Nonminimal Interaction Research Articles

Degenerate topological vortex solutions from a generalized abelian Higgs model with a Chern-Simons term

We consider a generalization of the abelian Higgs model with a Chern-Simons term by modifying two terms of the usual Lagrangian. We multiply a dielectric function with the Maxwell kinetic energy term and incorporate nonminimal interaction by considering the generalized covariant derivative. We show that for a particular choice of the dielectric function this model admits topological vortices satisfying the Bogomol'nyi bound for which the magnetic flux is not quantized even though the energy is quantized. Furthermore, the vortex solution in each topological sector is infinitely degenerate.

Supersymmetric self-gravitating solitons

We show that the “instantonic” soliton of five-dimensional Yang-Mills theory and the closely related BPS monopole of four-dimensional Yang-Mills/Higgs theory continue to be exact static, and stable, solutions of these field theories even after the inclusion of gravitational, electromagnetic and, in the four-dimensional case, dilatonic interactions, provided that certain non-minimal interactions are included. With the inclusion of these interactions, which would be required by supersymmetry, these exact self-gravitating solitons saturate a gravitational version of the Bogomol'nyi bound on the energy of an arbitrary field configuration.

Geometrical structure of gravitation and matter fields

Einstein's requirement of a unified geometrical description of gravitational fields and their matter sources is shown to become possible (at least for certain matter sources) by relaxing his other requirement of a minimal interaction of gravitation with matter. Arguments are presented to demonstrate that Schrodinger's discovery of pair creation by gravitational fields and the associated effects of virtual pairs make the relaxation of the latter requirement inevitable in order to obtain a complete macroscopic description (which needs no separate insertion to take account of averaged quantum effects). The gravitational field equations in case of a nonminimal interaction need higher derivatives of the metric than the second. The author's gauge theory on the manifold of the anti-de Sitter groupSO(3, 2) with the subgroupSO(3, 1) (proper Lorentz group) as gauge group and the factor space of the two group manifolds as space-time manifold gives rise to a Yang-Mills field which can be interpreted to be composed of Riemannian curvature and a tensor formed out of torsion. Einstein's equations with a cosmological member are satisfied by the Cartan-Killing metric on the group manifold so that the generalization to a Kaluza-Klein theory results in a minimal disturbance of the group symmetry. The separation of the Yang-Mills field results in a part of its energy-momentum tensor becoming purely Riemannian; this part may be interpreted to be due to the contribution of virtual matter, whereas the part with torsion is due to real matter and its interaction with curvature. The Yang-Mills field equations have a third-order derivative purely metric part, which is equivalent to the field equations suggested by Yang (in the latter, however, torsion should be inseparably present and has been ignored). The torsion part is the “matter source” of this term and it is tempting to relate it to elementary particle spin. The theory can be regarded as a gauge theory of space-time geometry. It needs generalizations to geometrize matter with an energy-momentum tensor of nonvanishing trace. The equations, however, already considerably modify the problem of gravitational collapse. Further developments should serve to eliminate the “absurdity of relativity”—the collapse to a point (of which Einstein himself never became convinced).

Group-renormalization approach in quantum field theory in curved spacetime with torsion

The nature of the interaction of the gauge models SU(N) and O(N) with an external torsion field is studied from the group-renormalization point of view. Consideration of the radiation corrections to the nonminimal interaction gives a possible explanation for the absence of a torsion field in observational data.

ASYMPTOTICAL CONFORMAL INVARIANCE IN “FINITE” SU(2) GAUGE THEORIES IN CURVED SPACE-TIME

The behavior of effective coupling constants in one-loop “finite” SU(2) gauge theories in curved space-time is investigated. It is shown that in strong gravitational field the effective coupling constants, corresponding to the parameters of non-minimal interaction of scalars and gravitational field, tend to the conformal values (asymptotical conformal invariance) or increase in an exponential fashion. The weak gravitational field limit is also considered in the same models.

The behaviour of effective coupling constants in 'finite' grand unification theories in curved spacetime

The question of the behaviour of effective coupling constants in one-loop 'finite' grand unification theories in curved spacetime is investigated. It is shown that in strong gravitational fields the effective coupling constant, corresponding to the parameter of non-minimal interaction of scalar and gravitational fields, tends to the conformal value or increases in an exponential fashion. The one-loop effective potential is obtained with accuracy to linear curvature terms. It is shown that, in external supergravity, supersymmetric finite theories admit asymptotic conformal invariance.

Divergences and anomalies for coupled gravitational and majorana spin- [formula omitted] fields

We show how to avoid the known difficulties of computing one-loop counterterms in gravitating systems with fermionic fields or some non-minimal interactions. The one-loop counter-terms and the axial anomaly are calculated for the system of coupled gravitational and Majorana spin- 1 2 fields with and without torsion. It is shown that the system is non-renormalizable in all cases. New terms containing the spinor background are found in the anomaly of the axial current. The dependence of the axial current and the axial anomaly on the gauge is studied.

Inconsistencies of Glass's equation for spin-32particles

A systematic study is made of the Glass equation for spin-3/2 particles with minimal electromagnetic interaction. The study is motivated by the knowledge that this equation is just as satisfactory as the Rarita-Schwinger equation in the absence of interactions and that a variety of problems crop up in the Rarita-Schwinger theory when minimal electromagnetic interaction is introduced. The hope that the Glass equation might fare better is belied, however, Not only does it suffer from the various ills (e.g., noncausal propagation, modes of complex frequency) which beset the Rarita-Schwinger theory but it also exhibits further troubles such as an increase in the number of ''spin'' degrees of freedom (something not encountered earlier in any theory with s < 2), nonlocality of anticommutators of field components, etc., depending on the nature of the external field. Further, unlike in the symmetric tensor theory for spin 2, nonminimal interactions do not help to remove the anomaly of the abnormal number of degrees of freedom resulting from the minimal electromagnetic interaction. The bearing of the alebra of the ..beta.. matrices on the difficulties of the interacting theories is briefly referred to.

Gravitational Born amplitudes and kinematical constraints

It is shown that in the Born approximation the helicity amplitudes for graviton-graviton scattering are completely determined by kinematical considerations alone, without detailed Feynman graph calculations, reflecting thus the uniqueness of pure Einstein theory. We show that the nonuniqueness of the matter-graviton amplitudes is related to the existence of nonminimal interactions. In the presence of such interactions, helicity is not conserved in elastic scattering of massless particles. A simplified three-graviton vertex with two on-shell gravitons is presented.

Massive gauge theories and the photon

A model containing the massless photon as well as other massive vector mesons is constructed from a gauge-invariant theory of massless vector mesons with scalars transforming under a mixed linear-non-linear group realization, so that one massive scalar also remains finally. A Georgi-Glashow-type Lagrangian in the unitary gauge can be induced by appropriate choice of non-minimal gauge-invariant interactions in the ancestor Lagrangian. It is thus likely that this ancestor Lagrangian, which is non-polynomial, is also renormalizable.

Minimal and nonminimal gravitational interactions, and the asymmetric energy momentum tensor

Minimal and nonminimal gravitational couplings are discussed in terms of the translation gauge fields b k μ, which are necessary to describe the gravitational interaction of the spin 1/2 field. For this purpose we carry out the extension of the conventional tetrad formalism of general relativity. Our general framework contains four arbitrary parameters; one of them represents the asymmetry of the affine connection (or equivalently that of the energymomentum tensor) and the others measure possible deviations from Einstein's gravitational Lagrangian, which will be responsible for spin effects. We also discuss the physical meaning of the invariance requirement with respect to the Poincare gauge transformation that uniquely leads us within the present framework to Einstein's theory of gravity.

Criterion for and the physical interpretation of minimal and nonminimal interactions

A classification of currents for finite- and infinite-component wave equations is proposed depending on their algebraic and convective nature. Algebraic terms with a consistent one-particle interpretation constitute the minimal interactions. The nonminimal interactions are interpreted as effective c-number currents describing many particle effects and/or composite structures. A number of applications are treated.

Inconsistency of interaction between the gravitational field and the tensor meson field

The minimal and nonminimal interactions between the gravitational and tensor meson fields are studied by performing a canonical analysis, starting from a Lagrangian which verifies the Fierz-Pauli condition and meaning by minimal interaction terms coming from the replacement of the usual derivatives by the Riemannian covariant derivatives in the flat Lagrangian. The nonminimal interaction, however, takes into account terms coupling first-order derivatives of the gravitational field with mesonic currents. It is very well known that the assumptions of minimal gravitational interaction for the scalar mesons, photons and massive spin-1/2 fermions give consistent theories. However, in the present work, it is shown that both coupling schemes are inconsistent.

Low's Non-Minimal Interaction and Heavy Electrons

Low's Non-Minimal Interaction and Heavy Electrons

Minimal Electromagnetic Currents and Commutation Relations

It is pointed out that within the quark model the equal-time commutation relations of currents provide us with a test of minimal electromagnetic interaction of the hadrons. When compared with experiment, the modifications of the Cabibbo-Radicati and Drell-Hearn sum rules resulting from nonminimal interactions may possibly fix the magnitudes of the isoscalar and the isovector Pauli interactions.

CP and non-minimal electromagnetic interactions

CP and non-minimal electromagnetic interactions