Field Theory In Flat Space-time Research Articles

Entanglement in Unruh, Hawking, and Cherenkov radiation from a quantum optical perspective

Free quantum field theory in flat space-time is often believed to be well established, holding no surprises. We hope, by the end of this paper, to have demonstrated that surprises still exist. For example, we will show that a uniformly accelerated atom in Minkowski space-time emits entangled photon pairs in a squeezed state which mimics entanglement of the Minkowski vacuum in that the entanglement is between Minkowski modes which are dominantly in opposite causal wedges of the space-time. Similar emission of photon pairs occurs if an atom is held above the black hole event horizon. Namely, a ground-state atom becomes excited by emitting a ``negative'' -energy photon under the horizon and then spontaneously decays back to the ground state by emitting a positive-energy photon outside the horizon, which propagates away from the black hole.

Absence of cosmological constant problem in special relativistic field theory of gravity

The principles of quantum field theory in flat spacetime suggest that gravity is mediated by a massless particle with helicity ±2, the so-called graviton. It is regarded as textbook knowledge that, when the self-coupling of a particle with these properties is considered, the long-wavelength structure of such a nonlinear theory is fixed to be that of general relativity. However, here we indicate that these arguments conceal an implicit assumption which is surreptitiously motivated by the very knowledge of general relativity. This is shown by providing a counterexample: we revisit a nonlinear theory of gravity which is not structurally equivalent to general relativity and that, in the non-interacting limit, describes a free helicity ±2 graviton. We explicitly prove that this theory, known as Weyl-transverse gravity (unimodular gravity with explicit Weyl invariance), can be understood as the result of self-coupling in complete parallelism to the well-known case of general relativity. We discuss the absence of cosmological constant problem in this theory, highlighting that it provides a particular realization of previous arguments formulated in studies of the emergence of the gravitational interaction from condensed-matter-like models. Overall, we conclude that the consideration that gravity is mediated by a massless particle with helicity ±2 does not inextricably lead to the cosmological constant problem.

Thermal bath in de Sitter space from holography

We consider the AdS/dS CFT correspondence and study the nature of the thermal bath of the de Sitter field theory using holography. Unlike the temperature of a thermal field theory in flat spacetime, the temperature of a superconformal field theory on de Sitter space is an integral part of the theory and leaves intact the conformal symmetry and supersymmetry. In the dual AdS side, there is no black hole. Instead we have cosmological expansion of the de Sitter factor. We consider a number of different observables, such as the entanglement entropy, two point correlation function, Wilson loops corresponding to static and spinning mesons in the field theory, and study their thermal properties using holography. The former two quantities have trivial temperature dependence due to conformal symmetry. We compute the energy of the quark anti-quark bound state for a static meson, as well as the energy and the angular momentum for a spinning meson. We find that there is a maximum distance, as well as a maximum spin for the latter case, beyond which the bound state become unstable. The temperature behavior of the physical quantities in these meson systems are similar to that of the usual thermal field theory with holographic black hole dual. With these examples, we show clearly how the field theory observables get their thermal properties from the bulk despite the absence of a black hole, with the role of the black hole horizon played by the cosmological expansion of the de Sitter factor of the AdS metric.

Nonlocal scalar quantum field theory from causal sets

We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.

Gravity as a field theory in flat space-time

We propose a formulation of gravity theory in the form of a field theory in a flat space-time with a number of dimensions greater than four. Configurations of the field under consideration describe the splitting of this space-time into a system of mutually noninteracting four-dimensional surfaces. Each of these surfaces can be considered our four-dimensional space-time. If the theory equations of motion are satisfied, then each surface satisfies the Regge-Teitelboim equations, whose solutions, in particular, are solutions of the Einstein equations. Matter fields then satisfy the standard equations, and their excitations propagate only along the surfaces. The formulation of the gravity theory under consideration could be useful in attempts to quantize it.

Surprising phenomena in a rich new class of inflationary models

We report on a new class of fast-roll inflationary models. In a huge part of its parameter space, inflationary perturbations exhibit quite unusual phenomena such as scalar and tensor modes freezing out at widely different times, as well as scalar modes reentering the horizon during inflation. One specific point in parameter space is characterized by extraordinary behavior of the scalar perturbations. Freeze-out of scalar perturbations as well as particle production at horizon crossing are absent. Also the behavior of the perturbations around this quasi-de Sitter background is dual to a quantum field theory in flat space-time. Finally, the form of the primordial power spectrum is determined by the interaction between different modes of scalar perturbations.

Nordström gravity coupled to point particles in (1+1) dimensions

We consider a (1+1)-dimensional model of general relativity that is based on a geometric theory of gravity due to Nordstrom. We show that the theory is formally equivalent to scalar field theory in flat spacetime, and we exploit this equivalence to solve the initial value problem for the system for the case of point particle sources. We illustrate our results by obtaining several example solutions to the model.

Non relativistic Dpbranes

We construct a kappa-symmetric and diffeomorphism-invariant non-relativistic Dp-brane action as a non-relativistic limit of a relativistic Dp-brane action in flat space. In a suitable gauge the world-volume theory is given by a supersymmetric free field theory in flat spacetime in p+1 dimensions of bosons, fermions and gauge fields.

Symmetry properties under arbitrary field redefinitions of the metric energy–momentum tensor in classical field theories and gravity

We derive a generic identity which holds for the metric (i.e. variational) energy–momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy–momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime. In this sense, a field theory in flat spacetime is not self-contained. When the identity is applied to the gauge invariant spin-2 field in Minkowski space, we obtain an alternative and direct derivation of a known no-go theorem: a linear gauge invariant spin-2 field, which is dynamically equivalent to linearized general relativity, cannot have a gauge invariant metric energy–momentum tensor. This implies that attempts to define the notion of gravitational energy density in terms of the metric energy–momentum tensor in a field-theoretical formulation of gravity must fail.

Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect.

We investigate the weak decay of uniformly accelerated protons in the context of standard quantum field theory. Because the mean proper lifetime of a particle is a scalar, the same value for this observable must be obtained in the inertial and coaccelerated frames. We are only able to achieve this equality by considering the Fulling-Davies-Unruh effect. This reflects the fact that the Fulling-Davies-Unruh effect is mandatory for the consistency of quantum field theory.

Electron-positron jets from a critically magnetized black hole

The curved spacetime surrounding a rotating black hole dramatically alters the structure of nearby electromagnetic fields. The Wald field which is an asymptotically uniform magnetic field aligned with the angular momentum of the hole provides a convenient starting point to analyze the effects of radiative corrections on electrodynamics in curved spacetime. Since the curvature of the spacetime is small on the scale of the electron's Compton wavelength, the tools of quantum field theory in flat spacetime are reliable and show that a rotating black hole immersed in a magnetic field approaching the quantum critical value of $B_k=m^2 c^3/(e\hbar) \approx 4.4 \times 10^{13}$~G $\approx 1.3\times10^{-11}$ cm$^{-1}$ is unstable. Specifically, a maximally rotating three-solar-mass black hole immersed in a magnetic field of $2.3 \times 10^{12}$~G would be a copious producer of electron-positron pairs with a luminosity of $3 \times 10^{52}$ erg s$^{-1}$.

Consistency of semiclassical gravity

We discuss some subtleties that arise in the semiclassical approximation to quantum gravity. We show that integrability conditions prevent the existence of Tomonaga--Schwinger time functions on the space of three-metrics but admit them on superspace. The concept of semiclassical time is carefully examined. We point out that central charges in the matter sector spoil the consistency of the semiclassical approximation, unless the full quantum theory of gravity and matter is anomaly-free. We finally discuss consequences of these considerations for quantum field theory in flat spacetime, but with arbitrary foliations.

Instability of flat spacetime in semiclassical gravity

The semiclassical theory of gravity is considered in which an asymptotically flat background metric is coupled to quantized matter. We show that, in general, there are modes with spacelike wave vectors for small metric fluctuations around flat spacetime. Besides the usual axioms of quantum field theory in flat spacetime, the proof rests on the existence of a hard trace anomaly in the energy-momentum tensor due to matter self-couplings. Two possible interpretations of the result are discussed.

The unpredictability of quantum gravity

Quantum gravity seems to introduce a new level of unpredictability into physics over and above that normally associated with the uncertainty principle. This is because the metric of spacetime can fluctuate from being globally hyperbolic. In other words, the evolution is not completely determined by Cauchy data at past or future infinity. I present a number of axioms that the asymptotic Green functions should obey in any reasonable theory of quantum gravity. These axioms are the same as for ordinary quantum field theory in flat spacetime, except that one axiom, that of asymptotic completeness, is omitted. This allows pure quantum states to decay into mixed states. Calculations with simple models of topologically non-trivial spacetime indicate that such loss of quantum coherence will occur but that the effect will be very small except for fundamental scalar particles, if any such exist.