Vacuum In Quantum Field Theory Research Articles

Determining the normalization of the quantum field theory vacuum, with implications for quantum gravity

In a standard quantum field theory the norm of the vacuum state is taken to be finite. In this paper we provide a procedure, based on constructing an equivalent wave mechanics, for determining whether or not actually is finite. We provide an example based on a second-order plus fourth-order scalar field theory, a prototype for quantum gravity, in which it is not. In this example the Lorentzian path integral with a real measure diverges though the Euclidean path integral does not. Thus in this example contributions from the Wick rotation contour cannot be ignored. Since is not finite, use of the standard Feynman rules is not valid. And while these rules not only lead to states with negative norm, they in fact lead to states with infinite negative norm. However, if the fields in that theory are continued into the complex plane, we show that then there is a domain in the complex plane known as a Stokes wedge in which one can define an appropriate time-independent, positive and finite inner product, viz. the overlap of left-eigenstates and right-eigenstates of the Hamiltonian; with the vacuum state then being normalizable, and with there being no states with negative or infinite norm. In this Stokes wedge it is the Euclidean path integral that diverges while the Lorentzian path integral does not. The concerns that we raise in this paper only apply to bosons since the matrices associated with their creation and annihilation operators are infinite dimensional. Since the ones associated with fermions are finite dimensional, the fermion theory vacuum is automatically normalizable. We discuss some general implications of our results for quantum gravity studies, and show that they are relevant to the construction of a consistent, unitary and renormalizable quantum theory of gravity.

Yoichiro Nambu and the Concept of Apparent Vacuum: A Stepping Stone to Spontaneous Symmetry Breaking

AbstractThe processes of discovery and concept formation are as mysterious as they are intriguing. In this article, they give a sketch of Yoichiro Nambu's long path toward the concept of spontaneous symmetry breaking focusing on the pivotal role played by his notion of “apparent vacuum”. This is instrumental to draw the original analogical correspondence between the vacuum of quantum field theory and solid matter, which, transforming over time in its use and purpose, enables Nambu to arrive at the concept of spontaneous symmetry breaking. From this historical episode they draw a methodological lesson and emphasise the broad cultural influences that conditioned the conceptual development.

Densities of states and the Cohen-Kaplan-Nelson bound

The holographic principle implies that quantum field theory (QFT) overcounts the number of independent degrees of freedom in quantum gravity. An argument due to Cohen, Kaplan, and Nelson (CKN) suggests that the number of degrees of freedom well described by QFT is even smaller than required by holographic bounds, and CKN interpreted this result as indicative of a correlation between the UV and IR cutoffs on QFT. Here, we consider an alternative interpretation in which the QFT degrees of freedom are depleted as a function of scale. We use a simple recipe to estimate the impact of depleted densities of states on precision observables, including the Lamb shift and lepton $g\ensuremath{-}2$. Although these observables are not sensitive to the level of depletion motivated by gravitational considerations, the phenomenological exercises also provide an interesting test of quantum field theory that is independent of underlying quantum gravity assumptions. A depleted density of states can also render the QFT vacuum energy UV insensitive, reconciling the success of QFT in describing ordinary particle physics processes and its apparent failure in predicting the cosmological constant.

Heuristic determination of the cosmological constant

The vacuum catastrophe results from the disagreement between the theoretical value of the energy density of the vacuum in quantum field theory and the estimated one observed in cosmology. In a similar attempt in which the ultraviolet catastrophe was solved, we search for the value of the cosmological constant by brute-force through computation. We explore combinations of the fundamental constants in physics performing a dimensional analysis, in search of an equation resulting in the measured energy density of the vacuum or cosmological constant that is assumed to cause the accelerated expansion of the universe.

Running vacuum in quantum field theory in curved spacetime: renormalizing rho _{vac} without sim m^4 terms

The Lambda -term in Einstein’s equations is a fundamental building block of the ‘concordance’ Lambda CDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we stick to the Lambda -term, but we contend that it can be a ‘running quantity’ in quantum field theory (QFT) in curved space time. A plethora of phenomenological works have shown that this option can be highly competitive with the Lambda CDM with a rigid cosmological term. The, so-called, ‘running vacuum models’ (RVM’s) are characterized by the vacuum energy density, rho _{vac}, being a series of (even) powers of the Hubble parameter and its time derivatives. Such theoretical form has been motivated by general renormalization group arguments, which look plausible. Here we dwell further upon the origin of the RVM structure within QFT in FLRW spacetime. We compute the renormalized energy-momentum tensor with the help of the adiabatic regularization procedure and find that it leads essentially to the RVM form. This means that rho _{vac}(H) evolves as a constant term plus dynamical components {{mathcal {O}}}(H^2) and mathcal{O}(H^4), the latter being relevant for the early universe only. However, the renormalized rho _{vac}(H) does not carry dangerous terms proportional to the quartic power of the masses (sim m^4) of the fields, these terms being a well-known source of exceedingly large contributions. At present, rho _{vac}(H) is dominated by the additive constant term accompanied by a mild dynamical component sim nu H^2 (|nu |ll 1), which mimics quintessence.

The critical transition of Coulomb impurities in gapped graphene

The effect of supercritical charge impurities in graphene is very similar to the supercritical atomic collapses in QED for Z > 137, but with a much lower critical charge. In this sense graphene can be considered as a natural testing ground for the analysis of quantum field theory vacuum instabilities. We analyze the quantum transition from subcritical to supercritical charge regimes in gapped graphene in a common framework that preserves unitarity for any value of charge impurities. In the supercritical regime it is possible to introduce boundary conditions which control the singular behavior at the impurity. We show that for subcritical charges there are also non-trivial boundary conditions which are similar to those that appear in QED for nuclei in the intermediate regime 118 < Z < 137. We analyze the behavior of the energy levels associated to the different boundary conditions. In particular, we point out the existence of new bound states in the subcritical regime which include a negative energy bound state in the attractive Coulomb regime. A remarkable property is the continuity of the energy spectral flow under variation of the impurity charge even when jumping across the critical charge transition. We also remark that the energy levels of hydrogenoid bound states at critical values of charge impurities act as focal points of the spectral flow.

Accelerated Detector Response Function in Squeezed Vacuum

Casimir/squeezed vacuum breaks Lorentz symmetry, by allowing light to propagate faster than c. We looked at the possible transformation symmetry group such vacuum could obey. By solving the semi-classical Einstein field equation in squeezed vacuum, we have found that the background geometry describes an Anti-deSitter (AdS) geometry. Therefore, the proper transformation symmetry group is the (A)dS group. One can describe quantum field theory in a finite volume as a quantum field theory (QFT) on AdS background, or vice versa. In particular, one might think of QFT vacuum on AdS as a QFT that posses a squeezed vacuum with boundary conditions proportional to R A d S 2 . Applying this correspondence to an accelerating detector-scalar field system, we notice at low acceleration the system is at equilibrium at ground state, however if the detector’s acceleration (a) is greater than a critical acceleration, the system experience a phase transition similar to Hawking-Page Phase transition at the detector gets excited, with equivalent temperature Θ = a 2 - R A d S ′ 2 2 π .

Thermally correlated states in loop quantum gravity

We study a class of loop-quantum-gravity states characterized by (ultra-local) thermal correlations that reproduce some features of the ultraviolet structure of the perturbative quantum field theory vacuum. In particular, they satisfy an analog of the Bisognano–Wichmann theorem. These states are peaked on the intrinsic geometry and admit a semiclassical interpretation. We study how the correlations extend on the spin network beyond the ultra local limit.

EXPLORING QUANTUM VACUUM WITH LOW-ENERGY PHOTONS

Although quantum mechanics (QM) and quantum field theory (QFT) are highly successful, the seemingly simplest state — vacuum — remains mysterious. While the LHC experiments are expected to clarify basic questions on the structure of QFT vacuum, much can still be done at lower energies as well. For instance, experiments like PVLAS try to reach extremely high sensitivities, in their attempt to observe the effects of the interaction of visible or near-visible photons with intense magnetic fields — a process which becomes possible in quantum electrodynamics (QED) thanks to the vacuum fluctuations of the electronic field, and which is akin to photon–photon scattering. PVLAS is now close to data-taking and if it reaches the required sensitivity, it could provide important information on QED vacuum. PVLAS and other similar experiments face great challenges as they try to measure an extremely minute effect. However, raising the photon energy greatly increases the photon–photon cross section, and gamma rays could help extract much more information from the observed light–light scattering. Here we discuss an experimental design to measure photon–photon scattering close to the peak of the photon–photon cross section, that could fit in the proposed construction of an FEL facility at the Cabibbo Lab near Frascati (Rome, Italy).

ISSUES WITH VACUUM ENERGY AS THE ORIGIN OF DARK ENERGY

In this paper, we address some of the issues raised in the literature about the conflict between a large vacuum energy density, a priori predicted by quantum field theory, and the observed dark energy which must be the energy of vacuum or include it. We present a number of arguments against this claim and in favor of a null vacuum energy. They are based on the following arguments: A new definition for the vacuum in quantum field theory as a frame-independent coherent state; results from a detailed study of condensation of scalar fields in Friedmann–Lemaître–Robertson–Walker (FLRW) background performed in a previous work; and our present knowledge about the Standard Model of particle physics. One of the predictions of these arguments is the confinement of nonzero expectation value of Higgs field to scales roughly comparable with the width of electroweak gauge bosons or shorter. If the observation of Higgs by the LHC is confirmed, accumulation of relevant events and their energy dependence in near future should allow us to measure the spatial extend of the Higgs condensate.

Stellar black holes and the origin of cosmic acceleration

The discovery of cosmic acceleration has presented a unique challenge for cosmologists. As observational cosmology forges ahead, theorists have struggled to make sense of a standard model that requires extreme fine-tuning. This challenge is known as the cosmological constant problem. The theory of gravitational aether is an alternative to general relativity that does not suffer from this fine-tuning problem, as it decouples the quantum field theory vacuum from geometry, while remaining consistent with other tests of gravity. In this paper, we study static black hole solutions in this theory and show that it manifests a UV-IR coupling: Aether couples the space-time metric close to the black hole horizon, to metric at infinity. We then show that using the trans-Planckian ansatz (as a quantum gravity effect) close to the black hole horizon, leads to an accelerating cosmological solution, far from the horizon. Interestingly, this acceleration matches current observations for stellar-mass black holes. Based on our current understanding of the black hole accretion history in the Universe, we then make a prediction for how the effective dark energy density should evolve with redshift, which can be tested with future dark energy probes.

Quantum vacuum noise in physics and cosmology.

The concept of the vacuum in quantum field theory is a subtle one. Vacuum states have a rich and complex set of properties that produce distinctive, though usually exceedingly small, physical effects. Quantum vacuum noise is familiar in optical and electronic devices, but in this paper I wish to consider extending the discussion to systems in which gravitation, or large accelerations, are important. This leads to the prediction of vacuum friction: The quantum vacuum can act in a manner reminiscent of a viscous fluid. One result is that rapidly changing gravitational fields can create particles from the vacuum, and in turn the backreaction on the gravitational dynamics operates like a damping force. I consider such effects in early universe cosmology and the theory of quantum black holes, including the possibility that the large-scale structure of the universe might be produced by quantum vacuum noise in an early inflationary phase. I also discuss the curious phenomenon that an observer who accelerates through a quantum vacuum perceives a bath of thermal radiation closely analogous to Hawking radiation from black holes, even though an inertial observer registers no particles. The effects predicted raise very deep and unresolved issues about the nature of quantum particles, the role of the observer, and the relationship between the quantum vacuum and the concepts of information and entropy. (c) 2001 American Institute of Physics.

Non-Abelian Aharonov-Bohm scattering of spinless particles

The Aharonov-Bohm scattering for spinless, isospin 1/2, particles interacting through a non-Abelian Chern-Simons field is studied. Starting from the relativistic quantum field theory and using a Coulomb gauge formulation, the one loop renormalization program is implemented. Through the introduction of an intermediary cutoff, separating the regions of high and low integration momentum, the nonrelativistic limit is derived. The next to leading relativistic approximation is also determined. In this approach quantum field theory vacuum polarization effects are automatically incorporated.

Quantum and classical statistics of the electromagnetic zero-point field.

A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED) wherein quantum measurements are imitated by the introduction of a stochastic classical background EM field. Random EM fluctuations are assumed to provide perturbations which can mimic some quantum phenomena while retaining a purely classical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb shift, spontaneous emission, the RMS radius of the harmonic oscillator, and the radius of the Bohr atom. This classical ZPF is represented as a homogeneous, isotropic ensemble of plane waves with fixed amplitudes and random phases. Averaging over the random phases is assumed to be equivalent to taking the ground-state expectation values of the corresponding quantum operator. We demonstrate that this is not precisely correct by examining the statistics of the classical ZPF in contrast to that of the EM quantum vacuum. We derive the distribution for the individual mode amplitudes in the ground-state as predicted by quantum field theory (QFT) and then carry out the same calculation for the classical ZPF analogue, showing that the distributions are only in approximate agreement, diverging as the density of k states decreases. We introduce an alternative classical ZPF with a different stochastic character, and demonstrate that it can exactly reproduce the statistics of the EM vacuum of QED. Incorporated into SED, this new field is shown to give the correct (QM) distribution for the amplitude of the ground-state of a harmonic oscillator, suggesting the possibility of developing further successful correspondences between SED and QED.

Some possible consequences of Zel’dovich’s cosmological term

According to Zel’dovich, the energy tensor of the polarized vacuum of quantum field theory implies the existence of a non-zero cosmological A term in i Einstein’s gravitational equation. I investigate the consequences of Zel’dovich’s λ in a spatially flat isotropic universe with the Hubble parameterH proportional tot−1 (t = the cosmic time); I find:tH > 2/3, -1 <q < 1/2, λt2= constant,Gt = constant, whereq is the deceleration parameter andG the gravitational coupling; another result is a mass creation process throughout the universe at the rate 10−47gs−3 cm−3. This approach explains two well-known empirical relations connecting microphysics to cosmology.

Instanton Aharonov-Bohm effect and macroscopic quantum coherence in charge-density-wave systems.

It is predicted that in a charge-density-wave (CDW) ring-shaped conductor, placed in an external vector-potential field, there should appear a new Aharonov-Bohm contribution to the magnetic susceptibility and the electrical conductivity oscillating as a function of the flux with the period ${\mathrm{\ensuremath{\Phi}}}_{0}$=hc/2e. This contribution arises from instanton transitions between degenerate vacua of the CDW condensate and is the solid-state realization of \ensuremath{\Theta} vacuum in quantum field theory. The period transforms into ${\mathrm{\ensuremath{\Phi}}}_{0}$/N in N strongly correlated parallel CDW chains.

Uniform acceleration and the quantum field theory vacuum, I

Free massless scalar and Dirac fields are quantized in two-dimensional Minkowski space in a representation in which the energy operator for a uniformly accelerating observer is diagonalized. The usual vacuum, and many other pure states, appear to be thermally excited in this representation. The crucial role ot PCT symmetry, as regards the general validity of this conclusion, is illustrated.

Uniform acceleration and the quantum field theory vacuum—I: Richard J. Hughes. CERN, Geneva, Switzerland

Uniform acceleration and the quantum field theory vacuum—I: Richard J. Hughes. CERN, Geneva, Switzerland

Particle creation during vacuum decay

The hamiltonian approach is developed with regard to the problem of particle creation during the tunneling process, leading to the decay of the false vacuum in quantum field theory. It is shown that, to the lowest order in h ̵ , the particle creation is described by the euclidean Schrödinger equation in an external field of a bounce. A technique for solving this equation is developed in an analogy to the Bogoliubov transformation technique, in the theory of particle creation in the presence of classical background fields. The technique is illustrated by two examples, namely, the particle creation during homogeneous vacuum decay and during the tunneling process leading to the materialization of the thin-wall bubble of a new vacuum in the metastable one. The curious phenomenon of intensive particle annihilation during vacuum decay is discussed and explicitly illustrated within the former example. The non-unitary extension of the Bogoliubov u, v transformations is described in the appendix.

Generating functional for the average field in quantum electrodynamics with an unstable vacuum

The generating functional for calculating the average field in the case of an unstable vacuum in quantum field theory is proposed. A continuous representation is found for the generating functional of the average field in the case of quantum electrodynamics with an external field, generating electron-positron pairs out of the vacuum.