Related papers: Causality, universality, and effective field theor…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
At long distances interactions between neutral ground state atoms can be described by the Van der Waals potential V(r) =-C6/r^6-C8/r^8 - ... . In the ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts given by an…
Renormalization ideas can profitably be exploited in conjunction with the superposition principle of boundary conditions in the description of model independent and universal scaling features of the singular and long range Van der Waals…
Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional…
Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angles scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and…
We investigate the potential energy curves of rare-gas dimers with various ranges and strengths of interparticle interactions (nuclear-electron, electron-electron, and nuclear-nuclear interactions). Our investigation is based on the highly…
Effective field theories exploit a separation of scales in physical systems in order to perform systematically improvable, model-independent calculations. They are ideally suited to describe universal aspects of a wide range of physical…
The late time response of vacuum black holes in General Relativity is notoriously governed by power law tails arising from the wave scattering off the curved spacetime geometry far from the black hole. While it is known that such tails are…
van der Waals interactions govern the physics of a plethora of molecular structures. It is well known that the leading term in the distance-based London expansion of the van der Waals energy for atomic and molecular dimers decays as…
In the ultra-cold regime Van der Waals forces between neutral atoms can be represented by short range effective interactions. We show that universal low energy scaling features of the underlying vdW long range force stemming from two photon…
Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional…
Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity…
Van der Waals forces as interactions between neutral and polarisable particles act at small distances between two objects. Their theoretical origin lies in the electromagnetic interaction between induced dipole moments caused by the vacuum…
The van der Waals interaction between two polarizable atoms is considered. In three dimensions the standard form with an attractive $1/|R|^6$ potential is obtained from second-order quantum perturbation theory. When the electron motion is…
We consider the system of three ${}^4$He atoms to assess whether a pure van der Waals potential can be used as a starting point for an effective field theory to describe three-body processes in ultracold atomic systems. Using a long-range…
We generalize Wigner's causality bounds and Bethe's integral formula for the effective range to arbitrary dimension and arbitrary angular momentum. Moreover, we discuss the impact of these constraints on the separation of low- and…
We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale…
It has been suggested that a certain class of UV-incomplete quantum field theories can avoid unitarity violation above the cut-off energy scale by forming classical configurations at a length scale much larger than the cut-off length. This…
Throughout this thesis, we investigate how effective field theories, combined with unitarization techniques, can be used to explore physics beyond the Standard Model, with particular emphasis on the dynamical origin of electroweak symmetry…
Particles that are heavy compared to the electroweak scale ($M \gg m_W$), and that are charged under electroweak SU(2) gauge interactions display universal properties such as a characteristic fine structure in the mass spectrum induced by…