Terms Of Auxiliary Fields Research Articles

U(1) gauged model of FJ-type chiral boson based on Batalin–Fradkin–Vilkovisky formalism

The BRST quantization of the U(1) gauged model of FJ-type chiral boson for [Formula: see text] and [Formula: see text] are performed using the Batalin–Fradkin–Vilkovisky formalism. BFV formalism converts the second-class algebra into an effective first-class algebra with the help of auxiliary fields. Explicit expressions of the BRST charge, the involutive Hamiltonian, and the preserving BRST symmetry action are given and the full quantization has been carried through. For [Formula: see text], this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess–Zumino term, while for [Formula: see text] the corresponding Lagrangian has the additional new type of the Wess–Zumino term. The spectra in both cases have been analysed and the Wess–Zumino actions in terms of auxiliary fields are identified.

On multifield Born and Born-Infeld theories and their non-Abelian generalizations

Starting from a recently proposed linear formulation in terms of auxiliary fields, we study $n$-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the symmetry properties (including the characteristic self-duality) of the corresponding non-linear theory are manifest as on-shell duality symmetries and depend on the choice of the (homogeneous) manifold spanned by the auxiliary scalar fields and the symplectic frame. By suitably choosing these defining properties of the quadratic Lagrangian, we are able to reproduce some known multi-field Born-Infeld theories and to derive new non-linear models, such as the $n$-field Born theory. We also discuss non-Abelian generalizations of these theories obtained by choosing the vector fields in the adjoint representation of an off-shell compact global symmetry group $K$ and replacing them by non-Abelian, $K$-covariant field strengths, thus promoting $K$ to a gauge group.

Holstein-Hubbard model at half filling: A static auxiliary field study

We study the Holstein-Hubbard model at half filling to explore the ordered phases such as the charge density wave and antiferromagnet. The Coulomb interaction is rewritten in terms of auxiliary fields. By treating the auxiliary fields and phonons as classical, we obtain real space features of the system and transition between the phases from weak to strong coupling. When both interactions are weak, mutual competition between them leads to a metallic phase in an otherwise insulator dominated phase diagram. Spatial correlations induced by thermal fluctuations lead to pseudogap features at intermediate range of coupling.

Quantum Monte Carlo diagonalization for many-fermion systems

In this study we present an optimization method based on the quantum Monte Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich transformation, employed to decompose the interactions in terms of auxiliary fields, we expand the true ground-state wave function. The ground-state wave function is written as a linear combination of the basis wave functions. The Hamiltonian is diagonalized to obtain the lowest energy state using the variational principle within the selected subspace of the basis functions. This method is free from the difficulty known as the negative sign problem. We can optimize a wave function using two procedures. The first procedure is to increase the number of basis functions. The second improves each basis function through the operators ${e}^{\ensuremath{-}\ensuremath{\Delta}\ensuremath{\tau}H}$ using the Hubbard-Stratonovich decomposition. We present an algorithm for the quantum Monte Carlo diagonalization method using a genetic algorithm and the renormalization method. We compute the ground-state energy and correlation functions of small clusters to compare with available data.

Effective quantum variational Monte Carlo study of Hubbard model

It is important to understand the physics of correlated itinerant electron systems characterized by the on-site Coulomb repulsion U . The two-dimensional Hubbard model is one of the simplest models for the description of such correlated systems. The Gutzwiller-projected wave function has been improved by considering effective electron correlation or long-range Jastrow-type correlation. Elaborate extra correlation operators optimize the electron correlation and lower the ground-state energy considerably. The kinetic operator effectively optimizes the Gutzwiller function: ψ λ = e - λ K P G ψ 0 , where K is the kinetic energy term of the Hubbard Hamiltonian and P G is the Gutzwiller operator. The Gutzwiller–Jastrow function is also an well optimized wave function. We have developed a quantum Monte Carlo optimization method for many fermion systems as an intensive extension of effective variational wave function ψ λ . We employ the Hubbard–Stratonovich method to decompose the interactions in terms of auxiliary fields and we use this in an expansion of the true ground-state wave function. The ground-state wave function is written as a linear combination of the basis states for which we diagonalize the Hamiltonian to obtain the lowest energy state.

From stochastic quantization to bulk quantization: Schwinger-Dyson equations and S-matrix

In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. This is advantageous, in particular for gauge theories, because it allows a different type of gauge fixing that avoids the Gribov problem. Traditionally, in this approach, the fictitious 5th time is the analog of computer time in a Monte Carlo simulation of 4-dimensional Euclidean fields. A Euclidean probability distribution which depends on the 5th time relaxes to an equilibrium distribution. However a broader framework, which we call ``bulk quantization", is required for extension to fermions, and for the increased power afforded by the higher symmetry of the 5-dimensional action that is topological when expressed in terms of auxiliary fields. Within the broader framework, we give a direct proof by means of Schwinger-Dyson equations that a time-slice of the 5-dimensional theory is equivalent to the usual 4-dimensional theory. The proof does not rely on the conjecture that the relevant stochastic process relaxes to an equilibrium distribution. Rather, it depends on the higher symmetry of the 5-dimensional action which includes a BRST-type topological invariance, and invariance under translation and inversion in the 5-th time. We express the physical S-matrix directly in terms of the truncated 5-dimensional correlation functions, for which ``going off the mass-shell'' means going from the 3 physical degrees of freedom to 5 independent variables. We derive the Landau-Cutokosky rules of the 5-dimensional theory which include the physical unitarity relation.

Lattice QCD and chiral mesons

The standard QCD action is improved by the addition of irrelevant operators built with chiral composites. An effective Lagrangian is derived in terms of auxiliary fields, which has the form of the phenomenological chiral Lagrangians. Our improved QCD action appears promising for numerical simulations as the pion physics is explicitely accounted for by the auxiliary fields.

Counterterms for linear divergences in real-time classical gauge theories at high temperature

Real-time classical SU( N) gauge theories at non-zero temperature contain linear divergences. We introduce counterterms for these divergences in the equations of motion in the continuum and on the lattice. These counterterms can be given in terms of auxiliary fields that satisfy local equations of motion. We present a lattice model with 6+1D auxiliary fields that for IR-sensitive quantities yields cut-off independent results to leading order in the coupling. Also an approximation with 5+1D auxiliary fields is discussed.