اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEquivalence between the Lovelock-Cartan action and a constrained gauge theory
237
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We show that the four-dimensional Lovelock-Cartan action can be derived from a massless gauge theory for the $SO(1,3)$ group with an additional BRST trivial part. The model is originally composed by a topological sector and a BRST exact piece and has no explicit dependence on the metric, the vierbein or a mass parameter. The vierbein is introduced together with a mass parameter through some BRST trivial constraints. The effect of the constraints is to identify the vierbein with some of the additional fields, transforming the original action into the Lovelock-Cartan one. In this scenario, the mass parameter is identified with Newtons constant while the gauge field is identified with the spin-connection. The symmetries of the model are also explored. Moreover, the extension of the model to a quantum version is qualitatively discussed.
قيم البحث
اقرأ أيضاً
The phase-integral and worldline-instanton methods are two widely used methods to calculate Schwinger pair-production densities in electric fields of fixed direction that depend on just one time or space coordinate in the same fixed plane of the elec
tromagnetic field tensor. We show that for charged spinless bosons the leading results of the phase-integral method integrated up through quadratic momenta are equivalent to those of the worldline-instanton method including prefactors. We further apply the phase-integral method to fermion production and time-dependent electric fields parallel to a constant magnetic field.
We develop the general theory of Noether symmetries for constrained systems. In our derivation, the Dirac bracket structure with respect to the primary constraints appears naturally and plays an important role in the characterization of the conserved
quantities associated to these Noether symmetries. The issue of projectability of these symmetries from tangent space to phase space is fully analyzed, and we give a geometrical interpretation of the projectability conditions in terms of a relation between the Noether conserved quantity in tangent space and the presymplectic form defined on it. We also examine the enlarged formalism that results from taking the Lagrange multipliers as new dynamical variables; we find the equation that characterizes the Noether symmetries in this formalism. The algebra of generators for Noether symmetries is discussed in both the Hamiltonian and Lagrangian formalisms. We find that a frequent source for the appearance of open algebras is the fact that the transformations of momenta in phase space and tangent space only coincide on shell. Our results apply with no distinction to rigid and gauge symmetries; for the latter case we give a general proof of existence of Noether gauge symmetries for theories with first and second class constraints that do not exhibit tertiary constraints in the stabilization algorithm. Among some examples that illustrate our results, we study the Noether gauge symmetries of the Abelian Chern-Simons theory in $2n+1$ dimensions. An interesting feature of this example is that its primary constraints can only be identified after the determination of the secondary constraint. The example is worked out retaining all the original set of variables.
In this paper new exact solutions in eight dimensional Lovelock theory will be presented. These solutions are vacuum static wormhole, black hole and generalized Bertotti-Robinson space-times with nontrivial torsion. All the solutions have a cross pro
duct structure of the type $M_{5}times Sigma_{3} $ where $M_{5}$ is a five dimensional manifold and $Sigma_{3}$ a compact constant curvature manifold. The wormhole is the first example of a smooth vacuum static Lovelock wormhole which is neither Chern-Simons nor Born-Infeld. It will be also discussed how the presence of torsion affects the navigableness of the wormhole for scalar and spinning particles. It will be shown that the wormhole with torsion may act as geometrical filter: a very large torsion may increase the traversability for scalars while acting as a polarizator on spinning particles. This may have interesting phenomenological consequences.
The equivalence between Chern-Simons and Einstein-Hilbert actions in three dimensions established by A.~Achucarro and P.~K.~Townsend (1986) and E.~Witten (1988) is generalized to the off-shell case. The technique is also generalized to the Yang-Mills
action in four dimensions displaying de Sitter gauge symmetry. It is shown that, in both cases, we can directly identify a gravity action while the gauge symmetry can generate spacetime local isometries as well as diffeomorphisms. The price we pay for working in an off-shell scenario is that specific geometric constraints are needed. These constraints can be identified with foliations of spacetime. The special case of spacelike leafs evolving in time is studied. Finally, the whole set up is analyzed under fiber bundle theory. In this analysis we show that a traditional gauge theory, where the gauge field does not influence in spacetime dynamics, can be (for specific cases) consistently mapped into a gravity theory in the first order formalism.
Constrained Differential Renormalization (CDR) and the constrained version of Implicit Regularization (IR) are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods which have rath
er distinct basis have been successfully applied to several calculations which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum space procedures of Implicit Regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to the regularized ones.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
