Related papers: Effective Theory for the non-relativistic three-bo…
We survey finite energy inverse results in N-body scattering, and we also sketch the proof of the extension of our recent two-cluster to two-cluster three-body result to the many-body case: this requires only minor modifications. We also…
The functional renormalisation group is applied to the effective action for scattering of two nonrelativistic fermions. The resulting physical effective action is shown to contain the correct threshold singularity. The corresponding "bare"…
While second-order phase transitions always cause strong non-local fluctuations, their effect on spectral properties crucially depends on the dimensionality. For the important case of three dimensions, we show that the electron self-energy…
We discuss shallow resonances in the nonrelativistic scattering of two particles using an effective field theory (EFT) that includes an auxiliary field with the quantum numbers of the resonance. We construct the manifestly renormalized…
Starting from a relativistic s-wave scattering length model for the two particle input we construct an unambiguous, unitary solution of the relativistic three body problem given only the masses $m_a,m_b,m_c$ and the masses of the two body…
We discuss the power counting for effective field theories with narrow resonances near a two-body threshold. Close to threshold, the effective field theory is perturbative and only one combination of coupling constants is fine-tuned. In the…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
Both the three-body system and the inverse square potential carry a special significance in the study of renormalization group limit cycles. In this work, we pursue an exploratory approach and address the question which two-body…
Renormalization group (RG) invariance implies that the predictions of effective field theory are independent of the momentum cutoffs introduced during regularization. Here we report the first systematic verification of RG invariance for…
Effective field theory requires all observables to be independent of the representation used for the quantum field operators. It means that off-shell properties of the interactions should not lead to any observable effects. We analyse this…
We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed…
The Lorentz symmetry group entails physical equations whose solutions are retarded. This leads to the concept of a relativistic engine resulting from retardation of electromagnetic fields. We have shown that Newton'n third law cannot…
I summarise a method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories which are non-perturbative at leading order. It uses the fact that the Renormalisation Group evolution of an observable…
We propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle is in an orbit exterior to the one of the…
The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…
Cutoff independence is an essential requirement for the predictive power of nuclear \textit{ab initio} calculations based on effective field theory (EFT). While it is conventionally assumed that such invariance necessitates high-order…
Effective field theories have established themselves as key pillars of modern nuclear physics. They enable a quantitative understanding of the strong nuclear force, provided low-energy constants that parametrize short-distance physics can…
The low-energy scattering of two charged particles is analyzed using a renormalization group approach based on dimensional regularization with power-divergence subtraction. A nontrivial solution with a marginally unstable direction is…
Low momentum two-nucleon interactions obtained with the renormalization group method and the similarity renormalization group method are used to study the cutoff dependence of low energy 3N and 4N scattering observables. The residual cutoff…
The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3->3 scattering amplitude for spinless particles, which contains an…