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Register a new userGauge Independence in a Higher-Order Lagrangian Formalism via Change of Variables in the Path Integral
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In this paper we work out the explicit form of the change of variables that reproduces an arbitrary change of gauge in a higher-order Lagrangian formalism.
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We present different non-perturbative calculations within the context of Migdals representation for the propagator and effective action of quantum particles. We first calculate the exact propagators and effective actions for Dirac, scalar and Proca fields in the presence of constant electromagnetic fields, for an even-dimensional spacetime. Then we derive the propagator for a charged scalar field in a spacelike vortex (i.e., instanton) background, in a long-distance expansion, and the exact propagator for a massless Dirac field in 1+1 dimensions in an arbitrary background. Finally, we present an interpretation of the chiral anomaly in the present context, finding a condition that the paths must fulfil in order to have a non-vanishing anomaly.
We evaluate four-gauge-particle tree level scattering amplitudes using the Polyakov string path integral in the proper-time gauge, where the string path integral can be cast into the Feynman-Schwinger proper-time representation. We compare the resultant scattering amplitudes, which include $ap$-corrections, with the conventional ones that may be obtained by substituting local vertex operators for the external string states. In the zero-slope limit, both amplitudes are reduced to the four-gauge-particle scattering amplitude of non-Abelian Yang-Mills gauge theory. However, when the string corrections become relevant with finite $ap$, the scattering amplitude in the proper-time gauge differs from the conventional one: The Polyakov string path integral in the proper-time gauge, equivalent to the deformed cubic string field theory, systematically provides the alpha prime corrections. In addition, we find that the scattering amplitude in the proper-time gauge contains tachyon poles in a manner consistent with three-particle-scattering amplitudes. The scattering amplitudes evaluated using the Polyakov string path integral in the proper-time gauge may be more suitable than conventional ones for exploring string corrections to the quantum field theories and high energy behaviors of open string.
We evaluate the four-closed-string scattering amplitude, using the Polyakov string path integral in the proper-time gauge. By identifying the Fock space representation of the four-closed-string-vertex, we obtain a field theoretic expression of the closed string scattering amplitudes. In the zero-slope limit, the four-closed-string scattering amplitude reduces to the four-graviton-scattering amplitude of Einsteins gravity. However, at a finite slope, the four-graviton scattering amplitude in the proper-time gauge differs not only from that of Einstein gravity, but also significantly differs from the conventional one obtained by using the vertex operator technique in string theory. This discrepancy is mainly due to the presence of closed string tachyon poles in the four-graviton-scattering amplitude, which are missing in previous works. Because the tachyon poles in the scattering amplitude considerably alter the short distance behavior of gravitational interaction, they may be important in understanding problems associated with the perturbative theory of quantum gravity and the dark matter within the framework of string theory.
In this work we investigate the effects of the Gribov prescription to get rid of zero-modes of the Faddeev-Popov operator, at one-loop order in perturbation theory, in the Landau-DeWitt gauge. Quantum fluctuations are taken around a transverse background gauge field. The one-loop effective action is explicitly computed, and the behavior of the gauge and ghost fields propagators are carefully investigated. At one-loop and for generic transverse background configurations the effective action is found to be textit{not} background invariant, as expected, due to a non-vanishing background contribution. The gauge field propagator has the same form as in the case {where the} background is a trivial field, $i.e.$ with complex conjugate poles, which are modified by the corresponding gap equation. The ghost-anti-ghost propagator still displays its enhanced $sim p^{-4}$ behavior.
We apply a recently presented BRST procedure to construct the Largangian cubic vertex of higher-spin gauge field triplets interacting with massive free scalars. In flat space, the spin-s triplet propagates the series of irreducible spin-s, s-2,..,0/1 modes which couple independently to corresponding conserved currents constructed from the scalars. The simple covariantization of the flat space result is not enough in AdS, as new interaction vertices appear. We present in detail the cases of spin-2 and spin-3 triplets coupled to scalars. Restricting to a single irreducible spin-s mode we uncover previously obtained results. We also present an alternative derivation of the lower spin results based on the idea that higher-spin gauge fields arise from the gauging of higher derivative symmetries of free matter Lagrangians. Our results can be readily applied to holographic studies of higher-spin gauge theories.
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