Principle Of Gauge Invariance Research Articles

Gauge invariance and the thermodynamics of the electromagnetic field

Recent discussions of the thermodynamics of the electromagnetic field interacting with two-level atoms demonstrate the existence of a phase transition. It is argued however that this only holds for field theories that do not satisfy the principle of gauge invariance.

Low-energy theorems for nuclear compton and raman scattering and 0 + → 0 + two-photon decays in nuclei

Low-energy theorems for elastic photon scattering (nuclear Compton scattering) from a nucleus of arbitrary spin are derived in the nonrelativistic approximation through terms quadratic in the photon frequency. The same derivation is made for the special case of 0 + → 0 + nuclear excitation by inelastic photon scattering (nuclear Raman scattering). Use is made of the general principle of gauge invariance, which bypasses the need to specify the form of the current operator explicitly. A general discussion of the contribution of mesonic exchanges is made and their effect is isolated. The center-of-mass correction to the nuclear diamagnetic susceptibility is calculated. The 0 + → 0 + two-photon decay amplitude is obtained from the nuclear Raman amplitude and the transition rate is calculated.

Einstein-Cartan cosmologies with a magnetic field

This note points out that the natural generalization of the Maxwell equations in spaces having torsion leads to a breakdown of the gauge invariance and charge conservation principle. The equations are, however, taken in a form so as to preserve gauge invariance; and the possibility of bounce is investigated in the presence of a magnetic field for Bianchi type-I universes with $p=0$ and $p=\ensuremath{\rho}$.

Remarks on gauge theories of fundamental forces

By clarifying the concepts of strong and weak gravity in a scalar-scalar-tensor theory of gravitation, we have studied an action principle from which we have discussed several theories of weak and (separately) strong gravity. By further appealing to the general principle of gauge invariance we are able to discuss gauge theories of spontaneously broken discrete symmetries. Finally, we find that super-heavy gauge bosons are automatically excluded when both gravities are properly understood.

Superfield Equations

AbstractCovariant free field equations are systematically derived for irreducible and bilinear superfields from representation theory of the Wess‐Zumino algebra. Interactions are introduced by covariance arguments alone or by the principle of local gauge invariance. Finally we construct propagators for massive superfields.

Experimental test forCPnoninvariance and neutral kaon "charge"

We discuss a theory of $\mathrm{CP}$ noninvariance in which the interaction is completely determined by the principle of gauge invariance. We also discuss its experimental test by observing anomalous phenomena of ${K}^{0}$ decay in the electric field. Moreover, the experimental result can also determine an accurate upper limit for the neutral kaon charge (which has never been directly measured) if the predicted phenomena are not observed.

Gauge invariance and the quantization of mass (of gravitational charge)

In a previous paper (referred to as I in the text) it was shown that the Weyl principle of gauge invariance leads to the relationshipGm2 =ħc for a particle of inertial massm obeying the Dirac equation, whereG is the Newtonian gravitational constant. Instead of interpreting this equation to mean thatG takes on the extremely large valueħc/m2 inside a particle like an electron (as we did in I), we now write it in the formGm2/c = ħ and treat it as a quantization condition on the square of the gravitational charge √Gm. We show that this same quantization condition can be obtained from an angular-momentum component in the general-relativistic two-body problem as well as from the Machian definition of inertial mass in a rotating universe by using the Dirac-Schwinger procedure for quantizing charge. From this quantization condition we now deduce that the fundamental particle in Nature (the uniton) has an inertial mass equal to about 10-5 g. The possibility of using the uniton to shed light on the mystery of the « missing mass » in the Universe is discussed. Other cosmological implications of the uniton are also discussed and it is suggested that unitons can clear up the solar-neutrino discrepancy.

On the “type II superconductor” model of self-trapped laser filaments

Self-trapped laser filaments are interpreted as the “photon superfluid” analog of the Abrikosov state in type II superconductors. The principle of local gauge invariance is used to derive Landau-Ginzburg equations for the filaments.

Gauge invariance and the structure of charged particles

The Weyl principle of gauge invariance is used to obtain an enlarged gauge invariant curvature tensor consisting of the usual Einstein-Ricci tensor plus terms involving the electromagnetic potentials and held strengths. An invariant Lagrangian density is constructed by multiplying this tensor by a metric tensor consisting of a symmetric and an anti-symmetric part. By introducing an arbitrary transformation of gauge into this Lagrangian density we obtain an operator which has exactly the form required by the second-order Dirac theory, and the variational principle then gives us the second-order Dirac equation provided we interpret the position occupied by the particle as being a localized noneuclidean region in which the Gaussian curvature is equal to the reciprocal of the square of the Compton wavelength. One of the consequences of this interpretation is that the Newtonian constant of gravitation inside a partiale must be enormously larger than it is in empty space and must depend on the mass of the particle. To obtain selfconsiatent results one has to assume this constant to be of the order of ħc/m2, that is, the reciprocal of the fine structure constant multiplied by the square of the specific charge of the particle. This assumption leads to a very interesting model of a charged particle in which the electrostatic repulsive forces are held in equilibrium by the large interior gravitational forces. Mass renormalization terms of the right form and order of magnitude as well as a mechanism to account for the capture of photons by charged particles are also obtained. The cosmological consequences of this theory are discussed.

On the Mass Gauge Invariance

Some consequences of gauge invariance are explored on the assumption that no experimentel measurement determines the phase of mass of an elementary particle. If the mass has a phase factor the phase could be removed by an adequate gauge transformation without any alteration in the physical situation. It is concluded that the principle of mass gauge invariance can be complementary to partial invariance. (W.D.M.)

A doublet scheme for the leptons

Abstract A scheme in which the leptons are paired in two doublets is proposed on the assumption that there exist two distinct neutrinos. It is shown that a simplification of the strangeness conserving weak interactions ensues. Some consequences of the gauge invariance principle of elementary particle interactions are discussed.

Derivation of strong interactions from a gauge invariance

A representation for the baryons and bosons is suggested, based on the Lie algebra of the 3-dimensional traceless matrices. This enables us to generate the strong interactions from a gauge invariance principle, involving 8 vector bosons. Some connections with the electromagnetic and weak interactions are further discussed.

Les invariances de jauge classiques de l’électrodynamique quantique

One first recalls the principles of gauge invariance and studies their violations occuring in perturbation theory:i.e., the well known photon self-energy; the commonly ignored photon-photon interaction term. One then constructs a new equation for the photon field, involving new renormalization constants, which is such that theS-matrix is gauge invariant, without using regularization. Gauge invariance of the field equations supplies relations for the new renormalization constants. Non perturbative calculation proves the consistency of these relations and connects the new constants to the observable quantities. The values of these constants are then calculated to every order of perturbation theory.

Low-Energy Theorems for Renormalizable Field Theories

A general method is described whereby the low-energy behavior of collision processes can be investigated systematically. The basic procedure is the construction of the renormalized Green's functions for the participating particles in the presence of external sources. For processes involving the collision of a boson with a fermion,---photon scattering, meson scattering, and photoproduction of mesons---one requires the propagation function of a nucleon in the presence of external electromagnetic and meson fields, as well as the propagator for a meson in an electromagnetic field. The rather direct relation of these functions to the various transition matrices is derived. The possible forms of the Green's functions are limited by the principles of Lorentz, gauge, and charge conjugation invariance. Their detailed structure is determined in part by the requirement that they describe particles of known mass, charge, magnetic moment, and mesic coupling constant. These conditions are sufficient to imply a number of theorems. For example, it is shown that the amplitude for photon-proton scattering is given correctly up to terms of first order in the photon energy by a Born approximation calculation, if one assigns to the proton its experimental charge and magnetic moment. If one includes the meson-nucleon coupling constant in this set of parameters, then perturbation theory is also valid for the leading terms in a momentum-energy expansion of the $P$-wave in meson-nucleon scattering, the $S$- and $P$-waves associated with the nucleon current in photomeson production, and the entire meson current for the same process.The methods employed to establish the theorems are extended in order to provide a phenomenological framework for the description of the experiments for energies low enough so that the expansions in boson energy are still valid, but for which the deviations from the theorems are of practical significance. Thus, it is suggested that for the description of photon scattering one should attribute an electric and a magnetic polarizability to the nucleon. The description of the $P$-wave in meson-nucleon scattering also requires the introduction of two additional parameters. From the manner in which these enter the scattering amplitude, it can be concluded that the phase shift in the state of angular momentum and isotopic spin $\frac{3}{2}$ is enhanced compared to its Born value, if only the phase shifts in the other states deviate in the opposite direction. Finally, parameters are introduced to describe the $S$-wave in meson-scattering, and the basis for a phenomenological description of photoproduction is indicated.

Conservation of Isotopic Spin and Isotopic Gauge Invariance

It is pointed out that the usual principle of invariance under isotopic spin rotation is not consistant with the concept of localized fields. The possibility is explored of having invariance under local isotopic spin rotations. This leads to formulating a principle of isotopic gauge invariance and the existence of a b field which has the same relation to the isotopic spin that the electromagnetic field has to the electric charge. The b field satisfies nonlinear differential equations. The quanta of the b field are particles with spin unity, isotopic spin unity, and electric charge $\ifmmode\pm\else\textpm\fi{}e$ or zero.

The Gravitational, Electromagnetic, and Vector Meson Fields and the Similarity Geometry

It is shown that a special case of the general conformal geometry, called here the similarity geometry, forms the basis for a unitary theory of the gravitational, electromagnetic, and vector meson fields. The field equations are obtained from a simple four-dimensional, gauge invariant variational principle involving the curvature scalar of a basic second rank symmetric similarity tensor ${S}_{\ensuremath{\sigma}\ensuremath{\tau}}$. Since ${S}_{\ensuremath{\sigma}\ensuremath{\tau}}$ is here specialized, there is the possibility of incorporating further fields when the restrictions are removed.

The Vector Meson Field and Projective Relativity

In the projective theory of relativity, if, instead of the projective metric ${G}_{\ensuremath{\alpha}\ensuremath{\beta}}$ of index $2N$, one uses the restricted metric ${\ensuremath{\gamma}}_{\ensuremath{\alpha}\ensuremath{\beta}}(\ensuremath{\equiv}\frac{{G}_{\ensuremath{\alpha}\ensuremath{\beta}}}{{G}_{00}})$ of index zero, one is led to a formal unification of the gravitational and electromagnetic fields of the general theory of relativity. The present paper discusses the case of the general metric ${G}_{\ensuremath{\alpha}\ensuremath{\beta}}$. It is shown that a natural four-dimensional, gauge invariant variational principle, involving the curvature scalar of ${G}_{\ensuremath{\alpha}\ensuremath{\beta}}$, yields field equations unifying the gravitational and vector meson fields, the range of the meson force being determined by the inverse length ${(12)}^{\frac{1}{2}}N$. Reasons are given for supposing that an extension to conformal geometry could prove of interest.