Presence Of Fermions Research Articles

Gauge theories with a layered phase

We study Abelian gauge theories with anisotropic couplings in 4 + D dimensions. A layered phase is present, in the absence as well as in the presence of fermions. A line of second order transitions separates the layered from the Coulomb phase, if D ⩽ 3.

Gauge theories with a layered phase

The mean field theory of gauge theories with anisotropic couplings shows that they possess a layered phase, in addition to the usual confining and Coulomb phases. We find that the layered to Coulomb phase transition is second order in the absence, as well as in the presence of fermions. This is supported by Monte Carlo simulations and leads to the possibility of defining sensible models with domain wall fermions.

A non-perturbative approach to the instability of the vacuum in the presence of fermions

We discuss in detail the possibility that states of fermion number one, consisting of the scalar field in its ground state and the occupancy of the zero-momentum plane-wave one for the fermionic quantum, may be unstable to the formation of a kink—antikink pair each carrying a fermion number of one-half. As a matter of fact we restrict ourselves to a bidimensional model which considers the Φ 4 theory coupled to fermions by means of a Yukawa term. In particular we take advantage of the well-known bosonization procedure so that the scalar—fermion system becomes in the sequel a pure scalar model. Eventually we consider non-perturbative methods on the lattice, thus going beyond the classical treatments used by other authors.

Sphaleron barrier in the presence of fermions.

We calculate the minimal energy path over the sphaleron barrier in the pre\-sen\-ce of fermions, assuming that the fermions of a doublet are degenerate in mass. This allows for spherically symmetric ans\"atze for the fields, when the mixing angle dependence is neglected. While light fermions have little influence on the barrier, the presence of heavy fermions ($M_F \sim$ TeV) strongly deforms the barrier, giving rise to additional sphalerons for very heavy fermions ($M_F \sim$ 10 TeV). Heavy fermions form non-topological solitons in the vacuum sector.

Callan-Symanzik and renormalization group equation in a model with spontaneous breaking of the symmetry

In a simple model with spontaneous breaking of the axialU(1)-symmetry via the Higgs mechanism we construct the Callan-Symanzik and renormalization group equation in the Goldstone mode. Aiming at questions of renormalization group improvement and the like we compare two different parametrizations the model can be described with. We show that in the presence of fermions a β-function for a physical mass or some equivalent of it enters unavoidably the Callan-Symanzik equation, which leads to significant differences to the symmetric theory starting with two loops. On the other hand in the asymptotic region the equivalence to the symmetric theory is manifest.

WEAK SKYRMIONS AS BAGS

It has been discussed that exotic objects might exist in the familiar Weinberg-Salam model. In particular skyrmions built out of the Higgs sector are examined. It is argued that the presence of fermions may give rise to some intriguing effects, and, indeed, may be responsible for the circumvention of usual arguments for the non-existence of these objects. The existence of a fourth, heavier generation would improve the chances for the existence of such weak skyrmion bags.

FERMIONS IN THE TOPOLOGICAL EXPANSION OF MATRIX MODELS

The hermitian matrix model with quartic interaction is studied in presence of fermionic variables. We obtain the contribution to the free energy due to the presence of fermions. The first two terms beyond the planar limit are explicitly found for all values of the coupling constant g. These terms represent the solution of the counting problem for vacuum diagrams with one or two fermionic loops.

Renormalized Bose condensation in the presence of fermions.

Bose condensation of a dilute charged Bose gas in contact with a dense Fermi liquid is examined. The particles have hard cores and hop on a lattice. It is argued that a ``Bose metal phase,'' i.e., a phase with vanishing condensate fraction, is unlikely to exist in this problem at zero temperature. However very strong renormalizations of the properties of the Bose system occur when the boson band is narrower than the fermion band. We find that the condensate fraction at zero temperature is suppressed by a factor 4(W/${\mathit{w}}_{\mathit{b}}$${)}^{2}$ exp(-W/${\mathit{w}}_{\mathit{b}}$) in two dimensions over Gutzwiller-type variational estimates. Here, ${\mathit{w}}_{\mathit{b}}$ and W are the boson and fermion half-band-widths, respectively. There is a similar reduction in the transition temperature. Thus the possibility that high-${\mathit{T}}_{\mathit{c}}$ superconductors are Bose metals in their normal states cannot be excluded on the basis of present experimental or theoretical evidence.

Dynamics of non-integrable phases and gauge symmetry breaking

On a multiply-connected space the non-integrable phase factor P exp(ig ∫ A μ dx μ }, a pathordered line integral along a non-contractable loop, becomes a dynamical degree of freedom in gauge theory. The dynamics of such non-integrable phases are examined in detail with the most general boundary condition for gauge fields and fermions. Sometimes the dynamics of the non-integrable phases compensate the arbitrariness in the boundary condition imposed, leading to the same physics results. In other cases the dynamics of the non-integrable phases induce spontaneous breaking of non-Abelian gauge symmetry. In other words the physically realized symmetry of the system differs from, and can be either greater or smaller than, the symmetry of the boundary condition. The effective potential for the non-integrable phases in the SU( N) gauge theory on S 1 ⊗ R 1, d−2 is computed in the one-loop approximation. It is shown that the gauge symmetry is dynamically broken in the presence of fermions in the adjoint representation, depending on the value of the boundary condition parameter.

Fermions and the Gaussian effective potential.

The effect of fermions on the Gaussian effective potential is studied in a variety of fermion-scalar models in 2, 3, and 4 dimensions. Both gphipsi-barpsi and gphi/sup 2/psi-barpsi couplings are considered. Stability requires the bare g to be infinitesimal; g/sub B/ /sup 2/ = G/sup 2//I/sub 0/ with I/sub 0/ a divergent integral. This contrasts with large-N studies in which g/sub B/ remains finite. The presence of fermions encourages spontaneous symmetry breaking, and in 3+1 dimensions the fermions destabilize the already ''precarious'' phi/sup 4/ theory.

Analytic structure of gauge fields

The analytic structure of gauge fields in the presence of fermions is studied in arbitrary symmetry. A Hamiltonian formalism is developed which relates Cauchy-Riemann equations to the symmetry. The formalism is applied to three problems in (2+1)-dimensional Euclidean space: (1) a free fermion, (2) a fermion interacting with a massless scalar field, and (3) a fermion interacting with a vector field. We find that the Hamiltonian for the free fermion is analytic and single-valued in a finite region of momentum space. With the addition of an auxiliary field, the Hamiltonian can be analytic in the entire momentum space. The scalar field then acquires spin-dependent coordinates by interaction with the fermion; the interactions break the Abelian symmetry ofφ so thatφ →φ 1∼ 1/(x1 −-im 1 −1 (x1 −-im 1 −1 ), wherem 1 are spin-dependent and multivalued. There are four solutions for each chirality eigenvalue of the fermion. For spinless fermionsφ gives the Jackiw-Nohl-Rebbi solution and is separable into Coulomb-like 1/x analytic functions on the first and fourth quadrants. For a vector field the results are similar except that the coordinates are not spindependent or multivalued; interactions break the initial symmetry andA μ(x μ)→A μ 1 (x μ) and theA μ 1 have a non-Abelian algebra. Thel indices represent directions fixed by spin matrices in a spin-dependent color space.

Localization of the dyon charge.

We consider three possible expressions for the dyon charge in the presence of fermions. We find that although none of them fully admit an interpretation as a localized charge, one expression may be identified as the core charge under suitable conditions. Comparison with Callan's expressions are also made.

Renormalizability of gauge theories for external-symmetry groups

Gauge theories for external-symmetry groups contain Yang-Mills fields which have nonminimal couplings to fermions. We show that, to the one-loop level, these theories are renormalizable without the presence of fermions, but not renormalizable with fermions.

Fractional charge and anomalous commutators

Non-integer charges on topological objects in the presence of fermions are further investigated. The connections with anomalous commutators is discussed. The reason for the identical results in two dimensional solitons and four dimensional monopoles is pointed out.

Numerical simulations of quantum chromodynamics

A previously proposed method to perform Monte Carlo simulations with dynamical fermions is applied to lattice QCD. The main features of the computational technique are reviewed and results for some selected quantities, such as the average plaquette action and the quark condensate 〈 ψψ〉 are presented. Both the dependence on the quark mass and on the number of flavors are considered. An estimate of the scale parameter in the presence of fermions is given.

Phases of renormalized lattice gauge theories with fermions

Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U(1) and SU(2) case. We determine the renormalized trajectories and the phases of the theory.

Fermions and vortex solutions in Abelian and non-Abelian gauge theories

The interaction of fermions with an extended vortex solution of the Higgs model is investigated. It is found that this interaction has a long-range inverse-square tail. It is caused by the coupling of the fermion angular momentum with the vortex gauge field itself. The fermion-vortex bound states present at the threshold and the fermion-vortex scattering are studied. The scattering phase shifts and the Jost functions are obtained for large and small fermion momenta as well as the low-energy cross section which diverges at zero momentum. The quantum field theory in the one-vortex sectors is developed. It is found that, in the presence of fermions, a vortex with an even (odd) number of flux quanta has a half-integer (integer) fermionic number. It follows that a two-quantum vortex is stable. Finally, the stable vortex solution of an SU(2) Higgs model is investigated. The appropriate ansatz for the field is given and radial equations are discussed. It is shown that the interaction of a vortex with any nonsinglet particle has a long-range inverse-square tail.