The pair-fluctuation contribution reduces the electrostatic screening length in superconductivity as compared to the normal state. When a conductor possesses a static background charge distribution, superconductivity arises even in the absence of an
explicit pairing interaction, such that the Coulomb repulsion is reduced and the total energy is lowered. We demonstrate that the superconducting gap increases with increased background charge at first, after which the mixing of the Higgs and plasma modes suppresses superconductivity in the pseudogap phase. This indicates that the mechanism may be relevant to the cuprates and iron pnictides. When the background charge is identified with the incoherent component of optical conductivity in the cuprates, our results reproduce the shape, size and position of the superconducting dome with zero free parameters. A superconducting critical temperature of about 1000 K is possible in ion-doped conductors.
We consider a 1+3 dimensional spin system. The spin-wave (magnon) field is described by the O(3) non-linear sigma model with a symmetry-breaking potential. This interacts with a slow spin SU(2) doublet Schrodinger fermion. The interaction is describe
d by a generalized nonperturbative Yukawa coupling, and the self-consistency condition is solved with the aid of a non-relativistic Gribov equation. When the Yukawa coupling is sufficiently strong, the solution exhibits supercriticality and soft confinement, in a way that is quite analogous to Gribovs light-quark confinement theory. The solution corresponds to a new type of spin polaron, whose condensation may lead to exotic superconductivity.
We argue that there is a spontaneously broken rotational symmetry between space-time coordinates and gauge theoretical phases. The dilatonic mode acts as the massive Higgs boson, whose vacuum expectation value determines the gauge couplings. This mec
hanism requires that the quadratic divergences, or tadpoles of the three gauge-theory couplings, unify at a certain scale. We verify this statement, and find that this occurs at Lambda_u ~ 4x10^7 GeV. The tadpole cancellation condition, together with the dilaton self-energy, fixes the value of the unified tadpole coefficient to be 1/[4 ln(Lambda_cut/Lambda_u)]. The observed values of the coupling constants at Lambda_u then implies Lambda_cut ~ 4x10^18 GeV, which is close to the value of the reduced Planck mass MR_Pl=M_Pl/sqrt(8 pi)=2.4 x 10^18 GeV. In other words, by assuming a cutoff at M_Pl or MR_Pl, we are able to obtain predictions for the gauge couplings which agree with the true values to within a few percent. It turns out that this symmetry breaking can only take place if mass is generated with the aid of some other means such as electroweak symmetry breaking. Assuming dynamical symmetry breaking originating at MR_Pl, we obtain M_chi ~ 10^9 GeV, which is not unreasonable but somewhat higher than Lambda_u. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three.
We argue that the general symmetry-breaking pattern in (quasi-)conventional (parity and time-reversal symmetric single-band spin-singlet) superconductivity is given by U(1)_V x U(1)_A -> U(1)_A, where V stands for vector and A stands for axial-vector
, as opposed to the breaking of U(1)_Vequiv U(1)_ele/mag by itself as is commonly thought. This symmetry-breaking pattern implies that there will be a Higgs mode which, together with the Goldstone boson that is absorbed by the photon (Meissner effect), characterize the symmetry-breaking dynamics. We obtain a number of strikingly simple analytical results, which amalgamate the findings of the standard BCS and Ginzburg-Landau theories.
We show that quadratic divergences in top-quark condensation are cancelled when the tadpoles cancel. This latter cancellation is naturally implemented as the cancellation among the top-quark, Goldstone and Higgs contributions. We also calculate the b
osonic correction terms to Gribovs mass formula for the Higgs boson. These reduce the prediction for M_H from 167 GeV to 132 GeV. The tadpole cancellation condition by itself is an independent condition on the mass of the Higgs boson which, in Gribovs U(1)_Y scenario, yields M_H approx 117 GeV with large theoretical uncertainty. More generally, we are able to obtain all three masses, M_W, m_t and M_H, in 100 MeV to 10 TeV energy range as a function of the cut-off scale and the gauge couplings only.
From general considerations of spin-symmetry breaking associated with (anti-)ferromagnetism in metallic systems with Coulomb repulsion, we obtain interesting and simple all-order rules involving the ratios of the densities of states. These are exact
for ferromagnetism under reasonable conditions, and nearly exact for anti-ferromagnetism. In the case of ferromagnetism, the comparison with the available experimental and theoretical numbers yields favourable results.
We discuss the consequences of spin current conservation in systems with SU(2) spin symmetry that is spontaneously broken by partial magnetic order, using a momentum-space approach. The long-distance interaction is mediated by Goldstone magnons, whos
e interaction is expressed in terms of the electron Greens functions. There is also a Higgs mode, whose excitation energy can be calculated. The case of fast magnons obeying linear dispersion relation in three spatial dimensions admits nonperturbative treatment using the Gribov equation, and the solution exhibits singular behaviour which has an interpretation as a tower of spin-1 electronic excitations. This occurs near the Mott insulator state. The electrons are more free in the case of slow magnons, where the perturbative corrections are less singular at the thresholds. We then turn our attention to the problem of high-Tc superconductivity, through the discussion of the stability of the antiferromagnetic ground state in two spatial dimensions. We argue that this is caused by an effective mixing of the Goldstone and Higgs modes, which in turn is caused by an effective Goldstone-boson condensation. The instability of the antiferromagnetic system is analyzed by studying the non-perturbative behaviour of the Higgs boson self-energy using the Dyson-Schwinger equations.
We discuss the stability of the antiferromagnetic ground state in two spatial dimensions. We start with a general analysis, based on Gribovs current-conservation techniques, of the bosonic modes in systems with magnetic order. We argue that the Golds
tone $phi$ and Higgs $h$ modes mix in antiferromagnetic systems, and this leads to an effective $hhphi$ three-point interaction. We then analyze the instability of the antiferromagnetic system in two spatial dimensions by studying the non-perturbative behaviour of the Higgs boson self-energy using the Dyson--Schwinger equations. The ground state turns out to be unstable for all values of the three-point coupling. We interpret this as being due to the formation of a (high-$T_C$) superconducting condensate. The carrier doping dependence of the energy gap has a general behaviour that is consistent with high-$T_C$ superconductivity. Superconductivity co-exists with antiferromagnetic order for large magnetization, or small doping.
We present a derivation of the Gribov equation for the gluon/photon Greens function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Tr ln D(q), which we interpret as the gauge-boson `self-loop. By considering th
e higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solving this equation, we obtain the non-perturbative running coupling in both QCD and QED. In the case of QCD, alpha_S has a singularity in the space-like region corresponding to super-criticality, which is argued to be resolved in Gribovs light-quark confinement scenario. For the QED coupling in the UV limit, we obtain a propto Q^2 behaviour for space-like Q^2=-q^2. This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.
This paper has been withdrawn by the author, due to obsolete reference [4], insufficient discussion in sec. 4, and major conceptual error in sec. 5.
