Field Theoretical Effects Research Articles

Quantum superpositions of Minkowski spacetime

Within any anticipated unifying theory of quantum gravity, it should be meaningful to combine the fundamental notions of quantum superposition and spacetime to obtain so-called "spacetime superpositions": that is, quantum superpositions of different spacetimes not related by a global coordinate transformation. Here we consider the quantum-gravitational effects produced by superpositions of periodically identified Minkowski spacetime (i.e.\ Minkowski spacetime with a periodic boundary condition) with different characteristic lengths. By coupling relativistic quantum matter to fields on such a spacetime background (which we model using the Unruh-deWitt particle detector model), we are able to show how one can in-principle "measure" the field-theoretic effects produced by such a spacetime. We show that the detector's response exhibits discontinuous resonances at rational ratios of the superposed periodic length scale.

Cavity Optimization for Unruh Effect at Small Accelerations.

One of the primary reasons behind the difficulty in observing the Unruh effect is that for achievable acceleration scales the finite temperature effects are significant only for the low frequency modes of the field. Since the density of field modes falls for small frequencies in free space, the field modes which are relevant for the thermal effects would be less in number to make an observably significant effect. In this Letter, we investigate the response of an Unruh-DeWitt detector coupled to a massless scalar field which is confined in a long cylindrical cavity. The density of field modes inside such a cavity shows a resonance structure, i.e., it rises abruptly for some specific cavity configurations. We show that an accelerating detector inside the cavity exhibits a nontrivial excitation and de-excitation rates for small accelerations around such resonance points. If the cavity parameters are adjusted to lie in a neighborhood of such resonance points, the (small) acceleration-induced emission rate can be made much larger than the already observable inertial emission rate. We comment on the possibilities of employing this detector-field-cavity system in the experimental realization of the Unruh effect, and argue that the necessity of extremely high acceleration can be traded off in favor of precision in cavity manufacturing for realizing noninertial field theoretic effects in laboratory settings.

Detecting Acceleration-Enhanced Vacuum Fluctuations with Atoms Inside a Cavity.

Some of the most prominent theoretical predictions of modern times, e.g., the Unruh effect, Hawking radiation, and gravity-assisted particle creation, are supported by from the fact that various quantum constructs like particle content and vacuum fluctuations of a quantum field are observer-dependent. Despite being fundamental in nature, these predictions have not yet been experimentally verified because one needs extremely strong gravity (or acceleration) to bring them within the existing experimental resolution. In this Letter, we demonstrate that a post-Newtonian rotating atom inside a far-detuned cavity experiences strongly modified quantum fluctuations in the inertial vacuum. As a result, the emission rate of an excited atom gets enhanced significantly along with a shift in the emission spectrum due to the change in the quantum correlation under rotation. We propose an optomechanical setup that is capable of realizing such acceleration-induced particle creation with current technology. This provides a novel and potentially feasible experimental proposal for the direct detection of noninertial quantum field theoretic effects.

Do spinors give rise to a frame-dragging effect?

We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity where torsion is constrained to be zero. This resolves a paradox regarding the counter-force needed to restore Newton's third law in the well-known spin-orbit interaction. In addition, the frame-dragging effect gives rise to a long-range gravitationally mediated spin-spin dipole interaction coupling the internal spins of two sources. We argue that despite the weakness of the interaction, the spin-spin interaction will dominate over the ordinary inverse square Newtonian interaction in any process of sufficiently high energy for quantum field theoretical effects to be non-negligible.

DBI in the sky: Non-Gaussianity from inflation with a speed limit

We analyze the spectrum of density perturbations generated in models of the recently discovered ``D-cceleration'' mechanism of inflation. In this scenario, strong coupling quantum field theoretic effects sum to provide a Dirac-Born-Infeld--like action for the inflaton. We show that the model has a strict lower bound on the non-Gaussianity of the cosmic microwave background radiation power spectrum at an observable level, and is thus falsifiable. This, in particular, observationally distinguishes this mechanism from traditional slow-roll inflation generated by weakly interacting scalar fields. The model also favors a large observable tensor component to the cosmic microwave background radiation spectrum.

QUASIPARTICLE UNIVERSES IN BOSE–EINSTEIN CONDENSATES

Recent developments in simulating fundamental quantum field theoretical effects in the kinematical context of analogue gravity are reviewed. Specifically, it is argued that a curved spacetime generalization of the Unruh–Davies effect — the Gibbons–Hawking effect in the de Sitter spacetime of inflationary cosmological models — can be implemented and verified in an ultracold gas of bosonic atoms.

Testing the equivalence principle by Lamb shift energies.

The Einstein equivalence principle has as one of its implications that the nongravitational laws of physics are those of special relativity in any local freely falling frame. We consider possible tests of this hypothesis for systems whose energies are due to radiative corrections, i.e., which arise purely as a consequence of quantum field theoretic loop effects. Specifically, we evaluate the Lamb shift transition (as given by the energy splitting between the $2{S}_{\frac{1}{2}}$ and $2{P}_{\frac{1}{2}}$ atomic states) within the context of violations of local position invariance and local Lorentz invariance, as described by the $\mathrm{TH}\ensuremath{\epsilon}\ensuremath{\mu}$ formalism. We compute the associated redshift and time dilation parameters, and discuss how (high-precision) measurements of these quantities could provide new information on the validity of the equivalence principle.

Field theoretical quantum effects on the Kerr geometry.

We study quantum aspects of the Einstein gravity with one time-like and one space-like Killing vector commuting with each other. The theory is formulated as a $\coset$ nonlinear $\sigma$-model coupled to gravity. The quantum analysis of the nonlinear $\sigma$-model part, which includes all the dynamical degrees of freedom, can be carried out in a parallel way to ordinary nonlinear $\sigma$-models in spite of the existence of an unusual coupling. This means that we can investigate consistently the quantum properties of the Einstein gravity, though we are limited to the fluctuations depending only on two coordinates. We find the forms of the beta functions to all orders up to numerical coefficients. Finally we consider the quantum effects of the renormalization on the Kerr black hole as an example. It turns out that the asymptotically flat region remains intact and stable, while, in a certain approximation, it is shown that the inner geometry changes considerably however small the quantum effects may be.

Quantum moduli spaces of N=1 string theories.

Generically, string models with $N=1$ supersymmetry are not expected to have moduli beyond perturbation theory; stringy nonperturbative effects as well as low energy field-theoretic phenomena such as gluino condensation will lift any flat directions. In this work, we describe models where some subspace of the moduli space survives nonperturbatively. Discrete $R$ symmetries forbid any inherently stringy effects, and dynamical considerations control the field-theoretic effects. The surviving subspace is a space of high symmetry; the system is attracted to this subspace by a potential which we compute. Models of this type may be useful for considerations of duality and raise troubling cosmological questions about string theory. Our considerations also suggest a mechanism for fixing the expectation value of the dilaton.

Field theoretic effects in highly charged ions

It is argued that the study of the spectroscopy of highly charged few-electron ions provides a uniquely powerful probe of our understanding of the relativistic many-body problem and its basis in quantum field theory. The use of S-matrix techniques is shown to lead to energy shifts defined in terms of a set of Feynman diagrams. Numerical issues involved in the evaluation of the one-loop self energy graph, which contributes to the Lamb shift, are discussed. Two-photon exchange graphs are shown to contribute simultaneously to correlation and to screening of the Lamb shift for two-electron ions. Particular emphasis is made on distinguishing field-theoretic effects from effects already contained in Hamiltonian formalisms.

Field theoretic aspects of meson-nucleus scattering

Field theoretic aspects of the pion field interacting with a nucleus are investigated. The quantum field nature of the pion is shown to be most simply and fundamentally incorporated into multiple scattering theory through the Klein-Gordon equation. This is accomplished so that crossing symmetry of the scattering amplitude is manifest and can be maintained without recourse to nonlinear equations. We give specific examples of calculating the first and second order optical potential in the static approximation. Our approach provides a clean separation between the energy and momentum dependence of the pion-nucleon amplitude and does not have the strong momentum cutoffs or the spurious reactive content of other approaches. An off-shell extrapolation of the pion-nucleon amplitude in terms of the four-momenta is required for the evaluation of second and higher order contributions to the optical potential. We discuss the conditions under which our static field theory can be regarded as a limit of a theory which allows for nucleon recoil.NUCLEAR REACTIONS Pion-nucleus elastic scattering, optical potential, field theoretic effects, crossing symmetry, off-shell behavior of two-body amplitudes.

Recoil and correlations in pion double scattering

The contribution to the optical potential due to double scattering of a pion by a pair of correlated nucleons has been calculated for nuclear matter taking account of nucleon and delta kinetic energies. The calculation includes a variety of field theoretical effects due to crossed processes and all possible time sequences of the two scattering events including overlap in time. For sequential processes, where the first scattering is complete before the second starts, it is found that inclusion of kinetic energies of the nucleon and delta reduces the contribution drastically. The contribution of these sequential processes is about 2% of the first-order optical potential as contrasted with about 50% at ${T}_{\ensuremath{\pi}}=140$ MeV when the fixed scatterer approximation is employed. The most important correlated double scattering contributions arise from the field theoretical effects which yield about 8% of the first-order optical potential at ${T}_{\ensuremath{\pi}}=0 \mathrm{and} 140$ MeV. Thus, the net contribution of correlated double scattering processes is about 10% of the first-order optical potential. Since the double scattering of the pion by a correlated nucleon pair is a major contributor to the Ericson-Ericson effect, the present work suggests reduced importance of the effect.NUCLEAR REACTIONS Correlations, fixed scatterer approximation, LLEE effect, double scattering, recoil, pion scattering.

An eikonal perturbation theory having applications in hadron dynamics. II. Massive quantum electrodynamics

An eikonal perturbation theory (EPT), derived in previous work for a superrenormalizable coupling, is here developed for massive quantum electrodynamics (MQED) involving scalar or spinor matter fields minimally coupled to neutral massive vector gluons. After summarizing the functional method, we present the EPT for the external field problem. In agreement with results known within ordinary perturbation theory (OPT) in the eikonal approximation (EA), from an exact eikonal equation derived here we show that the EPT for the external field problem provides an excellent approximation method for Green's functions at large momenta. We then discuss some general features of the EPT for MQED, and show that it leads to a renormalizable approximation method. Our approach is then illustrated by deriving explicit expressions for various renormalized Green's functions in lowest order EPT. We also discuss some asymptotic properties of such Green's functions and indicate how to proceed with calculations in higher orders. As in our previous work, we again find that the renormalization procedure in EPT bears close resemblance to the one for OPT. Contrary to what happens with the EA, the inclusion of self-interactions and of other field-theoretic effects does not spoil the virtues of the EPT as a far better high-momenta approximation than the OPT. As a typical example, if s is an energy parameter and g the coupling constant with g 2 4π < 1 , OPT to order g 2 n often fails to be a good approximation as soon as ( g 2 4π ) ln s ∼ 1 , while in such cases EPT to order g 2 n is still a good approximation as long as ( g 2 4π ) n+1 ln s < 1 . We also find that the EPT is superior to the EA in that, contrary to the EA, it provides a step-by-step rigorous and renormalizable iterative approximation method which can account for self-interactions and other field-theoretic effects. We emphasize that the EPT is much simpler and more general than other explicit approximate summation methods of classes of OPT Feynman graphs. In field theory, we consider the use of the EPT as a generalization of the EA for discussing, e.g. high-energy behaviors in MQED as well as infrared divergence and bound-state problems in the limit of massless gluons. It is also suggested that, in view of its nice field-theoretic and high-energy properties, the EPT for MQED might provide a useful laboratory where ideas and problems in hadron dynamics could be meaningfully investigated within a Lagrangian field theory.

Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization

In preparation for an investigation of whether field-theoretic effects helped to make the early universe become isotropic, we seek to determine the physical (divergence-free) energy-momentum tensor through which the geometry of spacetime is influenced by a quantized scalar field with conformal ("new improved") coupling to the metric. The cosmological models studied are the Kasner-like (type I) metrics (homogeneous, spatially flat, nonrotating, but anisotropic), and also the isotropic Robertson-Walker metrics. The methods employed have previously been expounded in the context of a minimally coupled scalar field and a Robertson-Walker metric. Three divergent leading terms are extracted from an adiabatic expansion of the formal expressions for the expectation values of the energy density and pressures. In the Kasner case a slight reshuffling of the leading terms in the energy density displays all divergences to be proportional to either the metric tensor or a second-order curvature tensor which vanishes when the spacetime is isotropic; hence a finite energy-momentum tensor remains after renormalization of the cosmological constant and one other coupling constant in a generalized Einstein equation. In the Robertson-Walker cases, because of conformal flatness, there is no divergence beyond the usual quartically divergent constant vacuum energy; when the mass is not zero, however, a finite renormalization of the gravitational constant is suggested. The correctness of the methods is tested by considering a coordinate system in which flat spacetime assumes the form of a Kasner universe: The adiabatic definition of particle number and vacuum, which is basic to our expansion and renormalization methods, is seen to be consistent with the usual flat-space concepts.

Field theoretical effects in X-ray spectra

The LI-LII screening doublet separation in the relativistic approximation up to Z20 has been compared with that obtained experimentally by the transitions MIVLII (Lβ 1) and MIVLI (Lβ 10). The experimental and theoretical values deviate considerably. If one retains terms up to Z4, an apparently close fit with the experimental values is obtained. It is shown that such a fit disappears on applying the field theoretical corrections and this stresses the need of retaining the terms up to Z20. The justification of neglecting the still higher powers of Z lies in the smallness of their magnitude when compared to the experimental errors. The field theoretical corrections modify the relativistic curve that contains terms up to Z20 in such a way that one again gets a good fit with the experimental values. This shows how the various field theoretical corrections and the contributions from relativistic terms with powers of Z greater than four compensate each other.