We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim of this (...) program is to develop equations which explicitly depend upon physically observable input variables, and do not require “renormalization” or “dressing” of these parameters to connect them to the boundary states. As a unitary, cluster decomposible, multichannel theory, physical systems whose constituents are confined can be readily described. (shrink)

This paper develops the notion of being right-with, a conceptual lens that underscores what happens when individuals turn to human rights law and other legal processes and proceedings to address injustices by the state. It does this through a critical multi-directional reading of two Uganda High Court appeal cases that overturned the decision of a lower court which at first instance had convicted Dr Stella Nyanzi of the offences of cyber harassment and offensive communications. Being right-with is a regulative and (...) coercive idea within human rights law that animates a violent irrepressible police drive. I use being right-with to assert that when individuals make rights claims under human rights law (however radical those assertions might be), they are still imbricated within a mode of liberal humanist subjecthood that is always conceptually unfree. In trying to move away from this conceptual and dialectical trap of being made right-with and unfree under liberal humanism, this paper tentatively considers Black feminist theorisations of care and freedom ‘to-come’, as well as Édouard Glissant’s notion of opacity to explore the concept of being with elsewhere as a way of articulating practices of Black life that make freedom elsewhere possible. (shrink)

Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle–antiparticle amplitude. This process differs from conventional on-shell Mandelstam s, t, u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel non-perturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations (...) recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle–antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the non-relativistic Coulomb problem, including the forward scattering singularity, the essential singularity in the phase, and the Bohr bound-state spectrum. (shrink)