Michael C. Birse

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A Wilsonian renormalisation group is used to study nonrelativistic twobody scattering by a short-ranged potential. We identify two fixed points: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the linearised renormalisation group are used to assign a systematic power-counting to terms in the potential near each(More)
The commonly used types of effective theory for vector mesons are reviewed and their relationships clarified. They are shown to correspond to different choices of field for spin-1 particles and the rules for transforming between them are described. The importance of respecting chiral symmetry is stressed. The choice of fields that transform homogeneously(More)
We apply the renormalisation-group to two-body scattering by a combination of known long-range and unknown short-range forces. A crucial feature is that the low-energy effective theory is regulated by applying a cut-off in the basis of distorted waves for the long range potential. We illustrate the method by applying it to scattering in the presence of a(More)
Group-theoretic arguments are used to determine the dependence of twopoint correlators of quark bilinears on the current quark masses. The leading difference between π and δ correlators is found to be of orderms times a U(1)Aviolating correlator. These general arguments are consistent with Schaefer’s observation that if U(1)A violation persists to high(More)
We study the instabilities of quark matter in the framework of a generalized Nambu–Jona-Lasinio model, in order to explore possible competition between three-quark clustering to form nucleons and diquark formation leading to color superconductivity. Nucleon and ∆ solutions are obtained for the relativistic Faddeev equation at finite density and their(More)
We investigate the time evolution of a system of quarks interacting with σ and pion fields starting from an initial configuration consisting of a tube of hot quark plasma undergoing a boost-invariant longitudinal expansion. We work within the framework of the linear sigma model using classical transport equations for the quarks coupled to the mean-field(More)
We study the ratio between the fermion-fermion scattering length and the dimer-dimer scattering length for systems of nonrelativistic fermions, using the same functional renormalisation technique as previously applied to fermionic matter. We find a strong dependence on the cutoff function used in the renormalisation flow for a two-body truncation of the(More)