New Method for Dynamical Fermions and Chiral-Symmetry Breaking

The reasons for the feasibility of the Microcanonical Fermionic Average ($MFA$) approach to lattice gauge theory with dynamical fermions are discussed. We then present a new exact algorithm, which is free from systematic errors and convergent even in the chiral limit.Comment: 3 pages, DFTUZ 93/20, to appear in the Proceedings of Lattice 93, Dalla

Strongly Coupled QED

A short review of some of the most relevant contributions to non-perturbative QED is done. Since a Gaussian behaviour of QED \`a la $\lambda\phi^4$ has been ruled out by the numerical data, I analyse the other two most reliable scenarios, i.e. triviality \`a la Nambu-Jona Lasinio and non-Gaussian critical behaviour. I give a suggestive theoretical argument against a Gaussian behaviour of QED \`a la Nambu-Jona Lasinio, and show how the numerical data for the susceptibility at the critical point of QED support this result.Comment: Plenary talk given at the International Symposium on Lattice Field Theory, 4-8 June 1996, St. Louis, Missouri, USA, 19 pages, latex, three Postscript figures and two table

Testing logarithmic violations to scaling in strongly coupled QED

Using very precise measurements of the critical couplings for the chiral transition of non compact $QED_4$ with up to 8 flavours, we analyse the behaviour of the order parameter at the critical point using the equation of state of a logarithmically improved scalar mean field theory, that of the Nambu-Jona Lasinio theory and a pure power law. The first case is definitively excluded by the numerical data. The stability of the fits for the last two cases, as well as the behaviour with the number of flavours of the exponent of the logarithmic violations to the scaling favour clearly a pure power law scaling with non mean field exponents.Comment: 6 pages, 3 postscript figures, 2 postscript tables (tar-ed, zip-ed, uu-encoded

Spontaneous Symmetry Breaking in Fermion-Gauge Systems- A Non Standard Approach

We propose a new method for the study of the chiral properties of the ground state in QFT's based on the computation of the probability distribution function of the chiral condensate. It can be applied directly in the chiral limit and therefore no mass extrapolations are needed. Furthermore this approach allows to write up equations relating the chiral condensate with quantities computable by standard numerical methods, the functional form of these relations depending on the broken symmetry group. As a check, we report some results for the compact Schwinger model.Comment: Latex file, 11 pages plus two figure

No-go theorem on spontaneous parity breaking revisited

An essential assumption in the Vafa and Witten's theorem on P and CT realization in vector-like theories concerns the existence of a free energy density in Euclidean space in the presence of any external hermitian symmetry breaking source. We show how this requires the previous assumption that the symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is plausible, actually a theorem is still lacking.Comment: Talk presented at LATTICE99(Theoretical Developments),3 pages. Latex using espcrc2.st

Chiral transition in a strongly coupled fermion-gauge-scalar model

We report the recent results from the computer simulations of a fermion-gauge-scalar model with dynamical chiral-symmetry breaking and chiral transition induced by the scalar field. This model might be considered to be a possible alternative to the Higgs mechanism of mass generation. A new scheme is developed for detecting the chiral transition. Our results show with higher precision than the earlier works that the chiral transition line joins the Higgs phase transition line, separating the Higgs and Nambu (chiral-symmetry breaking) phases. The end point of the Higgs transition with divergent correlation lengths is therefore suitable for an investigation of the continuum limit.Comment: 3 pages, 3 eps figs, encoded with uufiles (Contribution to Lattice 94

Eigenmodes of the Dirac Operator and Chiral Properties of QCD with Sea Quarks

I describe a mechanism to understand the relation between chiral-symmetry breaking and eigenmodes of the Dirac operator in lattice QCD with Kogut-Susskind sea quarks. It can be shown that if chiral symmetry is spontaneously broken, the eigenvalues $\lambda_i$ should behave as $z(i)/V$ for large volume $V$, where $z(i)$ is the i-th zero of the Bessel function. With neither chiral nor $\lambda$ extrapolation, one can precisely calculate the chiral condensate using only a small set of eigenvalues. Therefore, it is economical and free of systematic uncertainties. I present the first QCD data to support this mechanism and encourage the lattice community to test and use it.Comment: LATTICE98(confine

Fermionic effective action and the pahse estructure of non compact quantum electrodynamics in 2+1 dimensions

We study the phase diagram of non compact $QED_3$ using the microcanonical fermionic average method described elsewhere. We present evidence for a continuous phase transition line in the $\beta, N$ plane, extending down to arbitrarily small flavour number $N$.Comment: 12 pags + 1 table + 5 figs; Ref: DFTUZ 93.0

The Schwinger Model on the lattice in the Microcanonical Fermionic Average approach

The Microcanonical Fermionic Average method has been used so far in the context of lattice models with phase transitions at finite coupling. To test its applicability to Asymptotically Free theories, we have implemented it in QED$_2$, \it i.e.\rm the Schwinger Model. We exploit the possibility, intrinsic to this method, of studying the whole $\beta, m$ plane at negligible computer cost, to follow constant physics trajectories and measure the $m \to 0$ limit of the chiral condensate. We recover the continuum result within 3 decimal places.Comment: TeX file, 7 pages + 3 figures in Postscrip

Topology in the SU(Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology

We investigate the topological properties of unquenched $QCD$ on the basis of numerical results of simulations at fixed topological charge, recently reported by Borsanyi et al.. We demonstrate that their results for the mean value of the chiral condensate at fixed topological charge are inconsistent with the analytical prediction of the large volume expansion around the saddle point, and argue that the most plausible explanation for the failure of the saddle point expansion is a vacuum energy density $\theta$-independent at high temperatures, but surprisingly not too high $(T\sim 2T_c)$, a result which would imply a vanishing topological susceptibility, and the absence of all physical effects of the $U(1)$ axial anomaly at these temperatures. We also show that under a general assumption concerning the high temperature phase of $QCD$, where the $SU(N_f)_A$ symmetry is restored, the analytical prediction for the chiral condensate at fixed topological charge is in very good agreement with the numerical results of Borsanyi et al., all effects of the axial anomaly should disappear, the topological susceptibility and all the $\theta$-derivatives of the vacuum energy density vanish and the theory becomes $\theta$-independent at any $T>T_c$ in the infinite volume limit.Comment: 18 pages, no figures, typos added in section 4, small changes in the text and some references adde