119114701
Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry
Newtonian gravity was formulated as a geometrodynamic theory as far back in 1930s by Elie Cartan in what is named aptly as Newton Cartan space time. Though there are several approaches of realizing the algebraic structure of the Newton Cartan geometry from a contraction of the relativistic results, a dynamical (field theoretic) realization of it is lacking. In this paper we present such a realization from the localisation of the Galilean Symmetry of nonrelativistic matter field theories.
119226328
A new formulation of non-relativistic diffeomorphism invariance
Abstract We provide a new formulation of non-relativistic diffeomorphism invariance. It is generated by localising the usual global Galilean symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the theory of fractional quantum Hall effect has been discussed. Our construction is shown to open up a general approach of model building in theoretical condensed matter physics. Also, this formulation has the capacity of obtaining Newton–Cartan geometry from the gauge procedure.
122228736
A Minimal Dynamical Scheme for “Understanding” Hadronic Widths
Using a quark model scheme of ‘least Dynamics’, an inclusive determination of the total widths of mesons and baryons is proposed via the following mechanism: There exists a short (breathing) mode for the temporary dissociation of a hadron into a pair of “qausi-free” quarks and/or diquarks which eventually hadronize with certainty, so that the requisite widths correspond to this “first stage” dissociation itself. A detailed model (described elsewhere) based on the momentum dependence of the quark's mass function m(p) suggests a significant mass reduction of these quasi-free quarks w.r.t their “constituent” values m(O). Using this logic, a phenomenological coupling scheme for the meson-(quasifree)quark-vertex function is derived from Schwinger's Partial (broken chiral). Symmetry which incorporates the conservation of isospin, baryonic charge and hypercharge with respective ‘gauge mesons’ rho, omega, phi. A very similar structure is found for baryon couplings to quark (q)-diquark (D) pairs, with the same overall coupling constant (gs) for both systems. Its tentative identification with the QCD value yields a surprisingly good pattern of agreement with data for both hadron types, using two “quasi-free” masses (mud and ms) as inputs, with the corresponding diquark masses determined additively.
14276078
Three-Quark Bethe-Salpeter vertex function under pairwise gluon-exchange-like interaction: application to n-p mass difference
A qqq BSE formalism based on an input 4-fermion Lagrangian of 'current' u, d quarks interacting pairwise via a gluon-exchange-like propagator in its nonperturbative regime, is employed for the construction of a relativistic qqq-wave function under the Covariant Instantaneity Ansatz (CIA). The chiral invariance of the input Lagrangian is automatically ensured by the vector character of the gluonic propagator, while the 'constituent' masses are the low momentum limits of the dynamical mass function m(p) generated by the standard mechanism of DB χ S in the solution of the Schwinger Dyson Equation (SDE). The CIA gives an exact reduction of the BSE to a 3D form which is appropriate for baryon spectroscopy, while the reconstructed 4D form identifies the hadron quark vertex function as the key ingredient for evaluating transition amplitudes via quark-loop integrals. In this paper the second stage of this 'two-tier' BSE formalism is extended from the 4D qq-meson to the 4D qqq-baryon vertex reconstruction through a reversal of steps offered by the CIA structure. As a first application of this 4D qqq wave function, we evaluate the quark loop integrals for the neutron (n) - proton (p) mass difference which receives contributions from two sources : i) the strong SU(2) effect arising from the u-d mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference works out at 1.28 MeV (vs. 1.29 expt), with two free parameters C 0 , ω 0 characterizing the infrared structure of the gluonic, which have been precalibrated from a common fit to qq and qqq spectra as well as several other observable quark loop integrals. A formal derivation, based on Green's function techniques for 3 spinless quarks, of the CIA structure of the 4D qqq-baryon vertex function as employed in the text, is given for completeness in Appendix B.