Types Of Gauge Transformations Research Articles

THE PROTON SPIN DECOMPOSITION: PATH DEPENDENCE AND GAUGE SYMMETRY

We discuss the different types of decomposition of the proton spin. We stress that, despite their lack of uniqueness, the Chen et al. and Wakamatsu decompositions are perfectly measurable. We argue that a large part of the recent controversies boils down to the fact that there actually exist two types of gauge transformations in the Chen et al. approach, where physical and gauge degrees of freedom of the gauge potential are explicitly separated. By carefully distinguishing these two types of gauge transformations, one can easily understand how the concepts of gauge invariance, Stueckelberg symmetry, path dependence and measurability are linked to each other.

The Standard Model with one universal extra dimension

Effects of universal extra dimensions on Standard Model observables first arise at the one-loop level. The quantization of this class of theories is therefore essential in order to perform predictions. A comprehensive study of the SU C(3) × SU L(2) × U Y(1) Standard Model defined in a space-time manifold with one universal extra dimension, compactified on the oribifold \(S^1/Z_2\), is presented. The fact that the four-dimensional Kaluza–Klein theory is subjected to two types of gauge transformations is stressed and its quantization under the basis of the BRST symmetry discussed. A SU C(3) × SU L(2) × U Y(1)-covariant gauge-fixing procedure for the Kaluza–Klein excitations is introduced. The connection between gauge and mass eigenstate fields is established in an exact way. An exhaustive list of the explicit expressions for all physical couplings induced by the Yang–Mills, Currents, Higgs, and Yukawa sectors is presented. The one-loop renormalizability of the standard Green’s functions, which implies that the Standard Model observables do not depend on a cut-off scale, is stressed.

Gauge invariance and radiative corrections in an extra dimensional theory

The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S1 /Z2, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space–time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU4(N). A calculation of the one-loop contributions of the excited KK modes of the SUL(2) gauge group on the off-shell W+W−V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well–behaved at high energies.

Gauge invariance and quantization of Yang-Mills theories in extra dimensions

The gauge structure of the four-dimensional effective theory arising from a pure $S{U}_{5}(N)$ Yang-Mills theory in five dimensions compactified on the orbifold ${S}^{1}/{Z}_{2}$ is reexamined on the basis of Becchi-Rouet-Stora-Tyutin symmetry. In this context, the two scenarios that can arise are analyzed: if the gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields, but they are matter vector fields if these parameters are confined in the 3-brane. In the former case, it is shown that the four-dimensional theory is gauge invariant only if the compactification is carried out by using curvatures instead of gauge fields as fundamental objects. Then, it is shown that the four-dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters, ${\ensuremath{\alpha}}^{(0)a}$, and another by the excited KK modes, ${\ensuremath{\alpha}}^{(n)a}$. The Dirac method and the proper solution of the master equation in the context of the field-antifield formalism are employed to show that the theory is subject to first-class constraints. A gauge-fixing procedure to quantize the KK modes ${A}_{\ensuremath{\mu}}^{(n)a}$ that is covariant under the first type of gauge transformations, which embody the standard gauge transformations of $S{U}_{4}(N)$, is introduced through gauge-fixing functions transforming in the adjoint representation of this group. The ghost sector induced by these gauge-fixing functions is derived on the basis of the Becchi-Rouet-Stora-Tyutin formalism. The effective quantum Lagrangian that links the interactions between light physics (zero modes) and heavy physics (excited KK gauge modes) is presented. Concerning the radiative corrections of the excited KK modes on the light Green's functions, the predictive character of this Lagrangian at the one-loop level is stressed. In the case of the gauge parameters confined to the 3-brane, the known result in the literature is reproduced with some minor variants, although it is emphasized that the exited KK modes are not gauge fields but matter fields that transform under the adjoint representation of $S{U}_{4}(N)$. The Dirac method is employed to show that this theory is subject to both first- and second-class constraints, which arise from the zero and excited KK modes, respectively.

A GEOMETRIC MODEL OF THE ARBITRARY SPIN MASSIVE PARTICLE

A new model of the relativistic massive particle with arbitrary spin [the (m, s) particle] is suggested. The configuration space of the model is the product of Minkowski space and a two-dimensional sphere: ℳ6=ℝ3, 1×S2. The system describes Zitterbevegung at the classical level. Together with explicitly realized Poincare symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase space counterparts of the Casimir operators of the Poincaré group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin s field.

Determination of a gauge transformation group in gauge field theory

The existence of different types of gauge transformations in gauge theory and the theory of gravitation is established and they are defined in the language of fiber bundles.

On the Definition of Gauge Transformations in Gauge Theory

AbstractThe different types of gauge transformations in gauge theory are discerned and defined in fiber bundle terms. The gauge gravitation case is analysed in order to examine various versions of the gauge gravitation theory.

Hertzian electromagnetic potentials and associated gauge transformations

In spite of the wide use of Hertzian potentials in special problems there appears to be no account of the general theory which is completely satisfactory—especially with regard to (i) the arbitrariness of the potentials and the relation between different equivalent representations of the same electromagnetic field, (ii) the derivation of the Hertzian potentials for such equivalent representations from the physical sources, and (iii) electromagnetic fields not in vacuo. It is the purpose of this paper to fill this gap. It is shown that the Hertzian potentials may be subjected to a new type of gauge transformation which leaves invariant the electromagnetic field they represent. The particular integrals of the inhomogeneous Maxwell equations are generalized, so that they may be subjected to a related gauge transformation which leaves invariant the physical sources of the field; this leads to a treatment of (ii) above, which appears to be new. Examples, including the Whittaker and Debye—Bromwich two-scalar representations, are given. Finally, the theorem is established that, for any electromagnetic field in any stationary material medium, the particular integral of Maxwell equations may be so chosen that in general the complementary function can be expressed in terms of only two scalar functions (components of Hertzian potentials), previously only known to hold for source-free regions in vacuo .