579271
Temperature Dependence of Gluon and Quark Condensates as from Linear Confinement
The gluon and quark condensates and their temperature dependence are investigated within QCD premises. The input for the former is a gauge invariant $gg$ kernel made up of the direct (D), exchange (X) and contact(C) QCD interactions in the lowest order, but with the perturbative propagator $k^{-2}$ replaced by a `non-perturbative $k^{-4}$ form obtained via two differentiations: $ \mu^2 \partial_m^2 (m^2+k^2)^{-1}$, ($\mu$ a scale parameter), and then setting $m=0$, to simulate linear confinement. Similarly for the input $q{\bar q}$ kernel the gluon propagator is replaced by the above $k^{-4}$ form. With these `linear' simulations, the respective condensates are obtained by `looping' up the gluon and quark lines in the standard manner. Using Dimensional regularization (DR), the necessary integrals yield the condensates plus temperature corrections, with a common scale parameter $\mu$ for both. For gluons the exact result is $$ = {36\mu^4}\pi^{-3}\alpha_s(\mu^2)[2-\gamma - 4\pi^2 T^2/(3\mu^2)]$$. Evaluation of the quark condensate is preceded by an approximate solution of the SDE for the mass function $m(p)$, giving a recursive formula, with convergence achieved at the third iteration. Setting the scale parameter $\mu$ equal to the universal Regge slope $1 GeV^2$, the gluon and quark condensates at T=0 are found to be $0.586 Gev^4$ and $(240-260 MeV)^3$ respectively, in fair accord with QCD sum rule values. Next, the temperature corrections (of order $-T^2$ for both condensates) is determined via finite-temperature field theory a la Matsubara. Keywords: Gluon Condensate, mass tensor, gauge invariance, linear confinement, finite-temperature, contour-closing. PACS: 11.15.Tk ; 12.38.Lg ; 13.20.Cz
125652054
THE PROCESS pi- p ---> eta n WITH QPC MODEL FOR A2 EXCHANGE
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.
61725309
The three-body problem: third generation and beyond?
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
181778573
HARMONIC OSCILLATOR IN QUARK PHYSICS: SOME ASPECTS, A REVIEW
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.