Related papers: Implementing the three-neutron quantization condit…
We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of $\pi^+$…
We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization…
Lattice quantum chromodynamics (QCD) will soon become the primary theoretical tool in rigorous studies of single- and multi-hadron sectors of QCD. It is truly ab initio meaning that its only parameters are those of standard model. The…
As is well-known, for plasmas of high density and modest temperature, the classical kinetic theory needs to be extended. Such extensions can be based on the Schr\"odinger Hamiltonian, applying a Wigner transform of the density matrix, in…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the…
We examine the L\"uscher quantization condition to high order for the scattering of a spinless particle and a spin-1/2 particle in a periodic box. First, we derive the quantization conditions in a non-relativistic framework up to total…
We consider several subtle aspects of the theory of neutrino oscillations which have been under discussion recently. We show that the $S$-matrix formalism of quantum field theory can adequately describe neutrino oscillations if correct…
We consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless. Examples include $\pi^+\pi^+ K^+$ and $K^+K^+\pi^+$. We derive the formalism necessary to extract two- and…
There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…
A recently developed formulation for treating two- and three-nucleon bound states in a three-dimensional formulation based on spin-momentum operators is extended to nucleon-nucleon scattering. Here the nucleon-nucleon t-matrix is…
Strong interactions produce a rich spectrum of resonances that decay into three or more hadrons. Understanding their phenomenology requires a theoretical framework to extract parameters fromexperimental data and Lattice QCD simulations of…
An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and…
Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed L\"uscher's formula for extracting these quantities at lowest order. As the…
We derive self-consistent constraint conditions for collision terms in quantum kinetic theory using the Wigner function formalism. We present specific solutions for these collision terms that align with the constraints. we develop quantum…
We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum.…
We determine the quantization condition for the energy levels of two interacting particles in a finite box in a ``moving frame'', i.e. one in which the total momentum of pions is non-zero. This condition is valid up to corrections which…
Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses would start a new age of ab initio predictions in nuclear physics. Performed on a finite grid, such calculations demand extrapolation of their…
The relativistic approach to electroweak properties of two-particle composite systems developed in previous work is generalized here to the case of nonzero spin. This approach is based on the use of the instant form of relativistic…
We incorporate non-zero lattice-spacing effects into L\"uscher's finite-volume scattering formalism. The new quantization condition takes lattice energies as input and returns a version of the discretized scattering amplitude whose…