Generalized bogoliubov transformations in lattice gauge theory with staggered fermions

A transformation is investigated that mixes quarks with composites of N−1 antiquarks in a gauge-invariant way for QCD with gauge group SU (N). An infinite family of identities among fermionic Green functions is derived in the form of a generating functional.     

Progress and bottlenecks in simulating lattice gauge theory with fermions

We present a progress report in lattice gauge theory computer simulations which includes the effects of light, dynamical fermions. Microcanonical and hybrid microcanonical-Langevin alogrithms are presented and discussed. A method for “accelerating” stochastic differential equations and defeating critical slowing down is reviewed. Physics applications such as the thermodynamics of quantum chromodynamics, hierarchal energy scales in unified gauge theories, and the phase diagram of theories with many fermion species are discussed. Prospects for future research are assessed.     

On confinement of fermions in strongly coupled lattice gauge theory

A lattice theory of Fermi fields of massm coupled to gauge fields in the region wherem and the gauge field coupling constantg are large is studied. It is shown that the energy of some states composed of a fermion and a distant antifermion with a string in between grows at least linearly with the distance if 1<g ⁶<m<g ^logg .On leave from Department of Mathematical Methods of Physcis, Warsaw University, Hoa 74, PL 00-682 Warsaw, Poland     

Monte Carlo integration for lattice gauge theories with fermions

A Monte Carlo procedure is constructed for lattice gauge theories with fermions by replacing integration over fermion degrees of freedom in the path integral by conventional integration over effective boson degrees of freedom. The method is applied to gauge theories over two discrete subgroups of SU(2).     

Λ-parameters for asymmetric lattice gauge theories with fermions

Dimensional quantities obtained from Monte Carlo simulations on the lattice depend on the lattice mass parameter, Λ_L. To make a connection with continuum physics, a relationship is needed between Λ_L and the Λ-parameters of the continuum theory. This has been done for the euclidean symmetric lattice by others. However, in order to incorporate finite temperature into Monte Carlo studies, or to study the transition from the euclidean formulation to the hamiltonian formulation of gauge theories, asymmetric lattices (a_s≠a_t) may be used. In this paper, the assymetric calculations are extended and the ratio $\text{Λ}{}_{\mathrm{<mtext>min</mtext>}}\text{Λ}{}_{\mathrm{<mtext>L</mtext>}}$, where Λ_min is the continuum mass parameter in the minimal subtraction scheme, is given to one loop for n_f flavors of Wilson and Susskind massless fermions on an asymmetric four-dimensional lattice for two different asymmetric lattice actions.     

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.     

Improved lattice action for Wilson fermions

An improved lattice action for gauge theories with Wilson fermions is presented.     

Continuum regularization of gauge theory with fermions

The covariant-derivative regularization program is discussed ford-dimensional gauge theory coupled to fermions in an arbitrary representation.     

Variational study of vacuum structure with fermions ind+1 dimensional Hamiltonian lattice gauge theory

The physical vacuum state and general expression for the Hamiltonian ofd+1 dimensional lattice gauge theory are given by incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state. The applications toSU(2) andSU(3) gauge theories in 2+1 and 3+1 dimensions are demonstrated and the fermion condensates \(\left\langle {\bar \psi \psi } \right\rangle \) as functions of 1/g ² are calculated.     

Non-Grassmann formulation of regularized gauge theory with fermions

Regularized continuum gauge theory coupled to quadratic matter simplifies significantly on integration of the matter fields. As an illustration, we discuss in some detail the resulting non-Grassmann formulation of regularized gauge theory with Dirac fermions.     

Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4⁴ lattice. We compare our results for 〈S_eff〉 and $\text{〈}\text{ψ}\text{ψ〉}$ for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈S_eff〉 turns out to be quite small for $\text{κ?}\text{1}\text{8}$.     

Bosonic lattice gauge theory with noise

We apply the recently suggested linear updating algorithm of Kennedy and Kuti to four-dimensional SU(3) bosonic gauge theory with the Wilson action. The change in the action for each link update is estimated stochastically, and we find that the algorithm gives the mean plaquette correctly for reasonable parameter values. Our results indicate that this method should be efficient for Monte Carlo computations with complicated “improved” actions, and they also show the feasibility of using such “noisy” methods to include the dynamical effects of fermions.     

Improved continuum limit lattice action for QCD with wilson fermions

Two possible ways of extending Symanzik's improvement programme to lattice fermions namely improvement to first and second order in the lattice sppacing a are discussed. The corresponding lattice actions for fermions are constructed and tree-level improvement conditions are derived by considering “classical” improvement. The concept of “on-shell” improvement is generalized to the lattice fermions studied here and the free parameters are determined for O(a) and O(a²) on-shell improved actions to all orders of perturbation theory. No evidence is found that the complicated structure of the O(a²) on-shell improved action, especially thearising fermion contact terms can be removed beyond tree level. The effect of terms in the action that explicitly break chiral symmetry and therefore remove the phenomenon of species doubling are investigated by considering the energy-momentum relations of the arising tree-level improved actions. Our main result is that the O(a) improved action is a slightly modified Wilson fermion action can still be written with only nearest-neighbour fermion interactions.     

Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

On the chiral limit in lattice gauge theories with Wilson fermions

The chiral limit κ ? κ _c (β) in lattice gauge theories with Wilson fermions and problems related to near-to-zero (’exceptional’) eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $\tilde m_\pi$ for the calculation of the pseudoscalar mass m _π is proposed which does not suffer from ’divergent’ contributions at κ ? κ _c (β)We conclude that the main contribution to the pion mass comes from larger modes, and ’exceptional’ eigenvalues play no physical role. The behaviour of the subtracted chiral condensate $\left\langle {\bar \psi \psi } \right\rangle _{subt}$ near κ _c (β) is determined. We observe a comparatively large value of $\left\langle {\bar \psi \psi } \right\rangle _{subt} \cdot Z_P^{ - 1}$ , which could be interpreted as a possible effect of the quenched approximation.     

Phase transitions and renormalized structure of lattice gauge theories with fermions

Using recursion relations of the type proposed by Migdal and Kadanoff we discuss the fixed points relevant to the renormalization of lattice gauge theories in four dimensions. The role of the topological excitation for the U(1) case is evaluated.