Massive Propagator Research Articles

Twist-3 and quark mass contributions to the polarized nucleon structure function g2(x,Q2)

Quark mass effects are clarified in the parton model approach to the transversely polarized nucleon structure function. The special propagator technique is employed to obtain manifestly gauge invariant results and extract the buried short-distance contributions inside the soft part after momentum factorization in the collinear expansion approach. A generalized massive special propagator for a massive quark is constructed. We identify the corresponding matrix elements of the transversely polarized structure function in deep inelastic scatterings by the massive special propagator technique.

Feynman rules in N = 2 projective superspace (II).Massive hypermultiplets

Manifest N = 2 supersymmetric hypermultiplet mass terms can be introduced in the projective N = 2 superspace formalism. In the case of complex hypermultiplets, where the gauge covariantized spinor derivatives have an explicit representation in terms of gauge prepotentials, it is possible to interpret such masses as vacuum expectation values of an Abelian vector multiplet. The duality transformation that relates the N = 2 off-shell projective description of the hyper-multiplet to the on-shell description involving two N = 1 chiral superfields allows us to obtain the massive propagators of the N = 1 complex linear fields in the projective hypermultiplet. The N = 1 massive propagators of the component superfields in the projective hypermultiplet suggest a possible ansatz for the N = 2 massive propagator, which agrees with an explicit calculation in N = 2 superspace.

One-loop gap equations for the magnetic mass ind=3gauge theory

Recently several workers have attempted determinations of the so-called magnetic mass of d=3 non-Abelian gauge theories through a one-loop gap equation, using a free massive propagator as input. Self-consistency is attained only on-shell, because the usual Feynman-graph construction is gauge-dependent off-shell. We examine two previous studies of the pinch technique proper self-energy, which is gauge-invariant at all momenta, using a free propagator as input, and show that it leads to inconsistent and unphysical result. In one case the residue of the pole has the wrong sign (necessarily implying the presence of a tachyonic pole); in the second case the residue is positive, but two orders of magnitude larger than the input residue, which shows that the residue is on the verge of becoming ghostlike. This happens because of the infrared instability of d=3 gauge theory. A possible alternative one-loop determination via the effective action also fails. The lesson is that gap equations must be considered at least at two-loop level.

Three topics of monopole dynamics in abelian projected QCD

Three topics about monopole dynamics after abelian projection are reported. The first is the new and detailed analyses of SU(2) monopole action obtained after the block-spin transformation on the dual lattice. The b = na(β) dependence for all couplings are well fitted with a universal curve. The distance dependence of the couplings is well reproduced by a massive propagator with the mass m = 0.8 in unit of b. The second is the SU(3) monopole action recently obtained. The third is new interesting gauges showing abelian and monopole dominances as in the maximally abelian gauge.

Super Yang-Mills theory as a random matrix model.

We generalize the Gervais-Neveu gauge to four-dimensional N=1 superspace. The model describes an N=2 super Yang-Mills theory. All chiral superfields (N=2 matter and ghost multiplets) exactly cancel to all loops. The remaining Hermitian scalar superfield (matrix) has a renormalizable massive propagator and simplified vertices. These properties are associated with N=1 supergraphs describing a superstring theory on a random lattice world sheet. We also consider all possible finite matrix models, and find they have a universal large-color limit. These could describe gravitational strings if the matrix-model coupling is fixed to unity, for exact electric-magnetic self-duality.

Lattice study of the gluon propagator in momentum space.

We consider pure glue QCD at $\ensuremath{\beta}=5.7$, $\ensuremath{\beta}=6.0$, and $\ensuremath{\beta}=6.3$. We evaluate the gluon propagator both in time at zero three-momentum and in momentum space. From the former quantity we obtain evidence for a dynamically generated effective mass, which at $\ensuremath{\beta}=6.0$ and $\ensuremath{\beta}=6.3$ increases with the time separation of the sources, in agreement with earlier results. The momentum space propagator $G(k)$ provides further evidence for mass generation. In particular, at $\ensuremath{\beta}=6.0$, for $300 \mathrm{MeV}\ensuremath{\lesssim}k\ensuremath{\lesssim}1GeV$, the propagator $G(k)$ can be fit to a continuum formula proposed by Gribov and others, which contains a mass scale $b$, presumably related to the hadronization mass scale. For higher momenta Gribov's model no longer provides a good fit, as $G(k)$ tends rather to follow an inverse $\mathrm{power}\mathrm{law}\ensuremath{\approx}\frac{1}{{k}^{2+\ensuremath{\gamma}}}$. The results at $\ensuremath{\beta}=6.3$ are consistent with those at $\ensuremath{\beta}=6.0$, but only the high momentum region is accessible on this lattice. We find $b$ in the range of 300 to 400 MeV and $\ensuremath{\gamma}$ about 0.7. Fits to particle + ghost expressions are also possible, often resulting in low values for ${\ensuremath{\chi}}_{\mathrm{DF}}^{2}$, but the parameters are very poorly determined. On the other hand, at $\ensuremath{\beta}=5.7$ (where we can only study momenta up to 1 GeV) $G(k)$ is best fit to a simple massive boson propagator with mass $m$. We argue that such a discrepancy may be related to a lack of scaling for low momenta at $\ensuremath{\beta}=5.7$. From our results, the study of correlation functions in momentum space looks promising, especially because the data points in Fourier space turn out to be much less correlated than in real space.

Zero modes, Euclideanization, and quantization.

We consider the massless scalar field on the four-dimensional sphere ${S}^{4}$. Its classical action $S=\frac{1}{2}\ensuremath{\int}{{S}^{4}}^{}\mathrm{dV}{(\ensuremath{\nabla}\ensuremath{\varphi})}^{2}$ is degenerate under the global invariance $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\varphi}+\mathrm{const}$. We then quantize the massless scalar field as a gauge theory by constructing a Becchi-Rouet-Stora-Tyutin-invariant quantum action. The corresponding gauge-breaking term is a nonlocal one of the form ${S}^{\mathrm{GB}}=(\frac{1}{2\ensuremath{\alpha}V)}(\ensuremath{\int}{{S}^{4}}^{}\mathrm{dV}{\ensuremath{\varphi})}^{2}$ where $\ensuremath{\alpha}$ is a gauge parameter and $V$ is the volume of ${S}^{4}$. It allows us to correctly treat the zero-mode problem. The quantum theory is invariant under O(5), the symmetry group of ${S}^{4}$, and the associated two-point functions have no infrared divergence. The well-known infrared divergence which appears by taking the massless limit of the massive scalar field propagator is therefore a gauge artifact. By contrast, the massless scalar field theory on de Sitter space ${\mathrm{dS}}^{4}$, the Lorentzian version of ${S}^{4}$, is not invariant under the symmetry group of that spacetime O(1,4). Here, the infrared divergence is real. Therefore, the massless scalar quantum field theories on ${S}^{4}$ and ${\mathrm{dS}}^{4}$ cannot be linked by analytic continuation. In this case, because of zero modes, the Euclidean approach to quantum field theory does not work. Similar consideration also apply to massive scalar field theories for exceptional values of the mass parameter.

EQUIVALENCE OF MASSIVE PROPAGATOR DISTANCE AND MATHEMATICAL DISTANCE ON GRAPHS

It is shown that the assignment of distance according to the massive propagator method and according to the mathematical definition (length of minimal path) on arbitrary graphs with a bound on the degree leads to equivalent large scale properties of the graph. Especially, the internal scaling dimension is the same for both definitions. This result holds for any fixed, non-vanishing mass, so that a really inequivalent definition of distance requires the limit m→0.

The massive scalar field propagator on finite lattices

The propagator for the massive free scalar field is calculated for an arbitrary dimension on a finite lattice. The specific boundary conditions are shown, energy dispersion relation found, and applications to self-interacting fields are made. The weak and strong coupling expansions for self-interacting fields are discussed for the finite lattice. A few comments are made in regard to Monte Carlo simulations on finite lattices.

The Landau gauge gluon propagator in lattice QCD

A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β = 5.6 (200 4 3 × 8 lattices), β = 5.8 (400 4 3 × 10 lattices and 100 6 3 × 12 lattices), and β = 6.0 (100 4 3 × 8 lattices) indicate that the gluon propagator resembles a massive particle propagator in which the mass grows with separation. At the largest distances accessible with these lattices, the mass is about 600 MeV.

The gluon is massive: A lattice calculation of the gluon propagator in the Landau gauge

A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β=5.6(200 4 3×8 lattices), β=5.8(400 4 3×10 lattices), and β=6.0(100 4 3×8 lattices) indicate that the gluon propagator resembles a massive particle propagator with asymptotic mass near 600 MeV.

Mass corrections to some instanton effects

We develop an approximation scheme which allows us to determine the massive scalar propagator in a background instanton field to second order in a supposedly small mass parameter m , i.e., including terms of order m 2 ln m and m 2 , and the massive spinor propagator to the same order. The approximate scalar propagator is used to study the mass corrections to the short-distance behaviour of a two-point scalar loop. Applying this as a toy model for σ(e + e − → anything) we find that the large momentum behaviour of the leading mass corrections is at most of the same order as the massless instanton effects.

Mass corrections to some instanton effects

We develop an approximation scheme which allows us to determine the massive scalar propagator in a background instanton field to second order in a supposedly small mass parameter m, i.e., including terms of order m 2ln m and m 2, and the massive spinor propagator to the same order. The approximate scalar propagator is used to study the mass corrections to the short-distance behaviour of a two-point scalar loop. Applying this as a toy model for σ(e +e − → anything) we find that the large momentum behaviour of the leading mass corrections is at most of the same order as the massless instanton effects.

On asymptotic behaviour of vertex part in scalar electrodynamics

The vertex part in scalar electrodynamics with massive vector boson propagator is calculated. To satisfy Ward's identity contributions from two double corner diagrams are added. Asymptotic behaviour when one and two variables go to infinity is deduced, and compared with the remarks of Salam and Delbourgo.

An integral spectral representation of the massive Dirac propagator in the Kerr geometry in Eddington–Finkelstein-type coordinates

We consider the massive Dirac equation in the non-extreme Kerr geometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinates and derive a functional analytic integral representation of the associated propagator using the spectral theorem for unbounded self-adjoint operators, Stone's formula, and quantities arising in the analysis of Chandrasekhar's separation of variables. This integral representation describes the dynamics of Dirac particles outside and across the event horizon, up to the Cauchy horizon. In the derivation, we first write the Dirac equation in Hamiltonian form and show the essential self-adjointness of the Hamiltonian. For the latter purpose, as the Dirac Hamiltonian fails to be elliptic at the event and the Cauchy horizon, we cannot use standard elliptic methods of proof. Instead, we employ a new, general method for mixed initial-boundary value problems that combines results from the theory of symmetric hyperbolic systems with near-boundary elliptic methods. In this regard and since the time evolution may not be unitary because of Dirac particles impinging on the ring singularity, we also impose a suitable Dirichlet-type boundary condition on a time-like inner hypersurface placed inside the Cauchy horizon, which has no effect on the dynamics outside the Cauchy horizon. We then compute the resolvent of the Dirac Hamiltonian via the projector onto a finite-dimensional, invariant spectral eigenspace of the angular operator and the radial Green's matrix stemming from Chandrasekhar's separation of variables. Applying Stone's formula to the spectral measure of the Hamiltonian in the spectral decomposition of the Dirac propagator, that is, by expressing the spectral measure in terms of this resolvent, we obtain an explicit integral representation of the propagator.