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1.
After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 44 lattice. We compare our results for 〈Seff〉 and for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈Seff〉 turns out to be quite small for . 相似文献
2.
Noboru Kawamoto 《Nuclear Physics B》1981,190(3):617-669
We propose the phase structure of abelian and non-abelian lattice gauge theories with fermions. We especially analyse Wilson's lattice action with euclidean discrete space-time. We mainly analyse as an order parameter for the fermion-gauge coupled system. The Wilson loop integral and plaquette-plaquette two-point function are also useful in working out abelian phase diagrams. We will discuss physical implications of the phase diagrams, especially for the mass spectrum in the lattice continuum limit and chiral symmetry breaking. The 1/N expansion and a random walk idea are used in the formulation and play an important role in computing meson and baryon propagators in the strong coupling limit. 相似文献
3.
Ikuo Ichinose 《Nuclear Physics B》1985,249(4):715-732
U(N) and SU(N) lattice QCD are considered. By using a method of the strong-coupling expansion, the effective lagrangian of hadrons is calculated up to the first order in 1/(g2N). For the Susskind lattice fermions, it is shown that chiral symmetry is spontaneously broken and as a result there appears the Nambu-Goldstone boson (pion). The fermion condensation 〈t>, the masses of hadrons and the pion decay constant are calculated and compared with the results of Monte Carlo (MC) simulations. In the strong-coupling region, our result of the order parameter 〈〉 coincides very well with that calculated by MC simulations. 相似文献
4.
We show, in the euclidean path-integral formulation of strong-coupling lattice gauge theory, that continuous chiral symmetry is dynamically broken, and obtain the standard current algebra result that . We also remark that the center of the gauge group does not seem very relevant for this result; chiral symmetry breaking is a property of strong-coupling lattice theories both in the case where quark color is confined, and also in the case where it is screened by gauge field fluctuations. 相似文献
5.
A path integral is defined for the vacuum expectation values of Euclidean QED2 on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields on a lattice with spacing proportional to N?1, N?Z+, the Matthews-Salam formula for the vacuum expectation 〈G〉N has the form ()N=∫dnu;WN(,f), where dμ is an N-independent measure on a random electromagnetic field ? and is an N-dependent function of ? determined by . For a class of we prove that as N → ∞, has a limit except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫dnu;WN(,f) exists and limN→∞∫dnu;WN(,f). 相似文献
6.
Marco Bochicchio Luciano Maiani Guido Martinelli Giancarlo Rossi Massimo Testa 《Nuclear Physics B》1985,262(2):331-355
The chiral properties of the continuum limit of lattice QCD with Wilson fermions are studied. We show that a partially conserved axial current can be defined, satisfying the usual current algebra requirements.A proper definition of the chiral symmetry order parameter, , is given, and the chiral properties of composite operators are investigated. The implications of our analysis to the lattice determination of non-leptonic weak amplitudes are also discussed. 相似文献
7.
An algorithm for Monte Carlo simulation of lattice gauge theories with fermions is presented. The method is applied to the Schwinger model with two flavors of massless fermions, formulated on a two-dimensional euclidean lattice. Preliminary results of the Monte Carlo iteration of this system are presented, with special emphasis on the behavior of the Wilson loop and bilocal chiral correlation functions such as . 相似文献
8.
Ikuo Ichinose 《Annals of Physics》1984,152(2):451-474
Lattice fermion formulation is investigated using a solvable model which resembles quantum chromodynamics. CP2N?1 models with quarks are formulated on a lattice. For dynamical quarks, a generalized formulation of the Wilson and the Osterwalder-Seiler lattice fermion is used. In the expansion, the spontaneous breakdown of chiral symmetry (which is softly broken by the quark mass) apparently occurs in this model, and the “pion” mass is calculated. From the above results, it is shown that the above lattice fermion formulations have the desired continuum limit. The axial-vector current is investigated and it is proved that the usual anomaly appears in the continuum limit and the PCAC relation is satisfied. 相似文献
9.
Edward Witten 《Nuclear Physics B》1978,145(1):110-118
In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, vanishes in this model as |x|?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model. 相似文献
10.
We calculate the modification of the D = 4 CP(n) σ-model required by the existence of the effective action for composite fields which is finite in all orders in . We obtain the Higgs-like action with “free” bilinear terms for composite scalar and gauge fields. Contrary to the D = 2 case, due to the freedom of finite renormalization, the composite field excitations are not uniquely determined by the dynamics. 相似文献
11.
J.B. Kogut 《Physics Reports》1980,67(1):67-102
Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g2-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed. 相似文献
12.
N Papanicolaou 《Annals of Physics》1981,137(1):210-211
Quantum theories of N-component Fermi fields are formulated in terms of overcomplete sets of bilocal pseudo-spin operators in analogy with the Holstein-Primakoff theory of ordinary spin systems. Classical constrained Hamiltonian systems arise in the large N limit revealing the semi-classical nature of the large N approximation. Such systems are briefly analyzed in the context of the Gross-Neveu model, where the dynamics of c-number (rather than Grassman) fields governs the semi-classical limit. 相似文献
13.
The effect of virtual light quark loops on the chiral phase transition in lattice QCD with staggered fermions is investigated by employing the pseudo-fermion Monte Carlo method on a 63 × 2 lattice. The variation in the order parameter is found to become less sharp than the quenched case, indicating a second order chiral phase transitioon in the full theory. 相似文献
14.
Tamiaki Yoneya 《Nuclear Physics B》1978,144(1):195-218
We investigate the properties of Z(N) topological excitations in Wilson's lattice formulation of SU(N) Yang-Mills theories. We exhibit the Z(N) topological excitations as exact classical solutions on the lattice. After giving detailed qualitative discussions about the Z(N) excitations and their relevance to confinement, we investigate the Z(N) lattice gauge theories with the Wilson action and show that Z(2), Z(3) and Z(4) models are self-dual systems. (The self-duality of the Z(2) case has been known previously.) This property enables us to locate the critical points exactly in those systems under the assumption that the phase transition occurs at only one point in the coupling constant space. We then derive the effective action for the Z(N) topological excitations in the lattice SU(N) Yang-Mills theories in the steepest descent approximation. The critical coupling constants in the SU(N) models corresponding to the phase transition caused by the Z(N) excitations are estimated by using the information on the Z(N) models with the Wilson action. It is quite probable that the estimated value (for SU(3)) is an upper bound. This indicates that the Wilson model of the SU(3) gauge field can be effective action of the QCD gluons which exhibit permanent quark confinement and, at the same time, freedom up to the distance characterized by the energy, at least, ~1 TeV. 相似文献
15.
We study the strong coupling limit of U(N) or SU(N) gauge theories with fermions on a lattice. The integration over the gauge and fermion degrees of freedom is performed by analytic methods, leading to a partition function in terms of localized meson and baryon fields. A method for deriving a systematic expansion in the inverse of the space-time dimension of the corresponding Green functions is developed. It is applied to the study of spontaneous breakdown of chiral symmetry, which occurs for any U(N) or SU(N) theory with fermions in the fundamental representation. Meson and baryon spectra are then computed, and found to be in close agreement with those obtained by numerical methods at finite coupling. The pion decay constant is estimated. 相似文献
16.
17.
J. Kogut M. Stone H.W. Wyld S.H. Shenker J. Shigemitsu D.K. Sinclair 《Nuclear Physics B》1983,225(3):326-370
We study chiral symmetry breaking (χSB) in SU(2) lattice gauge theory with quarks in the , and l = 2 representations of the color group. We perform Monte Carlo evaluations of in the quenched approximation and extract the relevant length scales for χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain . Our results for the higher representations, , are consistent with Casimir scaling and give C2gmom2 ~ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices. 相似文献
18.
19.
In hamiltonian lattice gauge theory, the fermion vacuum at lowest order in 1/g2 can be determined from degenerate perturbation theory plus mean field-spin wave techniques. Using compact QED as an example, we show that: (i) chiral symmetry is spontaneously broken; and (ii) . The pseudoscalar pseudoGoldstone particles—the “pions” of this abelian theory—correspond to antiferromagnetic spin wave excitations of the fermion vacuum. 相似文献