Narrow Results

We describe a classical Schwinger-type model as a study of the projective modules over the algebra of complex-valued functions on the sphere. On these modules, classified by π₂(S²), we construct hermitian connections with values in the universal differential envelope. Instead of describing matter by the usual Dirac spinors yielding the standard Schwinger model on the sphere, we apply the Connes–Lott program to the Hilbert space of complexified inhomogeneous forms with its Atiyah–Kähler structure. This Hilbert space splits in two minimal left ideals of the Clifford algebra preserved by the Dirac–Kähler operator D=i(d-δ). The induced representation of the universal differential envelope, in order to recover its differential structure, is divided by the unwanted differential ideal and the obtained quotient is the usual complexified de Rham exterior algebra with Clifford action on the "spinors" of the Hilbert space. The subsequent steps of the Connes–Lott program allow to define a matter action, and the field action is obtained using the Dixmier trace which reduces to the integral of the curvature squared.

The Schwinger model with N_f ≥ 2 flavors is a simple example for a fermionic model with zero chiral condensate Σ (in the chiral limit). We consider numerical data for two light flavors, based on simulations with dynamical chiral lattice fermions. We test properties and predictions that were put forward in the recent literature for models with Σ = 0, which include IR conformal theories. In particular, we probe the decorrelation of low lying Dirac eigenvalues, and we discuss the mass anomalous dimension and its IR extrapolation. Here, we encounter subtleties, which may urge caution with analogous efforts in other models, such as multi-flavor QCD.

We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly.

The (1+1)-dimensional bosonized Schwinger model with a generalized gauge-invariant regularization has been studied in a noncommutative scenario. The original commutative model with the indicated regularization revealed the transition from confinement to deconfinement of the fermion.¹⁰ We show that though the introduction of spacetime noncommutativity gives rise to new features in the confinement scenario, it does not affect the deconfining limit.

We carry out an investigation imposing a chiral constraint in the phase space of vector and axial-vector Schwinger model. We find that resulting models become identical to a gauge non-invariant model which was obtained by the imposition of chiral constraint in the phase space of in Chiral Schwinger model with the parameter-free Faddeevian anomaly. Three different models having different types of interaction between the matter and gauge field become indistinguishable under a chiral constraint at the quantum mechanical level. The resulting gauge non-invariant model has an equivalent gauge-invariant version in the same phase space that can be identified with the vector Schwinger model.

The light-front Schwinger model in the bosonized form is analyzed focusing on its global properties. We point out that the gauge invariance of the original fermionic form of the model is lost after bosonization. Consequently, the previously found theta-vacuum structure based on the residual large gauge transformation is actually not an intrinsic property of the bosonized form of the model. We analyze the corresponding field equations without any “gauge fixing” in both the light-front and space-like (“instant-form”) versions of the model and find the coinciding results: the axial-vector anomaly is automatically present and the spectrum of the model is given by a massive boson with the mass $e^2/\pi$. Finally, we characterize and critically assess properties of the bosonized LF Schwinger model, found in the previous studies.

We solve the massless Schwinger model exactly in Hamiltonian formalism on a circle. We construct physical states explicitly and discuss the role of the spectral flow and nonperturbative vacua. Different thermodynamical correlation functions are calculated and after performing the analytical continuation are compared with the corresponding expressions obtained for the Schwinger model on the torus in Euclidean path integral formalism obtained before.

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an ansatz in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli–Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.

Propagator for spinning particle described in the Feshbach–Villars formalism is set up using fermionic coherent state path integral. The fermionization of the charge-spin symmetry is presented following the Schwinger recipe. The explicit calculations are done in the free case and magnetic interaction using the Foldy–Wouthuysen tranformation. The spectrum and wave functions are deduced.

Propagator for spinning particle described in the Feshbach–Villars formalism is set up using the bosonic coherent state path integral. The boson model for the charge-spin symmetry is presented following the Schwinger recipe. The calculations are explicitly evaluated in the case of the step potential. The perturbation technique is used and the series are exactly summed.

We study the Schwinger Model on the null-plane using the Dirac method for constrained systems. The fermion field is analyzed using the natural null-plane projections coming from the γ-algebra and it is shown that the fermionic sector of the Schwinger Model has only second class constraints. However, the first class constraints are exclusively of the bosonic sector. Finally, we establish the graded Lie algebra between the dynamical variables, via generalized Dirac bracket in the null-plane gauge, which is consistent with every constraint of the theory.

We address a recent puzzling result from the LHC: the jet fragmentation functions measured in Pb–Pb and pp collisions appear very similar in spite of a large medium-induced energy loss (we will call this jet fragmentation scaling (JFS)). To model the real-time nonperturbative effects in the propagation of a high energy jet through the strongly coupled QCD matter, we adopt an effective dimensionally reduced description in terms of the (1+1) quasi-Abelian–Schwinger theory. This theory is exactly soluble at any value of the coupling and shares with QCD the properties of dynamical generation of "mesons" with a finite mass and the screening of "quark" charge that are crucial for describing the transition of the jet into hadrons. We find that this approach describes quite well the vacuum jet fragmentation in e⁺e^- annihilation at z≥0.2 at jet energies in the range of the LHC heavy ion measurements (z is the ratio of hadron and jet momenta). In QCD medium, we find that the JFS is reproduced if the mean free path λ of the jet is short, λ≤0.3 fm, which is in accord with the small shear viscosity inferred from the measurements of the collective flow. The JFS holds since at short mean free path the quantum interference (analogous to the Landau–Pomeranchuk–Migdal (LPM) effect in QED) causes the produced mesons to have low momenta p~m, where m≃0.6 GeV is the typical meson mass. Meanwhile the induced jet energy loss at short mean free path is much larger than naively expected in string models.

The Schwinger model of nuclear fusion extended with account of localized anharmonic vibrations (LAV) has been applied to the nuclear reaction presumably taking place in the metal hydrides/deuterides. LAV excited in NiH lattice can enhance the fusion rate by 25 orders of magnitude. New method of the low-temperature catalysis of low energy nuclear reactions (LENR) is proposed, which is based on the excitation of LAV in solids by Bremsstrahlung gamma and Characteristic X-rays produced by accelerated electrons hitting a metallic converter. The main advantage of the high-frequency electromagnetic irradiation is its deep penetration into the reactor material as compared to the electrons of the same energies. Upon entering the metal hydride/deuteride lattice, Characteristic X-rays are converted to the electrons of the same energies throughout the crystal bulk due to the photoelectric effect. The keV electrons produced in this way interact with heavy (metal) and light (H/D) ions resulting in significant displacements of the light ions while leaving the heavy metal ions essentially unperturbed. In this way, it is possible to excite LAV in the H/D sub-lattice in the whole volume of fuel mixture, which act as catalysts of LENR due to the time-periodic modulation of the potential wells, in which protons or deuterons are trapped. Experimental evidence of irradiation effect on the rate of chemical and nuclear reactions in solids is discussed and new experiments based on the present method are proposed.

Recently computational resource of quantum computers sounds growing well. In this article, we discuss how we can apply this development to numerically simulate quantum field theories. In contrast to the conventional approach by (Marlov chain) Monte Carlo method suffering from the infamous sign problem, we work in Hamilton formalism and adopt quantum algorithms which do not rely on Monte Carlo sampling. After brief discussion on how to put quantum field theories on quantum computers, we present our recent numerical results on the charge-q Schwinger model, where q is an electric charge of a Dirac fermion. We observe an exotic phenomena such as negative string tension behavior in potential between heavy charged particles which essentially come from presense of non-small θ-angle.