Gauge invariance and renormalization schemes in quantum chromodynamics

A general analysis of the Slavnov-Taylor identity connecting the triple gluon and ghost-ghost-gluon vertices and its consequences for two momentum subtraction (symmetric and asymmetric) renormalization schemes are given. It is shown that in the asymmetric scheme proposed in this paper the relation follows directly from the identity for a simple and natural definition of the renormalization constants. Explicit one-loop expressions for the renormalization constants in an arbitrary covariant gauge, including quark masses are given in support of the general analysis.     

Primordial braneworld black holes: Significant enhancement of lifetimes through accretion

The Randall-Sundrum (RS-II) braneworld cosmological model with a fraction of the total energy density in primordial black holes is considered. Due to their 5d geometry, these black holes undergo modified Hawking evaporation. It is shown that during the high-energy regime, accretion from the surrounding radiation bath is dominant compared to evaporation. This effect increases the mass of the black holes till the onset of matter (or black hole) domination of the total energy density. Thus black holes with even very small initial masses could survive till several cosmologically interesting eras.     

A Vaidya-type radiating solution in Einstein-Gauss-Bonnet gravity and its application to braneworld

We consider a Vaidya-type radiating spacetime in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. Simply generalizing the known static black hole solutions in Einstein-Gauss-Bonnet gravity, we present an exact solution in arbitrary dimensions with the energy-momentum tensor given by a null fluid form. As an application, we derive an evolution equation for the “dark radiation” in the Gauss-Bonnet braneworld.     

Series solutions for a static scalar potential in a Salam-Sezgin Supergravitational hybrid braneworld

The static potential for a massless scalar field shares the essential features of the scalar gravitational mode in a tensorial perturbation analysis about the background solution. Using the fluxbrane construction of [8] we calculate the lowest order of the static potential of a massless scalar field on a thin brane using series solutions to the scalar field's Klein Gordon equation and we find that it has the same form as Newton's Law of Gravity. We claim our method will in general provide a quick and useful check that one may use to see if their model will recover Newton's Law to lowest order on the brane.     

Profiles of emission lines generated by rings orbiting braneworld Kerr black holes

In the framework of the braneworld models, rotating black holes can be described by the Kerr metric with a tidal charge representing the influence of the non-local gravitational (tidal) effects of the bulk space Weyl tensor onto the black hole spacetime. We study the influence of the tidal charge onto profiled spectral lines generated by radiating tori orbiting in vicinity of a rotating black hole. We show that with lowering the negative tidal charge of the black hole, the profiled line becomes to be flatter and wider keeping their standard character with flux stronger at the blue edge of the profiled line. The extension of the line grows with radius falling and inclination angle growing. With growing inclination angle a small hump appears in the profiled lines due to the strong lensing effect of photons coming from regions behind the black hole. For positive tidal charge (b > 0) and high inclination angles two small humps appear in the profiled lines close to the red and blue edge of the lines due to the strong lensing effect. We can conclude that for all values of b, the strongest effect on the profiled lines shape (extension) is caused by the changes of the inclination angle.     

Orbital resonances in discs around braneworld Kerr black holes

Rotating black holes in the brany universe of the Randall–Sundrum type with infinite additional dimension are described by the Kerr geometry with a tidal charge b representing the interaction of the brany black hole and the bulk spacetime. For b < 0 rotating black holes with dimensionless spin a > 1 are allowed. We investigate the role of the tidal charge in the orbital resonance model of quasiperiodic oscillations (QPOs) in black hole systems. The orbital Keplerian frequency v _K and the radial and vertical epicyclic frequencies v _r, v _θ of the equatorial, quasicircular geodetical motion are given. Their radial profiles related to Keplerian accretion discs are discussed, assuming the inner edge of the disc located at the innermost stable circular geodesic. For completeness, naked singularity spacetimes are considered too. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances of the oscillations with the radial and vertical epicyclic frequencies, for the relativistic precession model, and for some trapped oscillations of the warped discs, with resonant combinational frequencies involving the Keplerian and radial epicyclic frequencies. It is shown, how the tidal charge could influence matching of the observational data indicating the 3 : 2 frequency ratio observed in GRS 1915 + 105 microquasar with prediction of the orbital resonance model; limits on allowed range of the black hole parameters a and b are established. The “magic” dimensionless black hole spin enabling presence of strong resonant phenomena at the radius, where v _K: v _θ : v _r = 3 : 2 : 1, is determined in dependence on the tidal charge. Such strong resonances could be relevant even in sources with highly scattered resonant frequencies, as those expected in Sgr A*. The specific values of the spin and tidal charge are given also for existence of specific radius where v _K : v _θ : v _r = s : t : u with 5≥s >t >u being small natural numbers. It is shown that for some ratios such situation is impossible in the field of black holes. We can conclude that analysing the microquasars high-frequency QPOs in the framework of orbital resonance models, we can put relevant limits on the tidal charge of brany Kerr black holes.     

Gauge invariance and quantization applied to atom and nucleon internal structure

The prevailing theoretical quark and gluon momentum,orbital angular momentum and spin operators,satisfy either gauge invariance or the corresponding canonical commutation relation,but one never has these operators which satisfy both except the quark spin.The conflicts between gauge invariance and the canonical quantization requirement of these operators are discussed.A new set of quark and gluon momentum,orbital angular momentum and spin operators,which satisfy both gauge invariance and canonical momentum and angular momentum commutation relation,are proposed.To achieve such a proper decomposition the key point is to separate the gauge field into the pure gauge and the gauge covariant parts.The same conflicts also exist in QED and quantum mechanics,and have been solved in the same manner.The impacts of this new decomposition to the nucleon internal structure are discussed.     

Gauge invariance and renormalization

The renormalization of Abelian and non-Abelian local gauge theories is discussed. It is recalled that whereas Abelian gauge theories are invariant to local c-number gauge transformations δA_μ(x) = ?_μ,…, with □Λ = 0, and to the operator gauge transformation δA_μ(x) = ?_μφ(x), …, δφ(x) = α^?1?·A(x), with □φ = 0, non-Abelian gauge theories are invariant only to the operator gauge transformations $\text{δA}{}_{\mathrm{\mu }}\text{(x) ～}\textcolor{red}{}{}_{\mathrm{\mu }}\text{C(x)}$, …, introduced by Becchi, Rouet and Stora, where

_μ is the covariant derivative matrix and C is the vector of ghost fields. The renormalization of these gauge transformation is discussed in a formal way, assuming that a gauge-invariant regularization is present. The naive renormalized local non-Abelian c-number gauge transformation $\text{δA}{}_{\mathrm{\mu }}\text{(x) = (Z}{}_1\text{/Z}{}_3\text{)gA}{}_{\mathrm{\mu }}\text{(x) ×}\text{Λ}\text{(x)+?}{}_{\mathrm{\mu }}\text{Λ}\text{(x)}$, …, is never a symmetry transformation and is never finite in perturbation theory. Only for $\text{Λ}\text{(x) = (Z}{}_3\text{/Z}{}_1\text{)L}$ with L finite constants or for $\text{Λ}\text{(x) = Ω}\text{z}\text{?}{}_3\text{C(x)}$ with Ω a finite constant does it become a finite symmetry transformation, where $\text{z}\text{?}{}_3$ is the ghost field renormalization constant. The renormalized non-Abelian Ward-Takahashi (Slavnov-Taylor) identities are consequences of the invariance of the renormalized gauge theory to this formation. It is also shown how the symmetry generators are renormalized, how photons appear as Goldstone bosons, how the (non-multiplicatively renormalizable) composite operator A_μ × C is renormalized, and how an Abelian c-number gauge symmetry may be reinstated in the exact solution of many asymptotically fr ee non-Abelian gauge theories.     

Gauge invariance and daisies

Perturbative calculation of effective potentials based on fine-tuning of coupling constants must be carefully done in order to preserve its gauge invariant contents.     

Gauge invariance in fractional field theories

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order in the coupling constant . Based on the Riemann-Liouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non-relativistic fractional Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.     

Gauge invariance and Nielsen identities

The one-loop contribution to the effective potential and mass are computed within the context of scalar electrodynamics for the class of generalR gauges in the \(\overline {MS} \) scheme. These calculations are performed in order to construct a non-trivial verification of the corresponding Nielsen identities within the context of the Higgs model. Some brief comments on the Coleman-Weinberg model are also included.     

Gauge invariance and renormalization constants

Using only general considerations such as translation invariance, positive definite energy spectrum and gauge invariance, spectral representations have been set up for the vacuum expectation values of two photon and two electron operators in electrodynamics. The gauge dependence of such quantities is thus clearly exhibited, particularly that of equal time commutators and of propagators. Certain constants, related to the renormalization constants, integrals of the spectral functions are defined and shown to be gauge invariant. The generalized Ward identity is established in any gauge.     

Gauge invariance and fock states

The Fock-space formulation is extended to nonabelian gauge theories. Using a kinematical potential instead of the Yang-Mills field, we construct invariant creation operators. Physical states are selected by the requirement that they remain invariant under a new gauge-invariant global transformation.     

Gauge invariance for extended objects

Just as the vector potential (one-form) couples to charged point-particles, antisymmetric tensor fields of higher rank (p-forms) couple to elementary objects of higher dimensionality (strings, membranes, …). It is shown that the only possible gauge invariant interaction of such an extended object with a gauge field in spacetime is based on the abelian group U(1). This is unlike the situation for particles where Yang-Mills actions based on any gauge group may be written down. The properties of the abelian theory are explored. It is pointed out that a compact object is analogous to a particle-antiparticle pair and its quantum rate of production in a constant external field is calculated semiclassically. The analysis is performed keeping generic both the dimension of the object and that of spacetime.     

Non-abelian gauge structure in neutrino mixing

We discuss the existence of a non-abelian gauge structure associated with flavor mixing. In the specific case of two flavor mixing of Dirac neutrino fields, we show that this reformulation allows to define flavor neutrino states which preserve the Poincaré structure. Phenomenological consequences of our analysis are explored.     

Gauge natural formulation of conformal gravity

We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to conformal and diffeomorphism symmetries.     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.