6026408
Markov-Yukawa transversality principle and 3-D - 4-D interlinkage of Bethe-Salpeter amplitudes
This article is designed to focus attention on the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes, with a closely parallel treatment of qq and qqq systems, stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. This unique feature of MYTP owes its origin to a Lorentzcovariant 3D support to the BS kernel, which acts as a sort of 'gauge principle' and distinguishes it from most other 3D approaches to strong interaction dynamics. Some of the principal approaches in the latter category are briefly reviewed so as to set the (less familiar) MYTP in their context. Two specific types of MYTP which provide 3D support to the BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b) Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE reductions but produce sharply different 4D structures: Under CIA, the 4D loop integrals suffer from Lorentz mismatch of the vertex functions, leading to ill-defined time-like momentum integrals, but Cov LF is free from this disease. This is illustrated by the pion form factor under Cov LF. The reconstruction of the 4D qqq wave function is achieved by Green's function techniques.
123745795
*recoil effects* in a model of higher baryon couplings. i. photoproduction
A recently proposed model (MM) of higher baryon couplings for P and V mesons is reformulated by reviewing the fuller possibilities of the "recoil term" in the primitive quark-meson interaction. While this introduces no basic change in the P-meson coupling structures, it yields an entirely new (L-1)-wave coupling of V mesons to J = L+12 baryons, which is capable of generating helicity-flip amplitudes. The advantage of this new coupling structure over the earlier one is demonstrated through the excellent reproduction of (i) the E1 angular distribution in Y * →Λγ decay and (ii) the appreciable magnitudes as well as energy variations of the asymmetry parameter ∑(θ) in pion photoproduction. In addition to a comparison of the two coupling structures (old and new), the present paper is also designed to study the role of still another parametric structure for the form factor - one which exhibits better convergence properties at higher energies than those discussed in MM. The additional processes studied in this connection are (i) η and X 0 photoproduction at intermediate energies (> 2 GeV), (ii) polarization of the recoil proton in η and π photoproduction, and (iii) π 0 photoproduction at high energies (∼ 6 GeV), in accordance with our earlier scheme of s-channel resonances. In connection with η photoproduction the roles of some pertinent I =12 resonances such as S 11 , P 11 , and G 17 are discussed, especially in relation to supermultiplet assignments.
61725309
The three-body problem: third generation and beyond?
117884842
THREE-BODY VERTICES WITH TWO-BODY TECHNIQUES,
Publisher Summary This chapter discusses three-body vertices with two-body techniques. It has long been recognized that vertex functions for few particle systems provide a convenient medium for the analysis of reactions in the language of Feynman diagrams, analogously to elementary particle processes. The development of three-particle theory has provided considerably more impetus for the use of the language of three-body vertex functions through the possibility of their exact evaluation with only two-body input. While three-body vertices are probably superfluous for the description of only three-body processes, their practical usefulness often extends to reactions involving more than three-particle systems, as long as such systems can be meaningfully described in terms of not more than three particles playing the active role. This chapter reviews a simplified construction of three-body vertices. For a four system, the problem of normalization of the corresponding wave functions is so much more involved that at the present state of computer technology, there appears little chance of the exact evaluation of αdd and αtN vertex functions in terms of overlap integrals if wave functions calculated entirely in terms of N-N input potentials are to be used.
30997914
Null-plane Bethe-Salpeter dynamics: Mass spectra, decay constants of pseudoscalar mesons, and the pion form factor.
A new relativistic definition of the reduced mass ({mu}{sub 12}) of a {ital q{bar q}} pair, so as to be in conformity with the standard Wightman-Garding definition of its relative four-momenta {ital q}{sub {mu}}, is introduced into the kernel of an ongoing Bethe-Salpeter (BS) program on a two-tier basis. The new definition of {mu}{sub 12} (involving the hadron mass {ital M}) is found to produce a natural Regge asymptotic behavior ({ital M}{sup 2}{approximately}{ital N}) in the hadron mass spectra, while retaining the property of an asymptotically linear ({approximately}{ital r}) confinement in the three-dimensional structure of the BS kernel. The relativistic structure of {mu}{sub 12} is responsible for a significant improvement in the fits to the ground-state masses of {ital q{bar q}} and {ital Q{bar q}} mesons as compared to its nonrelativistic definition {ital m}{sub 1}{ital m}{sub 2}/({ital m}{sub 1}+{ital m}{sub 2}). The leptonic decay constants {ital f}{sub {ital p}} and the charge radii thus calculated are also in excellent agreement with data ({pi},{ital k}) where available, while {ital f}{sub {ital p}} predictions for {ital Q{bar q}} mesons have good overlap with recent lattice predictions. Further, the scaling property ({approximately}{ital k}{sub {mu}}{sup {minus}2}) of the hadron's electromagnetic form factor at largemore » {ital k}{sup 2} is a consequence of the on-shell'' form of its null-plane wave function. All these results (which are indicated in the barest outline) are preceded by a perspective summary of the theoretical premises and practical working of the BS equation with a four-fermion interaction kernel as a necessary background on a two-tier basis.« less
15889809
On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions
The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer-Duffin β-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard “trace” techniques. The results are compared with a recent derivation due to Bosanac.
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.
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.