Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCD

A method is proposed for computing effective lagrangians in QCD with N colors using lattice regularization. The meson field lagrangian is worked out in detail in the strong coupling limit with various lattice fermion formulations. For generalized Susskind fermions the spontaneous breakdown U(n) ? U(n) → U(n) (diagonal) is found at large N and a generalized version of the non-linear σ model emerges in a natural way. The Nambu-Goldstone spectrum is investigated and a continuous transition is made to Wilson fermions, for which the effective potential and the ππ scattering amplitude are tested on chiral symmetry. Large d (=dimension) approximations are compared with the large N limit and applied to N = 3.     

Proof of chiral symmetry breaking in strongly coupled lattice gauge theory

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     

Strength distributions and symmetry breaking in coupled microwave billiards

Flat microwave cavities can be used to experimentally simulate quantum mechanical systems. By coupling two such cavities, we study the equivalent to symmetry breaking in quantum mechanics. As the coupling is tunable, we can measure resonance strength distributions as a function of the symmetry breaking. We analyze the data by employing a qualitative model based on random matrix theory and show that the results derived from the strength distribution are consistent with those previously obtained from spectral statistics.     

Current rectification by spontaneous symmetry breaking in coupled nanomechanical shuttles

We investigate the transport and the dynamical properties of tunnel-coupled double charge shuttles. The oscillation frequencies of two shuttles are mode locked to integer multiples of the applied voltage frequency omega. We show that left-right-symmetric double shuttles may generate direct net current due to bistable motions caused by parametric instability. The symmetry-broken direct current appears near omega = Omega0/(2j-1), (j = 1,2,...), where Omega0 is the dressed resonance frequency of the relative motion of the two shuttles.     

W ± Z 0 signals from the strongly interacting symmetry breaking sector

We study the possibilities of unraveling the underlying dynamics of the symmetry breaking sector through the scattering of longitudinal weak bosons inpp collisions.W ^± Z ⁰ channels are considered in the context of a general approach based on chiral perturbation theory, supplemented by a unitarization procedure. The channels considered here are the relevant ones for symmetry breaking sector dynamics such as technicolor, where aI=J=1 resonance appears in the spectrum. DirectWZ production from quark annihilation viap _tc-W mixing is also considered and compared withWZ production from theWZ fusion mechanism.     

Spontaneous scale symmetry breaking in 2+1-dimensional QED at both zero and finite temperature

A complete analysis of dynamical scale symmetry breaking in 2+1-dimensional QED at both zero and finite temperature is presented by looking at solutions to the Schwinger-Dyson equation. In different kinetic energy regimes we use various numerical and analytic techniques (including an expansion in large flavour number). It is confirmed that, contrary to the case of 3+1 dimensions, there is no dynamical scale symmetry breaking at zero temperature, despite the fact that chiral symmetry breaking can occur dynamically. At finite temperature, such breaking of scale symmetry may take place. Received: 17 August 2000 / Revised version: 24 November 2000 / Published online: 23 January 2001