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Register a new userVacuum effective actions and mass-dependent renormalization in curved space
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We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newtons constant and the other gravitational couplings.
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The in-out formalism is a systematic and powerful method for finding the effective actions in an electromagnetic field and a curved spacetime provided that the field equation has explicitly known solutions. The effective action becomes complex when pairs of charged particles are produced due to an electric field and curved spacetime. This may lead to a conjecture of one-to-one correspondence between the vacuum polarization (real part) and the vacuum persistence (imaginary part). We illustrate the one-loop effective action in a constant electric field in a Minkowski spacetime and in a uniform electric field in a two-dimensional (anti-) de sitter space.
In $d$ dimensions, the model for a massless $p$-form in curved space is known to be a reducible gauge theory for $p>1$, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting $p$-form model, one ends up with an irreducible gauge theory which can be quantised `a la Faddeev and Popov. We derive a compact expression for the massive $p$-form effective action, $Gamma^{(m)}_p$, in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions $Gamma^{(m)}_p$ and $Gamma^{(m)}_{d-p-1}$ differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions $Gamma_p$ and $Gamma_{d-p-2}$ coincide modulo a topological term. Finally, our analysis is extended to the case of massive super $p$-forms coupled to background ${cal N}=1$ supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super $p$-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.
The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the renormalization-group framework in a consistent way. On the other hand, the version of effective action proposed by Vilkovisky and DeWitt does not depend on the gauge-fixing and parametrization off-shell, opening the way to explore the running of the cosmological and Newton constants as well as the coefficients of the higher-derivative terms of the total action. We argue that in the effective framework the one-loop beta functions for the zero-, two- and four-derivative terms can be regarded as exact, that means, free from corrections coming from the higher loops. In this perspective, the running describes the renormalization group flow between the present-day Hubble scale in the IR and the Planck scale in the UV.
In this work, based on a recently introduced localization scheme for scalar fields, we argue that the geometry of the space-time, where the particle states of a scalar field are localized, is intimately related to the quantum entanglement of these states. More specifically, we show that on curved space-time can only be localized entangled states, while separable states are located on flat space-time. Our result goes in parallel with recent theoretical developments in the context of AdS/CFT correspondence which uncovered connections between gravity and quantum entanglement.
In this paper, we theoretically investigate the time dilation and Doppler effect in curved space-time from the perspective of quantum field theory (QFT). A Coordinate Transformation which Maintains the Period of Clocks is introduced, and such coordinate transformation is named as CTMPC throughout this paper. By analogy with the Lorentz transformation in Minkowski space-time, CTMPC is a correct transformation in curved space-times in a sense that it shows the correct relation between the time measured by the two observers, moreover, Lorentz transformation is just a special case of CTMPC applied in Minkowski space-time. We demonstrate that the Coordinate Transformation which Maintains the Local Metric (CTMLM) is one CTMPC, while the mathematical forms of physics formulas in QFT will be maintained. As applications of CTMLM, the time dilation and Doppler effect with an arbitrary time-dependent relative velocity in curved space-time are analysed. For Minkowski space-time, the time dilation and Doppler effect agree with the clock hypothesis. For curved space-time, we show that even if the emitted wave has a narrow frequency range, the Doppler effect may, in general, broaden the frequency spectrum and, at the meantime, shift the frequencies values. These new findings will deepen our understanding on the nature of space-time and the Doppler effect in curved space-time, they may also provide theoretical guidance in future astronomical observations.
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