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1.
Using the method of infrared bounds and partial-integration formulas, we prove that there is a chiral phase transition in four-dimensional strongly coupled lattice gauge theory with gauge group U(N) and staggered fermions for all N5.  相似文献   

2.
We study chiral symmetry breaking (χSB) in SU(2) lattice gauge theory with quarks in the l = 12, l = 1, l = 32, and l = 2 representations of the color group. We perform Monte Carlo evaluations of ψψ〉 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 Tl = 1/Tl = 12 ~ 8. Our results for the higher representations, l = 32and l = 2, 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   

3.
We present an outline for a proof (the precise details of which will be presented in a follow-up paper) of a large-N phase transition in dimensions greater than two. The critical couplings are calculated in d=3 and d=4 and are found to be β=0.44 and β=0.40, respectively.  相似文献   

4.
5.
We study chiral symmetry in the strong coupling limit of lattice gauge theory with staggered fermions and show rigorously that chiral symmetry is broken spontaneously in massless QED and the gauge-invariant Nambu-Jona-Lasinio model if the dimension of spacetime is at least four. The results for the chiral condensate as a function of the mass imply that the mean-field approximation is an upper bound for this observable which becomes exact as the dimension goes to infinity. For the model with gauge groupU(N),N=2,3,4, we prove that chiral long-range order exists at zero mass in four or more dimensions. Address after August 1991: Mathematics Department, University of British Columbia, Vancouver, Canada V6T1Y4  相似文献   

6.
A change of variables is made in the hamiltonian of a U(N) gauge theory so that the independent variables are the path dependent phase factors. The resulting hamiltonian is similar in form to that of the Nambu-Gato string  相似文献   

7.
8.
It is shown that the limit as N → ∞ with g2N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft.  相似文献   

9.
We present specific examples that demonstrate the non-convergence of the 1/N expansion for the lattice theory of SU(N) gauge fields.  相似文献   

10.
It is pointed out that finding the partition function for U(N) gauge theory on a two-dimensional lattice in the limit N→∞ reduces, for a broad class of single-plaquette actions, to a well-known and solved mathematical problem. The case where in the single plaquette action the matrix U + U+ occuring in Wilson's formula is replaced by an arbitrary polynomial in this matrix, is discussed in detail and explicit results for the second-order polynomial are presented. A rich phase structure with second- and third-order phase transitions is found. The results are shown to have at the qualitative level a simple thermodynamical interpretation. They support the view that the phase structure of a lattice gauge theory is an artifact of the lattice action used rather than some reflection of the underlying group structure.  相似文献   

11.
The mean field can be considered as a classical solution of an appropriately reformulated version of lattice gauge theories. Axial gauge fixing renders it stable. The quadratic forms for the fluctuations in the gaussian approximation are analyzed. The gaussian correction to the mean field free energy is expressed for all U(N) and SU(N) in terms of structure functions that are explicitly calculated for U(N), SU(∞, and SU(∞) numerical calculations are performed for the phase transition point, its latent heat, and some correlation lengths that are characteristic for this kind of mean field approach.  相似文献   

12.
13.
The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to H = SU(3)C × SU(2)L × U(1)R × U(10)B?L. For all solutions, the fermions which are chiral with respect to H form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)G × U(1)G. For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)G × U(1)G. Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories.  相似文献   

14.
The phase structure of pure SU(N)/Z(N) lattice gauge theories in four dimensions is discussed. The presence of ZN monopoles plausibly leads to a phase transition. A Monte Carlo simulation of SO(3) shows the presence of a very strong, may be first order, phase transition.  相似文献   

15.
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 mpseudo-Goldstone2 ~ mquarkψψ〉. 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   

16.
In the framework of the formalism of Cornwall et al. for composite operators, we develop a new method for the calculation of the effective potential. We apply the method to the study of chiral symmetry breaking in an SU(N) color gauge theory with n massless flavors and derive analytically the complete effective potential at two fermion loops. We find that in this approximation the theory has two phases: the symmetric phase and the broken phase into the diagonal flavor sub-group.  相似文献   

17.
It is shown how to find the Wilson loop average for an arbitrary self-intersecting composite contour in two-dimensional U(N) gauge theory using the equation of motion in contour space. Some examples of contours are considered.  相似文献   

18.

Symmetry breaking solutions of several model theories are investigated with the result that constant gauge transformations of the fields describing zero mass Goldstone particles are responsible for the formal possibility of the spontaneous symmetry breaking.

  相似文献   

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) mpseudoGoldstone2 ∝ mfermionψψ〉. The pseudoscalar pseudoGoldstone particles—the “pions” of this abelian theory—correspond to antiferromagnetic spin wave excitations of the fermion vacuum.  相似文献   

20.
钱锋  黄洪斌  齐观晓  沈才康 《中国物理》2006,15(7):1577-1579
Based on Bogoliubov's truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a0+\lambda*a0+) to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose--Einstein condensation(BEC) occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schr\"{o}dinger eigenvalue equation and using the self-consistent condition.  相似文献   

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