DeWitt Approach Research Articles

Inspiraling corrugation-induced quantum effects on neutron star binary plane

We use the path-integral formula and investigate some dynamical quantum effects induced by the inspiraling lateral corrugation of orbital plane in gravitationally bound neutron star (NS) binaries, with orbital separation of 109 m. Based on Dewitt's approach, we calculate the gravitational Casimir energy cost of the binary plane, which consists of statically gravitational effects and deformation-induced effects. It is found that the static effects include a term coming from the self-gravity of the orbital plane and the contribution of Newtonian gravitational potential of the binary system. While the deformation-induced effect also results from two parts, i.e. the instability of orbital binding energy, scaling as 1(R−r)2, and the dynamically Casimir energy cost of the orbital binding energy, decaying as 1(R−r)4. The dynamically gravitational Casimir phenomena and the corresponding energy cost modify the spiral-in orbital motion of the binary and thus the frequency of released gravitational waves (GWs). We consider the mechanical response of two NS components and qualitatively study the corrections to the orbital motion of the system and the GW frequencies. It is found that the dynamical Casimir effects exert a dissipative force on the binary plane, depending on the frequency of GWs. The resultant dissipation may enhance with the decaying separation and increasing GW frequencies, which subsequently accelerates the orbital decay of the binary. However, the dissipation rate just has an order of 10−70 eV/s. So the corrections to the dynamics of NS binaries are very marginal, by considering the wide separation, the cosmological coalescence time, and low-frequency GWs of the system.

Top–Bottom Condensation Model: Symmetries and Spectrum of the Induced 2HDM

Here, we use the Schwinger–DeWitt approach to address the four-fermion composite Higgs effective model proposed by Miransky, Tanabashi and Yamawaki (MTY). The surprising benefit of such an approach is that it is possible to ascribe to a SM-type Higgs a quark–antiquark structure of predominantly a b¯b nature with a small t¯t admixture, which in turn yields a Higgs mass compatible with the observed value of 125 GeV. We discuss this result in a detailed and pedagogical way, as it goes against the common belief that this model and akin composite descriptions should predict a Higgs mass-of-order of twice the top quark mass, contrary to empirical evidence. A further aspect of this approach is that it highlights the link of the SU(2)L×U(1)R symmetric four-fermion MTY model interactions of the heavy quark family to a specific two-Higgs-doublet model (2HDM), and the necessity to go beyond the one Higgs doublet to obtain the empirical Higgs mass within composite models. By appropriately fixing the symmetry-defining interaction parameters, we show that the resulting CP-preserving spectrum harbors the following collective states at the electroweak scale ΛEW=246 GeV: a light scalar to which the standard Higgs is associated; a heavier neutral state preconized as the Nambu partner of the standard Higgs within the Nambu sum rule; the expected triplet of Goldstone bosons associated with the longitudinal polarizations of the electroweak massive bosons; and a neutral pseudoscalar state that in the limit of a global U(1)A symmetry would be a Goldstone mode. The anomalous breaking of this axial symmetry is a subleading effect in a large Nc counting scheme, and we discuss how it modifies the leading-order Nambu sum rule result and its relevance for the qualitative description of the spectrum.

Is the Wheeler–DeWitt equation more fundamental than the Schrödinger equation?

The Wheeler–DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler–DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrödinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler–DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler–DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference frame) may appear to be significant. Second, I suppose that the equation for the wave function of the universe must not be postulated but derived by means of a mathematically consistent procedure, which exists in path integral quantization. When applying this procedure to any gravitating system, one should take into account features of gravity, namely, nontrivial spacetime topology and possible absence of asymptotic states. The Schrödinger equation has been derived early for cosmological models with a finite number of degrees of freedom, and just recently it has been found for the spherically symmetric model which is a simplest model with an infinite number of degrees of freedom. The structure of the Schrödinger equation and its general solution appears to be very similar in these cases. The obtained results give grounds to say that the Schrödinger equation retains its fundamental meaning in constructing quantum theory of gravity.

Mixmaster revisited: wormhole solutions to the Bianchi IX Wheeler–DeWitt equation using the Euclidean-signature semi-classical method

A modified semi-classical method is used to construct both ground and excited state solutions to the canonically quantized vacuum Bianchi IX (Mixmaster) cosmological models. Employing a modified form of the semi-classical Ansatz we solve the relevant Wheeler–DeWitt equation asymptotically by integrating a set of linear transport equations along the flow of a suitably chosen solution to the corresponding Euclidean-signature Hamilton–Jacobi equation. For the Moncrief–Ryan (or ‘wormhole’) Hamilton–Jacobi solution, we compute the ground state quantum correction term associated with operator ordering ambiguities and show how higher order correction terms can be computed. We also determine the explicit, leading order forms of a family of excited states and show how to compute their quantum corrections as smooth, globally defined functions on the Bianchi IX minisuperspace. These excited state solutions are peaked away from the minisuperspace origin and are labeled by a pair of positive integers that can be plausibly interpreted as graviton excitation numbers for the two independent anisotropy degrees of freedom. The Euclidean-signature semi-classical method used here is applicable to more general models, representing a significant progress in the Wheeler–DeWitt approach to quantum gravity.

Landau's problem in the noncommutative quantum mechanics and linearized gravitational waves: DeWitt's approach

We present a systematic study of the noncommutative interaction of gravitational waves with matter at the quantum mechanical level in the long wavelength and small velocity limit. In particular, the noncommutative quantum dynamics of the Landau's problem is employed to measure the transmission amplitudes in terms of the Riemann's tensor elements by a gravitational wave in linearized approximation. It turns out that the Hamiltonian of the charged particles derived based on DeWitt's approach is valid by the deformed electromagnetic fields.

Quantum cosmology with effects of a preferred reference frame

Recently, we presented a gravity model by generalizing the Brans–Dicke theory which is suitable for studying the metric signature transition dynamics without using an imaginary time parameter. Adding a suitable scalar potential described in terms of the Brans–Dicke scalar field ‘’, this alternative theory is used to study the Wheeler–DeWitt approach of quantum cosmology. We assumed that the universe is defined in a flat Robertson–Walker metric with Lorentzian signature. In that case, the Wheeler–DeWitt wavefunctional is obtained as two-dimensional quantum harmonic oscillator convergent polynomials for both of the choices of positive and negative values of the Brans–Dicke parameter. Here we choose a preferred reference frame with a time coordinate of ‘γ’ which relates to time of cosmological free falling observer ‘t’ as ‘’.

Calculation of Quantum Probability in O(2,2) StringCosmology with a Dilaton Potential

The quantum properties of O(2,2) string cosmology with adilaton potential are studied in this paper. The cosmologicalsolutions are obtained on three-dimensional space-time.Moreover, the quantum probability of transition between twoduality universe is calculated through aWheeler–De Witt approach.

REVISED CANONICAL QUANTUM GRAVITY VIA THE FRAME FIXING

We present a new reformulation of the canonical quantum geometrodynamics, which allows one to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the restated dynamics. More precisely, to remove the ambiguity contained in the Wheeler–DeWitt approach, with respect to the possibility of a (3+1)-splitting when space–time is in a quantum regime, we fix the reference frame (i.e. the lapse function and the shift vector) by introducing the so-called kinematical action. As a consequence the new super-Hamiltonian constraint becomes a parabolic one and we arrive to a Schrödinger-like approach for the quantum dynamics. In the semiclassical limit our theory provides General Relativity in the presence of an additional energy–momentum density contribution coming from non-zero eigenvalues of the Hamiltonian constraints. The interpretation of these new contributions comes out in natural way that soon as it is recognized that the kinematical action can be recasted in such a way that it describes a pressureless, but, in general, non-geodesic perfect fluid.

Evolution in quantum causal histories

We provide a precise definition and analysis of quantum causal histories (QCHs). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum states and observables is described by completely positive maps between the algebras at causally related events. We show that this local description of evolution is sufficient and that unitary evolution can be recovered wherever it should actually be expected. This formalism may describe a quantum cosmology without an assumption of global hyperbolicity; it is thus more general than the Wheeler–De Witt approach. The structure of a QCH is also closely related to quantum information theory and algebraic quantum field theory on a causal set.

Canonical quantization of gravity without “frozen formalism”

We write down a quantum gravity equation which generalizes the Wheeler–DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries resulting from a “gauge-fixing” (3+1)-slicing of the space–time. Our leading idea relies on a criticism to the possibility that, in a quantum space–time, the notion of a (3+1)-slicing formalism (underlying the Wheeler–DeWitt approach) has yet a precise physical meaning. As solution to this problem we propose of adding to the gravity-matter action the so-called kinematical action (indeed in its reduced form, as implemented in the quantum regime), and then we impose the new quantum constraints. As consequence of this revised approach, the quantization procedure of the 3-geometries takes place in a fixed reference frame and the wave functional acquires a time evolution along a one-parameter family of spatial hypersurfaces filling the space–time. We show how the states of the new quantum dynamics can be arranged into an Hilbert space, whose associated inner product induces a conserved probability notion for the 3-geometries. Finally, since the constraints we quantize violate the classical symmetries (i.e., the vanishing nature of the super-Hamiltonian), then a key result is to find a (non-physical) restriction on the initial wave functional phase, ensuring that general relativity outcomes when taking the appropriate classical limit. However, we propose a physical interpretation of the kinematical variables which, based on the analogy with the so-called Gaussian reference fluid, makes allowance even for such classical symmetry violation.

Dynamical local-field factor and transport in strongly coupled plasmas

Based on a generalized linear response theory, the response function of an electron-ion plasma is considered. The relation to dynamical local-field factors is given. In the long-wavelength limit, different approximations for the dynamical conductivity are given. An extension of the Gould de-Witt approach is presented, accounting for dynamical screening as well as strong collisions. For a classical plasma, results for the dynamical collision frequency and the dielectric function are presented. Furthermore, it is shown, how to derive the Mermin dielectric function within the generalized linear response theory.

LOW-ENERGY QUANTUM STRING COSMOLOGY

We introduce a Wheeler–De Witt approach to quantum cosmology based on the low-energy string effective action, with an effective dilaton potential included to account for nonperturbative effects and, possibly, higher-order corrections. We classify, in particular, four different classes of scattering processes in minisuperspace, and discuss their relevance for the solution of the graceful exit problem.