Gauge-invariant Charge Research Articles

Gauge-invariant magnetic charges in linearised gravity

Abstract Linearised gravity has magnetic charges carried by (linearised) Kaluza–Klein monopoles. A gauge-invariant expression is found for these charges that is similar to Penrose’s gauge-invariant expression for the ADM charges. A systematic search is made for other gauge-invariant charges.

Gauge-noninvariant higher-spin currents in four-dimensional Minkowski space

We find the conserved currents of any spin t > 0 constructed from massless gauge fields of any integer spin s ≥ t in four-dimensional Minkowski space. In particular, we construct the stress-energy tensor for a field of any higher spin. Analogously to the spin-two stress (pseudo)tensor, the currents we consider are not gauge invariant, but we show that they generate gauge-invariant charges. In addition to the expected even-parity higher-spin currents, we find unexpected odd-parity currents that generate fewer symmetries than the even currents. We argue that these odd currents most likely do not admit a consistent AdS deformation.

Non-Abelian Magnetic Monopole in a Bose-Einstein Condensate

Recently, an effective non-Abelian magnetic field with a topology of a monopole was shown to emerge from the adiabatic motion of multilevel atoms in spatially varying laser fields [J. Ruseckas, Phys. Rev. Lett. 95, 010404 (2005)10.1103/PhysRevLett.95.010404]. We study this monopole in a Bose-Einstein condensate of degenerate dressed states and find that the topological charge of the pseudospin cancels the monopole charge resulting in a vanishing gauge invariant charge. As a function of the laser wavelength, different stationary states are classified in terms of their effect to the monopole part of the magnetic field and a crossover to vortex ground state is observed.

GAUGE-INVARIANT CHARGE NONCONSERVING PROCESSES AND THE SOLAR NEUTRINO PUZZLE

Using Kaluza-Klein’s five-dimensional unified theory as an example, we show that when the metric depends on a hidden dimension, only a gauge-invariant combination of the charge and mass of a particle: Q2/16πG−M2, is a constant of motion, but not M and Q separately. This indicates that in a spacetime with hidden dimensions, the charge of a particle is not absolutely conserved. There are gauge-invariant charge nonconserving processes that change the particle’s charge and mass. Neutrino oscillations resulting from such processes may have relevance to the solar neutrino puzzle.

Light-front QCD(1+1) coupled to adjoint scalar matter

We consider adjoint scalar matter coupled to QCD(1+1) in light-cone quantization on a finite ‘interval’ with periodic boundary conditions. We work with the gauge group SU(2) which is modified to SU(2) Z 2 by the non-trivial topology. The model is interesting for various nonperturbative approaches because it is the sector of zero transverse momentum gluons of pure glue QCD(2+1), where the scalar field is the remnant of the transverse gluon component. We use the Hamiltonian formalism in the gauge ∂− A + = 0. What survives in the dynamical zero mode of A +, which in other theories gives topological structure and degenerate vacua. With a point-splitting regularization designed to preserve symmetry under large gauge transformations, an extra A + dependent term appears in the current J +. This is reminiscent of an (unwanted) anomaly. In particular, the gauge invariant charge and the similarly regulated P + no longer commute with the Hamiltonian. We show that nonetheless one can construct physical states of definite momentum which are not invariant under large gauge transformations but do transform in a well-defined way. As well, in the physical subspace we recover vanishing expectation values of the commutators between the gauge invariant charge, momentum and Hamiltonian operators. It is argued that in this theory the vacuum is nonetheless trivial and the spectrum is consistent with the results of others who have treated the large N, SU( N), version of this theory in the continuum limit.

An invariance argument for confinement

The possibility of constructing gauge invariant charge densities in classical gauge theory is investigated. For the Yang-Mills-Dirac fields in the Minkowski space, it is shown that, unless the colour label belongs to the centre of the colour algebra, gauge invariant charge densities depend non-locally on the field variables and have non-local Poisson brackets. A quantization leading to observable charge density operators with commutators related to the classical Poisson bracket would violate the locality axiom of quantum field theory. For the Yang-Mills-Dirac fields in a bag the colour algebra is trivial and the colour charges vanish identically. In this sense the Yang-Mills-Dirac theory has to be considered as confining on the basis of a purely mathematical reasoning.

Construction of nondegenerate non-Abelian solutions and Coulomb-type solution for the same charge distribution in SU(2) Yang-Mills theory.

We propose a new cylindrical ansatz for SU(2) Yang-Mills theory which lifts the degeneracy between the two non-Abelian solutions in the presence of a time-independent charge current. We then construct explicit solutions for which we find that (i) Q=${Q}_{1}$ is the point of bifurcation between the two nondegenerate non-Abelian solutions and a Coulomb-type solution, (ii) for ${Q}_{1}$${Q}_{2}$, ${E}_{\mathrm{NA}{}^{\mathrm{I}{E}_{C}{E}_{\mathrm{NA}{}^{\mathrm{II}}}}}$, (iii) for Q=${Q}_{2}$, ${E}_{\mathrm{NA}{}^{\mathrm{I}{E}_{C}={E}_{\mathrm{NA}{}^{\mathrm{II}}}}}$, (iv) for Q>${Q}_{2}$, ${E}_{\mathrm{NA}}^{\mathrm{II}}$${E}_{\mathrm{NA}}^{\mathrm{II}}$${E}_{C}$. Here Q is the gauge-invariant charge and E is the total energy. Finally, we show that our ansatz is related to the usual cylindrical ansatz by a nonsingular gauge transformation.