Field In Spacetime Research Articles

Retrocausal model of reality for quantum fields

We show that one may interpret physical reality as random fields in space-time. These have a probability given by the expectation of a coherent state projection operator, called the Q-function. The resulting dynamical evolution includes retrocausal effects. This suggests that a physical universe exists without requiring observers, but with a well-defined probability for its field configuration. By including the meter dynamics, we show that field trajectories have quantum measurement properties without wave-function collapse, including sharp measured eigenvalues. We treat continuous and discrete measurements, and show that this model predicts Bell inequality violations for measurements on correlated spins. A discussion is give of a number of well-known quantum paradoxes, showing how these can be treated in a realistic model of measurement. Our theory resolves a number of practical and philosophical issues in quantum measurement, and we compare it with earlier theories.

A massless scalar field in Robertson-Walker spacetimes: Adiabatic regularization and Green’s function * * Supported by NSFC (11421303, 11675165, 11633001, 11961131007), B. Wang is supported by CPSF (2019M662168)

We study adiabatic regularization of a coupling massless scalar field in general spatially flat Robertson-Walker (RW) spacetimes. For the conformal coupling, the 2nd-order regularized power spectrum and 4th-order regularized stress tensor are zero, and no trace anomaly exists in general RW spacetimes. This is a new result that exceeds those found in de Sitter space. For the minimal coupling, the regularized spectra are also zero in the radiation-dominant and matter-dominant stages, as well as in de Sitter space. The vanishing of these adiabatically regularized spectra is further confirmed by direct regularization of the Green's function. For a general coupling and general RW spacetimes, the regularized spectra can be negative under the conventional prescription. At a higher order of regularization, the spectra will generally become positive, but will also acquire IR divergence, which is inevitable for a massless field. To avoid the IR divergence, the inside-horizon regularization is applied. Through these procedures, nonnegative UV- and IR-convergent power spectrum and spectral energy density will eventually be achieved.

Quantum Fisher information in the cosmic string spacetime

We analyze the quantum Fisher information (QFI) for a particle detector coupled to a thermal electromagnetic field in the cosmic string spacetime. It is found that vacuum fluctuation, temperature, detector polarization and nontrivial spacetime topology affect the QFI. Vacuum fluctuation and temperature degrade QFI. When deficit angle parameter ν = 1 and detector is far away from the string, the results in free Minkowski spacetime are restored. When detector is close to the string, QFI can be effectively enhanced; specially when detector lies in the string and is not polarized along axial direction, the detector seems like a closed system, and QFI completely is not affected by the thermal electromagnetic fluctuation. For nonzero detector–string distance, QFI appears oscillatory behaviors as detector–string distance varies. In addition, this detector eventually evolves to a thermal state, which is not related to the initial state and other various parameters, which implies QFI cannot persist in for long evolution time in the cosmic string spacetime. In principle, the detector polarization, detector–string distance, temperature and deficit angle parameter provide us with more parameters to steer the QFI behaviors, which might be helpful to enhance the precision of sensing the characters of cosmic string spacetime.

Resonant frequencies of a massless scalar field in the canonical acoustic black hole spacetime

In this work we consider the exact solution of the Klein-Gordon equation describing a massless scalar field in the spacetime of a four dimensional canonical acoustic black hole, which is given in terms of the general Heun function, to investigate the interesting phenomena related to the resonant frequencies.

Harvesting correlations in Schwarzschild and collapsing shell spacetimes

We study the harvesting of correlations by two Unruh-DeWitt static detectors from the vacuum state of a massless scalar field in a background Vaidya spacetime consisting of a collapsing null shell that forms a Schwarzschild black hole (hereafter Vaidya spacetime for brevity), and we compare the results with those associated with the three preferred vacua (Boulware, Unruh, Hartle-Hawking-Israel vacua) of the eternal Schwarzschild black hole spacetime. To do this we make use of the explicit Wightman functions for a massless scalar field available in (1+1)-dimensional models of the collapsing spacetime and Schwarzschild spacetimes, and the detectors couple to the proper time derivative of the field. First we find that, with respect to the harvesting protocol, the Unruh vacuum agrees very well with the Vaidya vacuum near the horizon even for finite-time interactions. Second, all four vacua have different capacities for creating correlations between the detectors, with the Vaidya vacuum interpolating between the Unruh vacuum near the horizon and the Boulware vacuum far from the horizon. Third, we show that the black hole horizon inhibits any correlations, not just entanglement. Finally, we show that the efficiency of the harvesting protocol depend strongly on the signalling ability of the detectors, which is highly non-trivial in presence of curvature. We provide an asymptotic analysis of the Vaidya vacuum to clarify the relationship between the Boulware/Unruh interpolation and the near/far from horizon and early/late-time limits. We demonstrate a straightforward implementation of numerical contour integration to perform all the calculations.

Emergence of classical behavior in the early Universe

We investigate three issues that have been discussed in the context of inflation: Fading of the importance of quantum non-commutativity; the phenomenon of quantum squeezing; and the ability to approximate the quantum state by a distribution function on the classical phase space. In the standard treatments, these features arise from properties of mode functions of quantum fields in (near) de Sitter space-time. Therefore, the three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times, through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another; and, (iii) the third notion is realized in a surprisingly strong sense; there is exact equality between completely general $n$-point functions in the classical theory and those in the quantum theory, provided the quantum operators are Weyl ordered. These features arise already for linear cosmological perturbations by themselves: considerations such as mode-mode coupling, decoherence, and measurement theory --although important in their own right-- are not needed for emergence of classical behavior in any of the three senses discussed. Generality of the results stems from the fact that they can be traced back to geometrical structures on the classical phase space, available in a wide class of systems. Therefore, this approach may also be useful in other contexts.

Quantum influence of magnetic flux on spin-0 scalar charged particles in the presence of external field in a spinning cosmic string space-time

In this work, we investigate spin-0 massive charged particles in the background space-time induced by a spinning cosmic string coupled to a homogeneous external magnetic field parallel to the string including a magnetic quantum flux. We compute the energy eigenvalues and eigenfunctions and analyze a relativistic analogue of the Aharonov-Bohm effect.

Relativistic quantum dynamics of a spin-0 massive charged particle in the presence of external fields in a Gödel-type space-time with Coulomb potentials and Aharonov–Bohm effect

In this paper, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in the presence of an external field in a Godel-type space-time with potentials. We derive the radial wave equation of the Klein–Gordon equation with an external uniform magnetic field including a magnetic quantum flux subject to a Coulomb-type scalar and vector potentials in the background of the Som–Raychaudhuri space-time with a cosmic string. We solve this radial wave equation and evaluate the energy eigenvalues and eigenfunctions and analyze a relativistic analogue effect of the Aharonov–Bohm effect for bound states.

Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field

We present firstly the equation of motion for the photon coupled to a special bumblebee vector field in a Kerr black hole spacetime and find that the propagation of light depends on its polarization due to the birefringence phenomenon. The dependence of black hole shadow on the light's polarization is dominated by the rotation of black hole. In the non-rotating case, we find that the black hole shadow is independent of the polarization of light. However, the status is changed in the rotating case, in which the black hole shadow depends on the light's polarization and the coupling between bumblebee vector field and electromagnetic field. These features of black hole shadow casted by polarized lights could help us to understand the bumblebee vector field with Lorentz symmetry breaking and its interaction with electromagnetic field.

Massless Infinite Spin Representations

A new twistorial formulation of a massless particle with infinite spin is presented. The twistor field of infinite spin is found; the twistor field transformation for obtaining the space-time field formulation is found. The $$N = 1$$ infinite spin supermultiplet formed by the fields of the infinite integer and half-integer spins is presented.

Simulating space-time random fields with nonseparable Gneiting-type covariance functions

Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial structure and a conditionally negative definite function associated with the temporal structure. In both cases, the simulated random field is constructed as a weighted sum of cosine waves, with a Gaussian spatial frequency vector and a uniform phase. The difference lies in the way to handle the temporal component. The first algorithm relies on a spectral decomposition in order to simulate a temporal frequency conditional upon the spatial one, while in the second algorithm the temporal frequency is replaced by an intrinsic random field whose variogram is proportional to the conditionally negative definite function associated with the temporal structure. Both algorithms are scalable as their computational cost is proportional to the number of space-time locations that may be irregular in space and time. They are illustrated and validated through synthetic examples.

⟨ϕ2⟩ for a massive scalar field in global monopole spacetime

We study the vacuum polarization of a massive scalar field $\phi$ with arbitrary coupling to gravity in pointlike global monopole spacetime. Using Schwinger-DeWitt proper time formalism, we calculate the vacuum expectation value $<\phi^{2}>$, when the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry, and we can ignore nonlocal contributions. Explicit analytic expressions are obtained for a general curvature coupling parameter, and specified to the more physical cases of minimal and conformal coupling. Comparing the leading term of $<\phi^{2}>$, proportional to the coincident limit of the Hadamard-DeWitt coeficcient $a_{2}$, with higher order terms, that include the coincident limits of coefficients up to $a_{5}$, we conclude that the next to next to next to leading approximation need to be used to give a more precise description of vacuum polarization effects in this structures. We also find the trace of the renormalized stress energy tensor for the quantized field in the leading approximation, using the existing relationship between this magnitude, the trace anomaly and the field fluctuation.

Scalarization of asymptotically anti–de Sitter black holes with applications to holographic phase transitions

We study the spontaneous scalarization of spherically symmetric, static and asymptotically Anti-de Sitter (aAdS) black holes in a scalar-tensor gravity model with non-mininal coupling of the form $\phi^2\left(\alpha{\cal R} + \gamma {\cal G}\right)$, where $\alpha$ and $\gamma$ are constants, while ${\cal R}$ and ${\cal G}$ are the Ricci scalar and Gauss-Bonnet term, respectively. Since these terms act as an effective ``mass'' for the scalar field, non-trivial values of the scalar field in the black hole space-time are possible for {\it a priori} vanishing scalar field mass. In particular, we demonstrate that the scalarization of an aAdS black hole requires the curvature invariant $-\left(\alpha{\cal R} + \gamma {\cal G}\right)$ to drop below the Breitenlohner-Freedman bound close to the black hole horizon, while it asymptotes to a value well above the bound. The dimension of the dual operator on the AdS boundary depends on the parameters $\alpha$ and $\gamma$ and we demonstrate that -- for fixed operator dimension -- the expectation value of this dual operator increases with decreasing temperature of the black hole, i.e. of the dual field theory. When taking backreaction of the space-time into account, we find that the scalarization of the black hole is the dual description of a phase transition in a strongly coupled quantum system, i.e. corresponds to a holographic phase transition. A possible application are liquid-gas quantum phase transitions, e.g. in $^4$He. Finally, we demonstrate that extremal black holes with $AdS_2\times S^2$ near-horizon geometry {\it cannot support regular scalar fields on the horizon} in the scalar-tensor model studied here.

Quasinormal modes of a scalar and an electromagnetic field in Finslerian-Schwarzschild spacetime

Quasinormal modes of scalar field and electromagnetic field in a specific Finslerian-Schwarzschild spacetime have been investigated in this paper. The equations of motion for scalar field and electromagnetic field have been constructed by Finslerian-Laplace operator and divergence operator. The solutions of the equations of motion are presented. The solutions of angular part for scalar field and electromagnetic field are different. The solutions of radial part are numerically analyzed via WKB approximation and finite difference method, which give the quasinormal frequencies and dynamic evolution of quasinormal modes, respectively. The spectrum splitting generated from spherical symmetry breaking of the Finslerian-Schwarzschild spacetime is shown. The analysis of the dynamical evolution of quasinormal modes shows that the Finslerian-Schwarzschild black hole is stable if the Finslerian parameter ${\ensuremath{\epsilon}}^{2}l0.8$.

Restrictions for n-point vertices in higher-spin theories

We give a simple classification of the independent n-point interaction vertices for bosonic higher-spin gauge fields in d-dimensional Minkowski spacetimes. We first give a characterisation of such vertices for large dimensions, d ≥ 2n − 1, where one does not have to consider Schouten identities due to over-antisymmetrisation of spacetime indices. When the dimension is lowered, such identities have to be considered, but their appearance only leads to equivalences of large-d vertices and does not lead to new types of vertices. We consider the case of low dimensions (d < n) in detail, where a large number of Schouten identities leads to strong restrictions on independent vertices. We also comment on the generalisation of our results to the intermediate region n ≤ d ≤ 2n − 2. In all cases, the independent vertices are expressed in terms of elementary manifestly gauge-invariant quantities, suggesting that no deformations of the gauge transformations are induced.

Constructing p, n-forms from p-forms via the Hodge star operator and the exterior derivative

In this paper, we aim to explore the properties and applications on the operators consisting of the Hodge star operator together with the exterior derivative, whose action on an arbitrary p-form field in n-dimensional spacetimes makes its form degree remain invariant. Such operations are able to generate a variety of p-forms with the even-order derivatives of the p-form. To do this, we first investigate the properties of the operators, such as the Laplace–de Rham operator, the codifferential and their combinations, as well as the applications of the operators in the construction of conserved currents. On the basis of two general p-forms, then we construct a general n-form with higher-order derivatives. Finally, we propose that such an n-form could be applied to define a generalized Lagrangian with respect to a p-form field according to the fact that it includes the ordinary Lagrangians for the p-form and scalar fields as special cases.

On the solution of a generalized Higgs boson equation in the de Sitter space-time through an efficient and Hamiltonian scheme

The present work is the first paper in the literature to report on a Hamiltonian discretization of the (fractional) Higgs boson equation in the de Sitter space-time, and its theoretical analysis. More precisely, we design herein a numerically efficient finite-difference Hamiltonian technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space-time. The model under investigation is a multidimensional equation with generalized potential and Riesz space-fractional derivatives of orders in (1,2]. An energy integral for the model is readily available, and we propose a nonlinear, implicit and consistent numerical technique based on fractional-order centered differences, with similar Hamiltonian properties in the discrete scenario. A fractional energy approach is used then to prove the properties of stability and convergence of the technique. For simulation purposes, we consider both the classical and the fractional Higgs real-valued scalar fields in the de Sitter space-time, and find results qualitatively similar to those available in the literature. For the sake of convenience, we provide the Matlab code of an alternative linear discretization of the method presented in this work. This linear implicit approach is thoroughly analyzed also.

Expansion of the universe and its correlation with dark energy

The Universe is expanding and science has got the relevant amount of evidence to prove that. The red shift of the distant galaxies prove that the Universe is expanding and at a good rate. The trouble is not with the expansion rather the force that is helping in this expansion. The Four Forces that is understood by physics are Gravitational Force, Electromagnetic Force, The Weak Force and The Strong Force. The four forces mentioned above unfortunately does not help in understanding the expansion of the Universe even after 13.8 billion years from the Big Bang. Initially it was thought that the Universe had an exponential expansion just after the Big Bang and this expansion will slow down before Gravity starts contracting the Universe. Well this theory got a setback after the Red Shift of the Galaxies showed that the Universe is still expanding.The expansion is happening still which means that the Gravitational Force is not being able to drift the galaxies towards one another. So what could be the unknown force that is repelling the galaxies from one another? Scientists have been working on this issue and many new concepts have been developed. Many scientists have argued that there is some force that is repelling the Universe but understanding this force has been difficult till now. Major scientists now agree that there is a force that is repelling the Universe and this force is not the four fundamental forces that are known to us. They have termed this force as the Dark Energy.What is this Dark Energy is a haunting question in today’s world. Only around 5% of the observable Universe is known till date. The rest around 95% is still a mystery to us. Of that 95% around 68% is Dark Energy. So the importance of understanding this force is the need of the hour. This force can tell a lot about the formation of the Universe from the start or it can even enlighten us if the Universe is eternal.The issue is as of now, this Dark Energy is hypothetical in nature as it has not been seen or felt by the instruments available to science today. The idea of Dark Energy goes to explain the expansion of the Universe, if Dark Energy is taken as some sort of Anti- Gravitational Force.Einstein’s theory of relativity talks of how space and time is intermingled with gravity. According to this theory space time gets modified due to the amount of matter that falls into the space. So if a planet sits on a space in the Universe it will cause a deviation in the space time field in such a way that it will accommodate the matter of the planet. So Einstein placed time as the fourth dimension and showed its importance in space. This theory stands true in majority of the cases in the Universe. The only hurdle being that inside the Black Hole this theory falters.Einstein and Schrodinger did interact with one another after he had understood that the Universe was expanding through the theory presented by Hubble. Earlier Einstein had stated that the Universe was Static. To counter the exigency that space time changes with matter he had proposed a constant by the name Cosmological Constant. Later he took the constant away stating that it was his blunder not to understand that the Universe was Expanding. Schrodinger had proposed to put the Cosmological Constant in the right side of the equation. This meant the constant may change with time and be considered more of a variable force. Though, Einstein later did not agree to the idea. Still it can be considered that both of them were talking about an extra force but could not come to any conclusion on this.Einstein in his special relativity theory had talked of conversion of energy to matter with his famous equation, E=mc^2. This meant that energy can be formed by matter and matter can be converted into energy. Though energy created from matter can be seen in Atom Bomb but matter created from energy is not seen. This paper will try to show how matter can be created from energy where Dark Energy acts as a Catalyst.This paper also tries to analyze the concept of Dark Energy as a non interacting supermassive energy (NISE). The paper will try to see the relationship between expanding Universe and Dark energy. The paper will try to develop a new spectrum that can make Dark Energy or NISE as stated in the paper visible or understandable. The paper will also like to see the relationship between Dark Energy and Photon. The paper will try to show how energy is converted from matter with the help of Dark Energy.Â

A data set of sea surface stereo images to resolve space-time wave fields

Stereo imaging of the sea surface elevation provides unique field data to investigate the geometry and dynamics of oceanic waves. Typically, this technique allows retrieving the 4-D ocean topography (3-D space + time) at high frequency (up to 15–20 Hz) over a sea surface region of area ~104 m2. Stereo data fill the existing wide gap between sea surface elevation time-measurements, like the local observation provided by wave-buoys, and large-scale ocean observations by satellites. The analysis of stereo images provides a direct measurement of the wavefield without the need of any linear-wave theory assumption, so it is particularly interesting to investigate the nonlinearities of the surface, wave-current interaction, rogue waves, wave breaking, air-sea interaction, and potentially other processes not explored yet. In this context, this open dataset aims to provide, for the first time, valuable stereo measurements collected in different seas and wave conditions to invite the ocean-wave scientific community to continue exploring these data and to contribute to a better understanding of the nature of the sea surface dynamics.

Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter spacetime

In classical general relativity, the values of fields on spacetime are uniquely determined by their values at an initial time within the domain of dependence of this initial data surface. However, it may occur that the spacetime under consideration extends beyond this domain of dependence, and fields, therefore, are not entirely determined by their initial data. This occurs, for example, in the well-known (maximally) extended Reissner–Nordström or Reissner–Nordström–deSitter (RNdS) spacetimes. The boundary of the region determined by the initial data is called the ‘Cauchy horizon.’ It is located inside the black hole in these spacetimes. The strong cosmic censorship conjecture asserts that the Cauchy horizon does not, in fact, exist in practice because the slightest perturbation (of the metric itself or the matter fields) will become singular there in a sufficiently catastrophic way that solutions cannot be extended beyond the Cauchy horizon. Thus, if strong cosmic censorship holds, the Cauchy horizon will be converted into a ‘final singularity,’ and determinism will hold. Recently, however, it has been found that, classically this is not the case in RNdS spacetimes in a certain range of mass, charge, and cosmological constant. In this paper, we consider a quantum scalar field in RNdS spacetime and show that quantum theory comes to the rescue of strong cosmic censorship. We find that for any state that is nonsingular (i.e., Hadamard) within the domain of dependence, the expected stress-tensor blows up with affine parameter, V, along a radial null geodesic transverse to the Cauchy horizon as T VV ∼ C/V 2 with C independent of the state and C ≠ 0 generically in RNdS spacetimes. This divergence is stronger than in the classical theory and should be sufficient to convert the Cauchy horizon into a singularity through which the spacetime cannot be extended as a (weak) solution of the semiclassical Einstein equation. This behavior is expected to be quite general, although it is possible to have C = 0 in certain special cases, such as the BTZ black hole.