Nonperturbative solution of the Nonconfining Schwinger Model with a generalized regularization

Nonconfining Schwinger Model [AR] is studied with a one parameter class of kinetic energy like regularization. It may be thought of as a generalization over the regularization considered in [AR]. Phasespace structure has been determined in this new situation. The mass of the gauge boson acquires a generalized expression with the bare coupling constant and the parameters involved in the regularization. Deconfinement scenario has become transparent at the quark-antiquark potential level.Comment: 13 pages latex fil

Chiral Bosons Through Linear Constraints

We study in detail the quantization of a model which apparently describes chiral bosons. The model is based on the idea that the chiral condition could be implemented through a linear constraint. We show that the space of states is of indefinite metric. We cure this disease by introducing ghost fields in such a way that a BRST symmetry is generated. A quartet algebra is seen to emerge. The quartet mechanism, then, forces all physical states, but the vacuum, to have zero norm.Comment: 9 page

Canonical Quantization of the Maxwell-Chern-Simons Theory in the Coulomb Gauge

The Maxwell-Chern-Simons theory is canonically quantized in the Coulomb gauge by using the Dirac bracket quantization procedure. The determination of the Coulomb gauge polarization vector turns out to be intrincate. A set of quantum Poincar\'e densities obeying the Dirac-Schwinger algebra, and, therefore, free of anomalies, is constructed. The peculiar analytical structure of the polarization vector is shown to be at the root for the existence of spin of the massive gauge quanta.The Coulomb gauge Feynman rules are used to compute the M\"oller scattering amplitude in the lowest order of perturbation theory. The result coincides with that obtained by using covariant Feynman rules. This proof of equivalence is, afterwards, extended to all orders of perturbation theory. The so called infrared safe photon propagator emerges as an effective propagator which allows for replacing all the terms in the interaction Hamiltonian of the Coulomb gauge by the standard field-current minimal interaction Hamiltonian.Comment: 21 pages, typeset in REVTEX, figures not include

Whirling Waves and the Aharonov-Bohm Effect for Relativistic Spinning Particles

The formulation of Berry for the Aharonov-Bohm effect is generalized to the relativistic regime. Then, the problem of finding the self-adjoint extensions of the (2+1)-dimensional Dirac Hamiltonian, in an Aharonov-Bohm background potential, is solved in a novel way. The same treatment also solves the problem of finding the self-adjoint extensions of the Dirac Hamiltonian in a background Aharonov-Casher

Duality Symmetry in the Schwarz-Sen Model

The continuous extension of the discrete duality symmetry of the Schwarz-Sen model is studied. The corresponding infinitesimal generator $Q$ turns out to be local, gauge invariant and metric independent. Furthermore, $Q$ commutes with all the conformal group generators. We also show that $Q$ is equivalent to the non---local duality transformation generator found in the Hamiltonian formulation of Maxwell theory. We next consider the Batalin--Fradkin-Vilkovisky formalism for the Maxwell theory and demonstrate that requiring a local duality transformation lead us to the Schwarz--Sen formulation. The partition functions are shown to be the same which implies the quantum equivalence of the two approaches.Comment: 10 pages, latex, small changes, final version to appear in Phys. Rev.

Chiral bosons and improper constraints

We argue that a consistent quantization of the Floreanini-Jackiw model, as a constrained system, should start by recognizing the improper nature of the constraints. Then each boundary conditon defines a problem which must be treated sparately. The model is settled on a compact domain which allows for a discrete formulation of the dynamics; thus, avoiding the mixing of local with collective coordinates. For periodic boundary conditions the model turns out to be a gauge theory whose gauge invariant sector contains only chiral excitations. For antiperiodoc boundary conditions, the mode is a second-class theory where the excitations are also chiral. In both cases, the equal-time algebra of the quantum energy-momentum densities is a Virasoro algebra. The Poincar\'e symmetry holds for the finite as well as for the infinite domain.Comment: 13 pages, Revtex file, IF.UFRGS Preprin

The measurement of muon g−2 at Fermilab

The Muon g −2 Experiment at Fermilab (E989) was built to repeat and improve the previous E821 Experiment at Brookhaven National Laboratory (BNL), aiming to reduce the experimental error by a factor of 4 to the final accuracy of 140 parts per billion (ppb). On April 7th, 2021, the E989 collaboration published the first result based on the first year of data taking (Run-1), measuring aμ = 0.001 165 920 40(54) with a precision of 460 ppb. The measured value is consistent with the BNL measurement and strengthens the long-standing tension with the data-driven SM prediction to a combined discrepancy of 4.2σ. On the theory side, however, new efforts involving lattice-QCD techniques are starting to question the current consensus on the theoretical prediction, demanding new improvements on both the experimental and theoretical sides. The Muon g−2 Experiment at Fermilab has now concluded its sixth and final year of data taking, and a new result based on the Run-2 and Run-3 data was published in August 2023. This paper briefly describes the Muon g − 2 Experiment at Fermilab and its current status

The precision measurement of the muon g−2 at Fermilab

The Muon g − 2 Experiment at Fermilab aims to measure the magnetic anomaly of the muon with the unprecedented precision of 140 parts per billion. In April 2021, the collaboration published the first measurement based on the first year of data collection, which was found to be consistent with the previous experiment at Brookhaven. The new global average of the experimental measurements strengthens the long-standing tension with the data-driven Standard Model prediction to a combined discrepancy of 4.2o. On the theory side, however, recent improvements in the theoretical calculation of the hadronic contribution based on Lattice-QCD techniques are introducing new tensions on the value predicted by the theory. The Muon g−2 Experiment at Fermilab has now concluded its sixth and final year of data taking and a new result based on the Run-2 and Run-3 data was published in August 2023. This paper briefly describes the precision measurement conducted by the Muon g − 2 Experiment at Fermilab and its current status

Path Integral Approach to Residual Gauge Fixing

In this paper we study the question of residual gauge fixing in the path integral approach for a general class of axial-type gauges including the light-cone gauge. We show that the two cases -- axial-type gauges and the light-cone gauge -- lead to very different structures for the explicit forms of the propagator. In the case of the axial-type gauges, fixing the residual symmetry determines the propagator of the theory completely. On the other hand, in the light-cone gauge there is still a prescription dependence even after fixing the residual gauge symmetry, which is related to the existence of an underlying global symmetry.Comment: revtex 13pages, slightly expanded discussion, version to be published in Physical Review

Hilbert Space of Isomorphic Representations of Bosonized Chiral QCD2QCD_2

We analyse the Hilbert space structure of the isomorphic gauge non-invariant and gauge invariant bosonized formulations of chiral $QCD_2$ for the particular case of the Jackiw-Rajaraman parameter $a = 2$. The BRST subsidiary conditions are found not to provide a sufficient criterium for defining physical states in the Hilbert space and additional superselection rules must to be taken into account. We examine the effect of the use of a redundant field algebra in deriving basic properties of the model. We also discuss the constraint structure of the gauge invariant formulation and show that the only primary constraints are of first class.Comment: LaTeX, 19 page