Quantum Matter Fields Research Articles

Field theory model giving rise to “quintessential inflation” without the cosmological constant and other fine-tuning problems

A field theory is developed based on the idea that the effective action of yet unknown fundamental theory, at energy scale below M_{p} has the form of expansion in two measures: S=\intd^{4}x[\Phi L_{1}+\sqrt{-g}L_{2}] where the new measure \Phi is defined using the third-rank antisymmetric tensor. In the new variables (Einstein frame) all equations of motion take canonical GR form and therefore models are free of the well-known "defects" that distinguish the Brans-Dicke type theories from GR. All novelty is revealed only in an unusual structure of the effective potential U(\phi) and interactions which turns over intuitive ideas based on our experience in field theory. E.g. the greater \Lambda we admit in L_{2}, the smaller U(\phi) will be in the Einstein picture. Field theory models are suggested with explicitly broken global continuos symmetry which in the Einstein frame has the form \phi\to\phi+const. The symmetry restoration occurs as \phi\to\infty. A few models are presented where U is produced with the following shape: for \phi<-M_{p}, U has the form typical for inflation model, e. g. U=\lambda\phi^4 with \lambda\sim 10^{-14}; for\phi>-M_{p}, U has mainly exponential form U\sim e^{-a\phi/M_{p}} with variable a: a=14 for -M_{p}<\phi<M_{p} that admits nucleosynthesis; a=2 for \phi>M_{p} that implies quintessence era. There is no need in any fine tuning to prevent appearance of the CC term or any other terms that could violate flatness of U at \phi\ggM_{p}. \lambda\sim 10^{-14} is obtained without fine tuning as well. Quantized matter fields models, including gauge theories with SSB can be incorporated without altering mentioned above results. Direct fermion-inflaton coupling resembles Wetterich's model but it does not lead to any observable effect at present. SSB does not raise any problem with CC.

BRST algebra on quantum bundles

A quantum analogue of the BRST algebra is given. The method is based on the construction of a differential algebra of generalized quantum forms carrying a bigraduation. This is realized over the base quantum space of a quantum vector bundle associated to a quantum principal bundle. Using this approach, we introduce the quantum gauge, ghost and matter fields via connections and sections. Imposing constraints on the curvatures leads to the quantum BRST transformations of these fields.

Black hole thermodynamics and spectral analysis

We deal with some problems concerning quantum matter fields thermodynamics on static spherosymmetric black hole backgrounds. By means of variable separation, we study the self-adjointness of the Euclidean wave operators relevant in the calculation of the partition function and of the thermal Green functions for the case of scalar quantum fields in thermal equilibrium with a Schwarzschild black hole. In this respect, the role of the horizon surface is analyzed. An approach to this topic, related to completeness of the Euclidean manifold, is also discussed. It is found that, if the horizon surface is not included in the Euclidean manifold (or if it cannot be included, as in the case of a temperature different from the black hole one), essential self-adjointness is missing and boundary conditions on the horizon are required. We also analyze some qualitative spectral properties of the given wave operators after introducing an infrared regularization by means of a spherical box. We find that in the standard Euclidean path integral approach the spectrum is purely discrete. The same analysis is carried out for the noncovariant choice of the functional measure in the Euclidean path integral. An analogous study is carried for an extremal Reissner–Nordström black hole and it is sketched in the nonextremal one. The latter is completely analogous to the Schwarzschild case, whereas in the extremal case it is found that the corresponding Riemannian manifold is complete for every choice of the temperature and that at finite four volume there is a nonvoid continuous spectrum. Physical implications of our results are discussed.

Quantum corrections to critical phenomena in gravitational collapse

We investigate conformally coupled quantum matter fields on spherically symmetric, continuously self-similar backgrounds. By exploiting the symmetry associated with the self-similarity the general structure of the renormalized quantum stress-energy tensor can be derived. As an immediate application we consider a combination of classical, and quantum perturbations about exactly critical collapse. Generalizing the standard argument which explains the scaling law for black hole mass, $M \propto |\eta-\eta^*|^\beta$, we demonstrate the existence of a quantum mass gap when the classical critical exponent satisfies $\beta \geq 0.5$. When $\beta < 0.5$ our argument is inconclusive; the semi-classical approximation breaks down in the spacetime region of interest.

Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories

It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric. We demonstrate that at least part of this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points, are densely defined operators. This Hamiltonian, surprisingly, does not suffer from any singularities, it is completely finite without renormalization. This property is shared by string theory. In contrast to string theory, however, we are dealing with a particular phase of the standard model coupled to gravity which is entirely non-perturbatively defined and second quantized. Of course, to show that the entire theory is finite requires more: one would need to know what the physical observables are, apart from the Hamiltonian constraint, and whether they are also finite. However, with the results given in this paper this question can now be answered, at least in principle.

Second Quantization of the Stueckelberg Relativistic Quantum Theory and Associated Gauge Fields

The gauge compensation fields induced by the differential operators of the Stueckelberg-Schrodinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields; An action is constructed and the second quantization of the fields carried out using a constraint procedure. The properties of the second quantized matter fields are discussed.

A further look at waveguide lasers

A new approach to the dynamical evolution of a waveguide laser is presented which goes beyond the usual Maxwell-Bloch (MB) equations in that it takes fully into account the phase of the matter quantum field that describes the atomic systems. As an experimental check of its effectiveness, we analyze in its light a recent set of experiments on the effects of a dephasing of the electromagnetic laser field that find no explanation within the MB equations but, on the contrary, are in very good agreement with its expectations.

Limits on the Validity of the Semiclassical Theory — A Minisuperspace Example

For want of a more natural proposal, it is generally assumed that the back-reaction of a quantized matter field on a classical metric is given by the expectation value of its energy–momentum tensor, evaluated in a specified state. This semiclassical theory can be reliable only when the fluctuations in the energy–momentum densities of the quantum field are negligible. Based on this condition, Kuo and Ford have constructed a dimensionless quantity, whose magnitude reflects the amount of fluctuation in the back-reaction term and hence on the validity of the semiclassical theory. In this paper, we evaluate this quantity for the minisuperspace model of a quantized massless scalar field in a Friedmann universe. We conclude that the semiclassical theory for the model we consider here can be relied upon only if the scalar field is in states like coherent states. The implications of our investigation on the complete field theory are also discussed.

Einstein-Langevin equations from running coupling constants

The Einstein-Langevin equations take into account the backreaction of quantum matter fields on the background geometry. We present a derivation of these equations to lowest order in a covariant expansion in powers of the curvature. For massless fields, the equations are completely determined by the running coupling constants of the theory.

Wave Packet in Quantum Cosmology and Definition of Semiclassical Time

We consider a quantum cosmology with a massless background scalar field ϕB and adopt a wave packet as the wave function. This wave packet is a superposition of the WKB form wave functions, each of which has a definite momentum of the scalar field ϕB. In this model it is shown that to trace the formalism of the WKB time is seriously difficult without introducing a complex value for a time. We define a semiclassical real time variable TP from the phase of the wave packet and calculate it explicitly. We find that, when a quantum matter field ϕQ is coupled to the system, an approximate Schrödinger equation for ϕQ holds with respect to TP in a region where the size a of the universe is large and |ϕB| is small.

Decoherence of quantum fields: Pointer states and predictability.

We study environmentally induced decoherence of an electromagnetic field in a homogeneous, linear, dielectric medium. We derive an independent oscillator model for such an environment, which is sufficiently realistic to encompass essentially all of linear physical optics. Applying the ``predictability sieve'' to the quantum field, and introducing the concept of a ``quantum halo'', we recover the familiar dichotomy between background field configurations and photon excitations around them. We are then able to explain why a typical linear environment for the electromagnetic field will effectively render the former classically distinct, but leave the latter fully quantum mechanical. Finally, we suggest how and why quantum matter fields should suffer a very different form of decoherence.

Toy model for the zero-mode problem in the conformal sector of de Sitter quantum gravity.

In de Sitter space, the theory of the conformal factor of quantum gravity becomes nontrivial when corrections from quantum matter fields are considered. In the corresponding theory there appear five zero modes associated with five-dimensional gauge invariance. We quantize a toy model which possesses that same property. The construction of the states of the theory is unusual: indeed, the ground state is a de Sitter-invariant but unnormalizable state; moreover, the space of states is a superposition of Fock spaces, each of which contains a vacuum which breaks de Sitter invariance. We then argue that quantum gravity must spontaneously break the O(1,4) symmetry group of the gravitational background. This could provide a simple dynamical solution to the cosmological-constant problem.

Self-consistent infrared and ultraviolet asymptotically free unitary renormalizable theory of quantum gravity and matter fields

A way to a self-consistent physically acceptable formulation of quantum gravity field theory is found. The simplified model of quantized conformally-flat gravity and a massive scalar field is analyzed.

Classical gravity and quantum matter fields in unified field theory

The Einstein-Schrodinger purely affine field theory of the non-symmetric field provides canonical field equations without constraints. These equations imply the Heisenberg-Pauli commutation rules of quantum field theory. In the Schrodinger gauging of the Einstein field coordinatesUkli=Γkli−δliΓkmm, this unified geometric field theory becomes a model of the coupling between a quantized Maxwellian field in a medium and classical gravity. Therefore, independently of the question as to the physical truth of this model, its analysis performed in the present paper demonstrates that, in the framework of a quantized unified field theory, gravity can appear as a genuinely classical field.

EFFECTIVE POTENTIAL FOR A NONRELATIVISTIC NON-ABELIAN CHERN-SIMONS MATTER SYSTEM IN CONSTANT BACKGROUND FIELDS

We present the effective potential for nonrelativistic matter coupled to non-Abelian Chern-Simons gauge fields. We perform the calculation using a functional method in constant background fields to satisfy Gauss’s law and to simplify the computation. Both the quantum gauge and matter fields are integrated over. The gauge-fixing is achieved with an Rξ gauge in the ξ→0 limit. Divergences appearing in the matter sector are regulated via operator regularization. We find no correction to the Chern-Simons coupling constant and the system experiences conformal symmetry breaking to one-loop order except at the known value of self-duality. These results agree with previous analysis of the non-Abelian Aharonov-Bohm scattering.

TIME IN THE SEMICLASSICAL APPROXIMATION TO QUANTUM GRAVITY COUPLED WITH A BACKGROUND SCALAR FIELD AND KALUZA-KLEIN THEORY

We consider the semiclassical approximation to quantum gravity coupled with a background scalar field and a quantum matter field. We define the semiclassical time variable and write down the Schrödinger equation for the quantum matter field. This can be rewritten into the form whose time variable is the original time coordinate, when the relation of Hamilton-Jacobi holds. It is shown that the four-dimensional semiclassical time with a background scalar field is related to the five-dimensional semiclassical time without it by means of the Kaluza-Klein dimensional reduction.

Can vacuum energy gravitate?

In this essay we discuss an interesting recent development in semiclassical gravity. Using an improved Born-Oppenheimer approximation, the semiclassical reduction of the Wheeler-DeWitt equation turns out to give important insights into the nature and the level of validity of the semi-classical Einstein equations (SCEE). Back reactions from the quantized matter fields in SCEE are shown to be completely determined by adiabatically induced geometricU(N) gauge potentials. The finite energy from the vacuum polarization, in particular, is found to be intimately related to the ‘magnetic’ type geometric gauge potential. As a result the vacuum energy in a universe emerging from a ‘source-free’ flat simply-connected superspace is gauge equivalent to zero, leading to some dramatic consequences.

Fluctuation-dissipation relation for semiclassical cosmology

Using the concept of open systems where the classical geometry is treated as the system and the quantum matter field as the environment, we derive a fluctuation-dissipation theorem for semiclassical cosmology. This theorem, which exists under very general conditions for dissipations in the dynamics of the system, and the noise and fluctuations in the environment, can be traced to the formal mathematical relation between the dissipation and noise kernels of the influence functional depicting the open system, and is ultimately a consequence of the unitarity of the closed system. In particular, for semiclassical gravity, it embodies the back reaction effect of matter fields on the dynamics of spacetime. The back reaction equation derivable from the influence action is in the form of an Einstein-Langevin equation. It contains a dissipative term in the equation of motion for the dynamics of spacetime and a noise term related to the fluctuations of particle creation in the matter field. Using the well-studied model of a quantum scalar field in a Bianchi type-I universe we illustrate how this Langevin equation and the noise term are derived and show how the creation of particles and the dissipation of anisotropy during the expansion of the Universe can be understood as a manifestation of this fluctuation-dissipation relation.

Geometric gauge fields, particle production, and time.

The geometric magnetic- and electric-type fields are shown to have nontrivial effects in the form of semiclassical back reactions from quantized matter fields on the adiabatically evolving classical background geometry. As a consequence of the gauge invariance of the induced reaction forces it then follows that the matter vacuum polarization in a space-time emerging out from a flat simply connected superspace does not have a gravitational effect. However, the vacuum instability and the associated particle production do have a nonzero back reaction which gets encoded in the electric scalar potential. The relationship between the standard semiclassical definition of time and the existence of a nontrivial Berry phase is also explored. This offers an interesting constraint on the initial quantum state of the Universe.

Inside two-dimensional black holes

Some properties of charged, black hole solutions of two-dimensional string inspired gravity are presented. These black holes have the same causal structure as the Reissner--Nordström solution of general relativity and exhibit a similar instability of the inner horizon. A generic perturbation, by a two-dimensional scalar field, transforms the horizon into a curvature singularity. We investigate semiclassical effects near to this singularity. The calculations suggest that the curvature diverges more strongly in the presence of quantized matter fields. Our results are then contrasted with four-dimensional estimates.