Theoretical and Experimental Status of Magnetic Monopoles

Milton, Kimball A.; Kalbfleisch, G.; Luo, Wei

doi:10.1142/s0217751x02010066

Cited by 39 publications

(52 citation statements)

References 128 publications

(218 reference statements)

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“…They are non-linear objects in which energy is localised around a point in space and which therefore appear as point particles, and they carry non-zero magnetic charge. It is possible that these monopoles actually exist in nature, but so far they have not been discovered 1 despite extensive searches [5]. However, 't Hooft-Polyakov monopoles are very important theoretically, because they provide a new way of looking at non-Abelian gauge field theories, complementary to the usual perturbative picture.…”

Section: Introductionmentioning

confidence: 99%

Mass of a quantum 't Hooft-Polyakov monopole

Rajantie

2006

J. High Energy Phys.

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The quantum mechanical mass of 't Hooft-Polyakov monopoles in the fourdimensional Georgi-Glashow is calculated non-perturbatively using lattice Monte Carlo simulations. This is done by imposing twisted boundary conditions that ensure there is one unit of magnetic charge on the lattice, and measuring the free energy difference between this ensemble and the vacuum. In the weak-coupling limit, the results can be used to determine the quantum correction to the classical mass, once renormalisation of couplings is taken properly into account. The methods can also be used to study the masses at strong coupling, i.e., near the critical point, where there are hints of a possible electric-magnetic duality.

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Section: Introductionmentioning

confidence: 99%

Mass of a quantum 't Hooft-Polyakov monopole

Rajantie

2006

J. High Energy Phys.

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“…The equation for Θ λ (θ) is exactly the same as in the theory of magnetic monopoles (cf. for example, [15,16]). We wrote λ 2 instead of 1 to have the form of Eq.…”

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confidence: 99%

Uncertainty Relation for Photons

Bialynicki‐Birula¹,

Bialynicka‐Birula²

2012

Phys. Rev. Lett.

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The uncertainty relation for the photons in three dimensions that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in configuration space. It is shown that the measure of the spatial extension based on the energy distribution in space leads to an inequality that is a natural counterpart of the standard Heisenberg relation. The equation satisfied by the photon wave function in momentum space which saturates the uncertainty relations has the form of the Schrödinger equation in coordinate space in the presence of electric and magnetic charges.The uncertainty relations that first appeared in the fundamental Heisenberg paper on the conceptual content of quantum mechanics [1] play an important role in elucidating specific properties of the quantum world. The aim of this Letter is to derive in the framework of quantum electrodynamics a sharp uncertainty relation for photons treated as three-dimensional objects. The photon wave function that saturates our inequality has already appeared in different contexts.An uncertainty relation for the momentum and the center of mass coordinate along a given direction can easily be obtained from the commutators between the generators of the Poincaré group. It follows from general principles [2] that the commutators between the components of the momentum and the Lorentz boost are:Therefore, each component of the center of mass coordinate (the boost operator divided by the energy operator with proper symmetrization to secure Hermiticity),is a canonically conjugate variable to the corresponding component of momentum, [R i ,P j ] = i δ ij . Hence, the standard Heisenberg relation ∆x 2 i ∆p 2 i ≥ 2 /4 follows separately for every direction, with Gaussian functions saturating each inequality. These simple one-dimensional uncertainty relations hold for every relativistic system. In the special case of photons they were obtained by Holevo [3] in the framework of estimation theory. Holevo also proved that "the transversality condition precludes the three inequalities from becoming equalities simultaneously." This was to be expected because the existence of one wave function that saturates all three standard Heisenberg uncertainty relations would mean that photons are not any different from nonrelativistic particles. In a general approach based on the properties of the Poincaré group, the impossibility to saturate simultaneously the three uncertainty relations follows from the noncommutativity of the components ofR,The expression in parentheses on the right side represents the spin: the total angular momentum minus the orbital part. Schwinger [4] has shown that for massless particles with helicity λ the right-hand side in (3) becomes:He also found a very rough estimate of the lower bound in the three-dimensional uncertainty relation.In what follows we fully realize the Schwinger program by deriving a precise form of the uncertainty relation for phot...

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“…when we take the equations of motion (20) and the LF Hamiltonian P − (21a). However here we would like to propose a novel LF canonical procedure, which uses P + instead of P − .…”

Section: Gauge Invariant Canonical Quantization For Free Fieldsmentioning

confidence: 99%

“…one may restore the Lorentz symmetry. Within the ET formulation, one may prove [18], [19], [20], that the dependence on a space like vector n µ finally disappears. We hope that a similar phenomenon happens also for (47), though here we have a dependence on a null vector n 2 = 0.…”

Section: Path Integral For Electric and Magnetic Sourcesmentioning

confidence: 99%

Light-front gauge invariant formulation and electromagnetic duality

Przeszowski¹

2005

J. Phys. A: Math. Gen.

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Abstract. The gauge invariant formulation of Maxwell's equations and the electromagnetic duality transformations are given in the light-front (LF) variables. The novel formulation of the LF canonical quantization, which is based on the kinematic translation generator P + rather then on the Hamiltonian P − , is proposed. This canonical quantization is applied for the free electromagnetic fields and for the fields generated by electric and magnetic external currents. The covariant form of photon propagators, which agrees with Schwinger's source theory, is achieved when the direct interaction of external currents is properly chosen. Applying the path integral formalism, the equivalent LF Lagrangian density, which depends on two Abelian gauge potentials, is proposed. Some remarks on the Dirac strings and LF non local structures are presented in the Appendix.

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Theoretical and Experimental Status of Magnetic Monopoles

Cited by 39 publications

References 128 publications

Mass of a quantum 't Hooft-Polyakov monopole

Mass of a quantum 't Hooft-Polyakov monopole

Uncertainty Relation for Photons

Light-front gauge invariant formulation and electromagnetic duality

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