No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Full Action for an Electromagnetic Field with Electrical and Magnetic Charges
Abstract
The paper offers the full action for an electromagnetic field with electrical and magnetic charges; Feynman laws are formulated
for the calculation of the interaction cross-sections for electrically and magnetically charged particles on the base of offered
action within relativistic quantum field theory. Derived with formulated Feynman rules cross-section of the interaction between
an elementary particle with magnetic charge and an elementary particle with electrical charge proves to be equal zero.
KeywordsMagnetic monopole–Full action–Lagrangian
... However, there is a enough of a general consensus concerning generalized 'Maxwell' equations and the generalized forces that these fields exert on electric and magnetic charges. These equations are the following [18][19][20][21][22][23][24][25]: ...
... First, the generation of the electric field (equation (3)) is due to the existence of magnetic current term in addition to the temporal variation of the magnetic field. Secondly, the action of the electric and magnetic fields [18][19][20][21][22][23] on the motion of the magnetic charges is due to the dual Lorentz force (equations (4) and (5a)). This produces its action on those structures which resemble the magnetic monopoles in behaviour. ...
... From equations (2)-(5a), one can determine the frequency dependent conductivity of the plasma state of these systems. On the right-hand side of the temporal evolution of current magnetic densities (equations (4) and (5a)), there are two dynamical terms which come from the generalized Lorentz force [18][19][20][21]. One can estimate that if the absolute values of these two terms of the right side of equalities are quantitatively compared, we ...
Excited states in magnetic structures of the so-called spin-ices and in some artificial magnetic materials present a behaviour as being a magnetic neutral plasma. In this state the electromagnetic waves in confined systems (waveguides) filled with materials with magnetic charges are able to transmit information and energy. In the natural spin-ices, the difficulty is the very low temperature for which these magnetic entities appear, whose phenomenology under the electromagnetic interaction is that of solids containing magnetic charges. However, similar behaviour may be present in other compounds at higher temperatures, even at room temperature and they are named artificial spin-ice compounds. This analysis is addressed to obtain theoretical results about magnetic responses and frequency-dependent magnetricity. The key physical magnitudes are the plasmon frequency (ωP) which is related to the cut-off frequency in a wave guide and the effective inertial masses (m) of these magnetic charges. All properties of the electromagnetic propagation in these compounds with effective magnetic monopoles depend on ωP and m. This is carried out including the dissipative forces among magnetic charges which give new characteristic features to the electromagnetic propagation. The main goal of this work is the analysis of these electromagnetic properties in order to find possible circuital applications of these materials to be utilized by devices.
We analyze the conditions of the electromagnetic potentials for systems with electric and magnetic charges and the Lagrangian theory with these potentials. The constructed Lagrangian function is valid for obtaining the field equations and the extended Lorentz force for dyonic charges for both relativistic particles in vacuum and non-relativistic entities in solids. In a second part, with the one-body Hamiltonian of independent particles in external fields, we explore some dual properties of the dyonic system under external fields. We analyze the possible diamagnetic (and ‘diaelectric’) response of magnetic monopoles under a weak and constant electromagnetic field and the theory of Landau levels in the case of magnetic charges under strong electromagnetic constant fields.
A theory containing both electric and magnetic charges is formulated
using two vectors potentials, A μ and C μ.
This has the aesthetic advantage of treating electric and magnetic
charges both as gauge symmetries, but it has the experimental
disadvantage of introducing a second massless gauge boson (the
“magnetic” photon) which is not observed. This problem is
dealt with by using the Higgs mechanism to give a mass to one of the
gauge bosons while the other remains massless. This effectively
“hides” the magnetic charge, and the symmetry associated
with it, when one is at an energy scale far enough removed from the
scale of the symmetry breaking.
It is considered a dimensional reduction of Ue(1)×Ug(1) (3+1)-dimensional electromagnetism with a gauge field (photon) and a pseudo-vector gauge field (pseudo-photon) to (2+1) dimensions. In the absence of boundary effects, the quantum structure is maintained, while when boundary effects are considered, as have been previously studied, a cross Chern-Simons term between both gauge fields is present, which accounts for topological effects and changes the quantum structure of the theory. Our construction maintains the dimensional reduced action invariant under parity (P) and time-inversion (T). We show that the theory has two massive degrees of freedom, corresponding to the longitudinal modes of the photon and of the pseudo-photon and briefly discuss the quantization procedures of the theory in the topological limit (wave functional quantization) and perturbative limit (an effective dynamical current theory), pointing out directions to solve the constraints and deal with the negative energy contributions from pseudo-photons. We recall that the physical interpretation of the fields in the planar system is new and is only meaningful in the context of Ue(1)×Ug(1) electromagnetism. In this work it is shown that all the six electromagnetic vectorial fields components are present in the dimensional reduced theory and that, independently of the embedding of the planar system, can be described in terms of the two gauge fields only. As far as the author is aware it is the first time that such a construction is fully justified, thus allowing a full vectorial treatment at the variational level of electromagnetism in planar systems.
In Abelian monopole theories the magnetic coupling is required to be enormous. Using the electric-magnetic duality of electromagnetism, it is argued that the existence of such a large, nonperturbative magnetic coupling should lead to a phase transition where magnetic charge is permanently confined and the photon becomes massive. The apparent masslessness of the photon could then be used as an argument against the existence of such a large, nonperturbative magnetic charge. Finally it is shown that even in the presence of this conjectured dynamical mass generation the Cabbibo-Ferrari (1962) formulation of magnetic charge gives a consistent theory.
The Dirac approach to include magnetic charge in Maxwell's equations places
the magnetic charge at the end of a string on which the the fields of the
theory develop a singularity. In this paper an alternative formulation of
classical electromagnetism with magnetic and electric charge is given by
introducing a second pseudo four-vector potential, C_mu, in addition to the
usual four- vector potential, A_mu. This avoids the use of singular, non-local
variables (i.e. Dirac strings) in electrodynamics with magnetic charge, and it
makes the treatment of electric and magentic charge more symmetric, since both
charges are now gauge charges.
We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed actions which have only one magnetic and one electric physical fields and are invariant under the discrete symmetries $P$ and $T$. We conclude that neither the Lagrangian, nor the Hamiltonian, are invariant under the electromagnetic duality rotations. This agrees with the weak-strong coupling mixing characteristic of the duality due to the Dirac quantization condition providing a natural way to differentiate dual theories related by the duality rotations (the energy is not invariant). Also the standard electromagnetic duality rotations considered in this work violate both $P$ and $T$ by inducing Hopf terms (theta terms) for each sector and a mixed Maxwell term. The canonical structure of the theory is briefly addressed and the 'magnetic' gauge sector is interpreted as a ghost sector.
The Tevatron has inspired new interest in the subject of magnetic monopoles. First there was the 1998 D0 limit on the virtual production of monopoles, based on the theory of Ginzburg and collaborators. In 2000 the first results from an experiment (Fermilab E882) searching for real magnetically charged particles bound to elements from the CDF and D0 detectors were reported. This also required new developments in theory. The status of the experimental limits on monopole masses will be discussed, as well as the limitation of the theory of magnetic charge at present.
The Tevatron has inspired new interest in the subject of magnetic monopoles. First there was the 1998 D0 limit on the virtual production of monopoles, based on the theory of Ginzburg and collaborators. In 2000 and 2004 results from an experiment (Fermilab E882) searching for real magnetically charged particles bound to elements from the CDF and D0 detectors were reported. The strongest direct experimental limits, from the CDF collaboration, have been reported in 2005. Less strong, but complementary, limits from the H1 collaboration at HERA were reported in the same year. Interpretation of these experiments also require new developments in theory. Earlier experimental and observational constraints on point-like (Dirac) and non-Abelian monopoles were given from the 1970s through the 1990s, with occasional short-lived positive evidence for such exotic particles reported. The status of the experimental limits on monopole masses will be reported, as well as the limitation of the theory of magnetic charge at present. Comment: 84 pages, 23 figures
A classical system of $n$ electric and ${n}^{*}$ magnetic point charges is considered. The field equations (Maxwell-Lorentz equations, suitably generalized) and the particle equations are obtained by postulating duality invariance and coherence with the theory of only electric point charges. The particle equations together with the solutions of the field equations yield the (generalized) Lorentz-Dirac equations including radiation reaction. The question is then raised whether this system of equations can be derived from an action principle, as is the case for only electric or only magnetic charges. It is shown that the particle equations can be derived only from a nonlocal action integral. If an electric and a magnetic point charge are allowed to meet (crossing of world lines), they must do so with equal velocity (in magnitude and direction) at the instant of crossing. An action integral from which the field equations can be derived is not difficult to obtain, but it is proven that no action integral exists from which both the particle equations and the field equations can be derived. Nevertheless, there exist a local symmetric energy tensor and a corresponding angular momentum tensor which yield ten conservation laws when the field and particle equations hold.
This chapter describes asymptotic formulae of quantum electrodynamics. The asymptotic constancy of the total cross-section is a characteristic property of scattering processes whose diagrams can be cut across internal photon lines. It occurs even when more than two particles are present in the final state of the reaction. The double-logarithmic corrections occur in cases of two kinds. One kind includes scattering through a fixed finite angle. The cross-sections decrease in the asymptotic high-energy range. In such cases, the double-logarithmic corrections are associated with the infrared divergence. These cases include elastic scattering of electrons in an external Coulomb field. The other class of cases includes reaction cross-sections, which decrease with increasing energy for a given square of the momentum transfer, that is, for scattering angles, which asymptotically approach zero or π.
This volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems. Two theories covered by the book in great detail are the Maxwell-Lorentz electrodynamics and Yang-Mills-Wong theory.
The S matrix for photon and graviton processes is studied in perturbation theory, under the restriction that the only creation and annihilation operators for massless particles of spin j allowed in the interaction are those for the physical states with helicity +/-j. The most general covariant fields that can be constructed from such operators cannot represent real photon and graviton interactions, because they give amplitudes for emission or absorption of massless particles which vanish as pj for momentum p-->0. In order to obtain long-range forces it is necessary to introduce noncovariant "potentials" in the interaction, and the Lorentz invariance of the S matrix requires that these potentials be coupled to conserved tensor currents, and also that there appear in the interaction direct current-current couplings, like the Coulomb interaction. We then find that the potentials for j=1 and j=2 must inevitably satisfy Maxwell's and Einstein's equations in the Heisenberg representation. We also show that although the existence of magnetic monopoles is consistent with parity and time-reversal invariance [provided that P and T are defined to take a monopole into its antiparticle], it is nevertheless impossible to construct a Lorentz-invariant S matrix for magnetic monopoles and charges in perturbation theory.
We present a local Lagrangian density, depending on a pair of four-potentials A and B, and charged fields ψn with electric and magnetic charges en and gn. The resulting local Lagrangian field equations are equivalent to Maxwell's and Dirac's equations. The Lagrangian depends on a fixed four-vector, so manifest isotropy is lost and is regained only for quantized values of (engm-gnem). This condition results from the requirement that the representation of the Poincaré Lie algebra which results from Poincaré invariance, integrate to a representation of the finite Poincaré group. The finite Lorentz transformation laws of A, B, and ψn are presented here for the first time. The familiar apparatus of Lagrangian field theory is applied to yield directly the canonical commutation relations, the energy-momentum tensor, and Feynman's rules.
A quantized theory for the interactions of the electromagnetic field ; with magnetic monopoles and electrically charged particles is developed, without ; making use of potentials. Monopoles and charged particles are treated in a ; symmetrical way; the internal consistency of the theory requires the fulfillment ; of the Dirac condition (that the magnetic charge of the monopoles be equal to 2/ ; pi n/e, where n is an integer). The symmetry properties of the theory are ; discussed. It is shown that although parity is not conserved, parity ; nonconservation effects can appear only if physical magnetic monopoles are ; present. (T.F.H.);
· doi:10.1103/PhysRev
- F Rohrlich
- F Rohrlich
· doi:10.1103/PhysRevD.3
- D Zwanziger
- D Zwanziger
- S Weinberg
S. Weinberg, Phys. Rev. 138, B988 (1965).
- D Zwanziger
D. Zwanziger, Phys. Rev. 3, 880 (1971).