field theories in four dimensions and quantum field theories interpolating between conformal fixed points, supersymmetric and non-supersymmetric. The talk is structured in three parts: i) central…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
On the perturbatively non-renormalizable and non-perturbatively finite examples (delta-function type potential in non-relativistic quantum mechanics and the mathematical model of the propagator by Redmond and Uretsky in quantum field…
We study the mixing of operators under renormalization group flow in quantum theories, and prove a non-renormalization theorem at non-linear order. It dictates zeros up to a certain number of loops in anomalous dimension tensors that…
The recent formulation of the factorization theorem for transverse momentum spectra in terms of well-defined transverse momentum dependent distributions (TMDs), allows for a better understanding of the role of the perturbative and…
A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and…
We discuss the importance of using partially quenched theories with three degenerate quarks for extrapolating to QCD, and present some relevant results from chiral perturbation theory.
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional scalar theories. It is based on 1/N-expansion and results in a logarithmically divergent perturbation theory in…
Single-spin asymmetries were long thought to vanish in high-energy scattering processes because of their specific time-reversal behavior. Time-reversal-odd phenomena, however, appear naturally when one includes effects of intrinsic…
We discuss the renormalization properties of noncommutative non-gauge supersymmetric field theories.
We review the history of non-renormalisation theorems in global supersymmetry, as well as their importance in all attempts to apply supersymmetry to the real world.
A short survey of the renormalization problem in QCD and its non-perturbative solution by means of numerical simulations on the lattice is given. Most emphasis is on scale dependent renormalizations, which can be reliably addressed via a…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
We show that a non-wandering endomorphism of the torus with invertible linear part without invariant directions and for which the critical points are in some sense generic is transitive. This improves a result of Andersson by allowing…
The rapidity anomalous dimension controls the scaling of transverse momentum dependent observables in the Sudakov region. In a conformal theory it is equivalent to the soft anomalous dimension, but in QCD this relation is broken by…
We study non-linear phenomena in quantum dots. Non linearities are reflected in the I-V characteristic curve as bistabilities, instabilities and time dependent oscillations of the currents. The nature of the non-linear behavior depends upon…
Abelian quiver gauge theories provide nonsupersymmetric candidates for the conformality approach to physics beyond the standard model. Written as ${\cal N}=0$, $U(N)^n$ gauge theories, however, they have mixed $U(1)_p U(1)_q^2$ and $U(1)_p…