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M. Faber

Publications and source records attributed to M. Faber.

At least 55 records · Page 3Linked to original sources
arXiv2003

Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model

A BCS-type wave function describes the ground state of the massless Thirring model in the chirally broken phase. The massless Thirring model with fermion fields quantized in the chirally broken phase bosonizes to the quantum field theory of the free massless (pseudo)scalar field (Eur. Phys. J. C20, 723 (2001)). The wave functions of the ground state of the free massless (pseudo)scalar field are obtained from the BCS-type wave function by averaging over quantum fluctuations of the Thirring fermion fields. We show that these wave functions are orthogonal, normalized and non-invariant under shifts of the massless (pseudo)scalar field. This testifies the spontaneous breaking of the field-shift symmetry in the quantum field theory of a free massless (pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude calculated for the bosonized BCS-type wave functions coincides with the generating functional of Green functions defined only by the contribution of vibrational modes (Eur. Phys. J. C 24, 653 (2002)) . This confirms the assumption that the bosonized BCS-type wave function is defined by the collective zero-mode (hep-th/0212226). We argue that the obtained result is not a counterexample to the Mermin-Wagner-Hohenberg and Coleman theorems.

hep-th↗
arXiv2002

Quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-time as a test for the massless Thirring model

We analyse different approaches to the description of the quantum field theory of a free massless (pseudo)scalar field defined in 1+1-dimensional space-time which describes the bosonized version of the massless Thirring model. These are (i) axiomatic quantum field theory, (ii) current algebra and (iii) path-integral. We show that the quantum field theory of a free massless (pseudo)scalar field defined on the class of Schwartz's test functions S_0(R^2) connects all these approaches. This quantum field theory is well-defined within the framework of Wightman's axioms and Wightman's positive definiteness condition. The physical meaning of the definition of Wightman's observables on the class of test functions from S_0(R^2) instead of S(R^2), as required by Wightman's axioms, is the irrelevance of the collective zero-mode related to the collective motion of the ``center of mass'' of the free massless (pseudo)scalar field, which can be deleted from the intermediate states of correlation functions (Eur. Phys. J. C 24, 653 (2002)). In such a theory the continuous symmetry, induced by shifts of the massless (pseudo)scalar field, is spontaneously broken and there is a non-vanishing spontaneous magnetization. The obtained results are discussed in connection with Coleman's theorem asserting the absence of Goldstone bosons and spontaneously broken continuous symmetry in quantum field theories defined in 1+1-dimensional space-time.

hep-th↗
arXiv2002

Massless Thirring fermion fields in the boson field representation

We show that the boson field representation of the massless fermion fields, suggested by Morchio, Pierotti and Strocchi in J. Math. Phys. 33, 777 (1992) for the operator solution of the massless Thirring model, agrees completely with the existence of the chirally broken phase in the massless Thirring model revealed in EPJC 20, 723 (2001) and hep-th/0112183, when the free massless boson fields are described by the quantum field theory, free of infrared divergences in 1+1-dimensional space-time, formulated in hep-th/0112184 and hep-th/0204237.

hep-th↗
arXiv2002

Analytical study of low temperature phase of 3D LGT in the plaquette formulation

We develop an analytical approach for non-abelian gauge models within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and show how it can be modified in such a way that each non-abelian Bianchi identity contains two connectors instead of four. Using this representation we construct the low-temperature expansion for U(1) and SU(N) models on a finite lattice and discuss its uniformity in the volume. Next, we derive a dual representation for the 't Hooft loop in the SU(2) model and describe monopoles in the maximal axial gauge.

hep-lat↗
arXiv2002

On free massless (pseudo)scalar quantum field theory in 1+1-dimensional space-time

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that a continuous symmetry of (pseudo)scalar field translations is spontaneously broken. Goldstone bosons appear as quanta of a free massless (pseudo)scalar field. We show that the main inequality between vacuum expectation values of certain operators which has been used for the derivation of the Mermin-Wagner-Hohenberg theorem is fulfilled in the quantum field theory of a free massless (pseudo)scalar field free of infrared divergences.

hep-th↗
arXiv2002

On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin-Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows to identify the topological charge in the sine-Gordon model with the fermion number.

hep-th↗
arXiv2002

Status of center dominance in various center gauges

We review arguments for center dominance in center gauges where vortex locations are correctly identified. We introduce an appealing interpretation of the maximal center gauge, discuss problems with Gribov copies, and a cure to the problems through the direct Laplacian center gauge. We study correlations between direct and indirect Laplacian center gauges.

hep-lat↗
arXiv2001

On the solution of the massless Thirring model with fermion fields quantized in the chiral symmetric phase

Correlation functions of fermionic fields described by the massless Thirring model are analysed within the operator formalism developed by Klaiber and the path-integral approach with massless fermions quantized in the chiral symmetric phase. We notice that Klaiber's composite fermion operators possess non-standard properties under parity transformations and construct operators with standard parity properties. We find that Klaiber's parameterization of a one-parameter family of solutions of the massless Thirring model is not well defined, since it is not consistent with the requirement of chiral symmetry. We show that the dynamical dimensions of correlation functions depend on an arbitrary parameter induced by ambiguities of the evaluation of the chiral Jacobian. A non-perturbative renormalization of the massless Thirring model is discussed. We demonstrate that the infrared divergences of Klaiber's correlation functions can be transferred into ultra-violet divergences by renormalization of the wave function of fermionic fields. This makes Klaiber's correlation functions non-singular in the infrared limit. We show that the requirement of non-perturbative renormalizability of the massless Thirring model fixes a free parameter of the path-integral approach. In turn, the operator formalism is inconsistent with non-perturbative renormalizability of the massless Thirring model. We carry out a non-perturbative renormalization of the sine-Gordon model and show that it is not an asymptotically free theory as well as the massless Thirring model. We calculate the fermion condensate by using the Fourier transform of the two-point Green function of massless Thirring fermion fields quantized in the chiral symmetric phase.

hep-th↗
arXiv2001

Center vortex model for the infrared sector of Yang-Mills theory

A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortices represented by (closed) random surfaces, is presented. The model quantitatively describes both confinement (including the finite-temperature transition to a deconfined phase) and the topological susceptibility of the Yang-Mills ensemble. A first (quenched) study of the spectrum of the Dirac operator furthermore yields a behavior for the chiral condensate which is compatible with results obtained in lattice gauge theory.

hep-lat↗
arXiv2001

Center Dominance Recovered: Direct Laplacian Center Gauge

We introduce a variation of direct maximal center gauge fixing: the "direct Laplacian" center gauge. The new procedure consists of first fixing to the Laplacian adjoint Landau gauge, followed by overrelaxation to the nearby Gribov copy of the direct maximal center gauge. Certain shortcomings of maximal center gauge, associated with Gribov copies, are overcome in the new gauge, in particular center dominance is recovered.

hep-lat↗
arXiv2001

On the D-wave state component of the deuteron in the Nambu-Jona-Lasinio model of light nuclei

The D-wave state component of the neutron-proton bound state in the deuteron is calculated in the Nambu-Jona-Lasinio model of light nuclei - the relativistically covariant quantum field theoretic approach to the description of low-energy nuclear forces. The theoretical value of the fraction of the D-wave state relative to the S-wave state is equal to eta_d = 0.0238. This agrees well with the phenomenological value eta_d = 0.0256(4) quoted by Kamionkowski and Bahcall (ApJ. 420, 884 (1994)).

nucl-th↗
arXiv2001

Direct Laplacian Center Gauge

We introduce a variation of direct maximal center gauge fixing: the ``direct Laplacian'' center gauge. The new procedure overcomes certain shortcomings of maximal center gauge, associated with Gribov copies, that were pointed out by Bornyakov et al. in hep-lat/0009035.

hep-lat↗
arXiv2001

Topological Susceptibility of Yang-Mills Center Projection Vortices

The topological susceptibility induced by center projection vortices extracted from SU(2) lattice Yang-Mills configurations via the maximal center gauge is measured. Two different smoothing procedures, designed to eliminate spurious ultraviolet fluctuations of these vortices before evaluating the topological charge, are explored. They result in consistent estimates of the topological susceptibility carried by the physical thick vortices characterizing the Yang-Mills vacuum in the vortex picture. This susceptibility is comparable to the one obtained from the full lattice Yang-Mills configurations. The topological properties of the SU(2) Yang-Mills vacuum can thus be accounted for in terms of its vortex content.

hep-lat↗
arXiv2001

Remarks on the Gribov Problem in Direct Maximal Center Gauge

We review the equivalence of maximal center gauge fixing to the problem of finding the best fit, to a given lattice gauge field, by a thin vortex configuration. This fit is necessarily worst at the location of P-plaquettes. We then compare the fits achieved in Gribov copies generated by (i) over-relaxation; (ii) over-relaxation after Landau gauge preconditioning; and (iii) simulated annealing. Simulated annealing yields the best fit if all links on the lattice are included, but the situation changes if we consider only the lattice volume exterior to P-plaquettes. In this exterior region, the fit is best for Gribov copies generated by over-relaxation, and worst for Gribov copies generated after Landau gauge preconditioning. The two fitting criteria (including or not including the P-plaquettes) yield string tensions differing by -34% to +20% respectively, relative to the full string tension. Our usual procedure (``quenched minimization'') seems to be a compromise between these criteria, and yields string tensions at an intermediate value close to the full string tension.

hep-lat↗
arXiv2000

On the path integral representation for Wilson loops and the non-Abelian Stokes theorem II

This paper is a revised version of our recent publication Faber et al., Phys. Rev. D62 (2000) 025019, hep-th/9907048. The main revision concerns the expansion into group characters that we have used for the evaluation of path integrals over gauge degrees of freedom. In the present paper we apply the expansion recommended by Diakonov and Petrov in hep-lat/0008004. Our former expansion was approximate and in the region of the particular values of parameters violated the completeness condition by 1.4%. We show that by using the expansion into characters recommended by Diakonov and Petrov in hep-lat/0008004 our previous results are retained and the path integral over gauge degrees of freedom for Wilson loops derived by Diakonov and Petrov (Phys. Lett. B224 (1989) 131 and hep-lat/0008004) by using a special regularization is erroneous and predicts zero value for the Wilson loop. We give comments on the paper hep-lat/0008004.

hep-th↗
arXiv2000

Dynamics of low-energy nuclear forces and Solar Neutrino Problems in the Nambu-Jona-Lasinio model of light nuclei

The Solar Neutrino Problems (SNP's) are analysed in the Nambu-Jona-Lasinio model of light nuclei. In this model a possible clue to the solution of the SNP's is in the reduction of the solar neutrino fluxes relative to the predicted by the Standard Solar Model through the decrease of the solar core temperature. The former can be realized through the enhancement of the astrophysical factor for the solar proton burning. The enhancement the upper bound of which is restricted by the helioseismological data goes dynamically via the contribution of the nucleon tensor current coupled to the deuteron. The agreement of the reduced solar neutrino fluxes with the experimental data can be reached within a scenario of vacuum two-flavour neutrino oscillations without a fine tuning of the neutrino-flavour oscillation parameters. In the Nambu-Jona-Lasinio model of light nuclei an enhancement of the astrophysical factor for the solar proton burning entails a change of the cross sections for neutrino and anti-neutrino disintegration of the deuteron at low energies. This provides a theoretical foundation for a new check of a value of the astrophysical factor in terrestrial laboratories.

astro-ph↗
arXiv2000

Center Vortices at Strong Couplings

A long-range effective action is derived for strong-coupling lattice SU(2) gauge theory in D=3 dimensions. It is shown that center vortices emerge as stable saddlepoints of this action.

hep-lat↗