Vacuum Cherenkov effect in logarithmic nonlinear quantum theory
Konstantin G. Zloshchastiev
备注：
Updates: v2: changed title, added comments about vacuum instability and Hawking radiation, added some refs previously missed due to certain linguistic subtlety, v3 [pub]: removed comments about Hawking radiation (requested by referees as it requires a separate study), changed title, added more refs
We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics - cone angle, flash duration, radiation yield and spectral distribution - are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lorentz-invariance-violating theory describing the vacuum by (effectively) continuous medium in the long-wavelength approximation.
A charged particle moving through a medium emits Cherenkov radiation when its velocity exceeds the phase velocity of light in that medium. Under the influence of a strong electromagnetic field, quantum fluctuations can become polarized, imbuing the vacuum with an effective anisotropic refractive index and allowing the possibility of Cherenkov radiation from the quantum vacuum. We analyze the properties of this vacuum Cherenkov radiation in strong laser pulses and the magnetic field around a pulsar, finding regimes in which it is the dominant radiation mechanism. This radiation process may be r…
This work reviews our current understanding of Cherenkov-type processes in vacuum that may occur due to a possible violation of Lorentz invariance. The description of Lorentz violation is based on the Standard Model Extension (SME). To get an overview as general as possible, the most important findings for vacuum Cherenkov radiation in Minkowski spacetime are discussed. After doing so, special emphasis is put on gravitational Cherenkov radiation. For a better understanding, the essential properties of the gravitational SME are recalled in this context. The common grounds and differences of vac…
The current article reviews results on vacuum Cherenkov radiation obtained for modified fermions. Two classes of processes can occur that have completely distinct characteristics. The first one does not include a spin flip of the radiating fermion, whereas the second one does. A résumé will be given of the decay rates for these processes and their properties.
A detailed analysis of vacuum Cherenkov radiation in spacelike Maxwell-Chern-Simons (MCS) theory is presented. A semiclassical treatment reproduces the leading terms of the tree-level result from quantum field theory. Moreover, certain quantum corrections turn out to be suppressed for large energies of the charged particle, for example, the quantum corrections to the classical MCS Cherenkov angle. It is argued that MCS-theory Cherenkov radiation may, in principle, lead to anisotropy effects for ultra-high-energy cosmic rays (UHECRs). In addition, a qualitative discussion of vacuum Cherenkov ra…
We show that in the framework of noncommutative classical electrodynamics Cherenkov radiation is permitted in vacuum and we explicitly compute its spectrum at first order in the noncommutative parameter. We discuss the phenomenological impact of the merge of this new analysis with the old results of the substantial modification to the spectrum of the synchrotron radiation obtained in P.Castorina, A.Iorio and D.Zappala, Phys. Rev. D 69 (2004)065008. We propose to consider the pulsars' radiation spectrum - due to its very strong magnetic field - to investigate these Lorentz violating effects in …
We present a general parametrization for the leading order terms in a momentum power expansion of a non-universal Lorentz-violating, but rotational invariant, kinematics and its implications for two-body decay thresholds. The considered framework includes not only modified dispersion relations for particles, but also modified energy-momentum conservation laws, something which goes beyond effective field theory. As a particular and relevant example, bounds on the departures from special relativistic kinematics from the non-observation of vacuum Cherenkov radiation are discussed and compared wit…
We study phenomena predicted by a renormalizable, CPT invariant extension of the Standard Model that contains higher-dimensional operators and violates Lorentz symmetry explicitly at energies greater than some scale Lambda_{L}. In particular, we consider the Cherenkov radiation in vacuo. In a rather general class of dispersion relations, there exists an energy threshold above which radiation is emitted. The threshold is enhanced in composite particles by a sort of kinematic screening mechanism. We study the energy loss and compare the predictions of our model with known experimental bounds on …
In this paper we examine the thermal effects of the vacuum Cherenkov radiation in a Lorentz- and CPT-violating electrodynamics. We compute the thermal contribution to the Cherenkov radiation rate within the Thermofield Dynamics approach. Since the model under consideration possess a consistent canonical quantization and also fulfils the physical constraints in order to this vacuum process to happen, it is a perfect candidate to implement the study at finite temperature. We evaluate in details the instantaneous rate of energy loss for a charge, and show that the radiation rate is significantly …
We consider a CPT-noninvariant scalar model and a modified version of quantum electrodynamics with an additional photonic Chern-Simons-like term in the action. In both cases, the Lorentz violation traces back to a spacelike background vector. The effects of the modified field equations and dispersion relations on the kinematics and dynamics of decay processes are discussed, first for the simple scalar model and then for modified quantum electrodynamics. The decay widths for electron Cherenkov radiation in modified quantum electrodynamics and for photon triple-splitting in the corresponding low…
The simplest way to modify gravity is to extend the gravitational sector to include an additional scalar degree of freedom. The most general metric that can be built in such a theory includes disformal terms, so that standard model fields move on a metric which is the sum of the space time metric and a tensor constructed from first derivatives of the scalar. In such a theory gravitational waves and photons can propagate at different speeds, and these can in turn be different from the maximum speed limit for matter particles. In this work we show that disformal couplings can cause charged parti…
The current work focuses on the process of vacuum Cherenkov radiation for Lorentz-violating fermions that are described by the minimal Standard-Model Extension (SME). To date, most considerations of this important hypothetical process have been restricted to Lorentz-violating photons, as the necessary theoretical tools for the SME fermion sector have not been available. With their development in a very recent paper, we are now in a position to compute the decay rates based on a modified Dirac theory. Two realizations of the Cherenkov process are studied. In the first scenario, the spin project…
Based on the new quantum Vavilov-Cherenkov,s radiation(VCR) theory (PRL,2004),it is stated the possibility of threshold realization in the modern epoch of the novel VCR effect by the relict photon gas, when it is traversed by relativistic particles of the cosmic rays with γ\geq γ_th \cong 2 \cdot 10^10, where γ^2 = 1 - \frac{V^2}{C^2}, v is the speed of particles, and c is the speed of the light in vacuum.
A covariant criterion for the Cherenkov radiation emission in the field of a non-linear gravitational wave is considered in the framework of exact integrable models of particle dynamics and electromagnetic wave propagation. It is shown that vacuum interacting with curvature can give rise to Cherenkov radiation. The conically shaped spatial distribution of radiation is derived and its basic properties are discussed.
We discuss in this paper the vacuum Cherenkov radiation in the $z=2$ Lifshitz electrodynamics. The improved ultraviolet behavior, in terms of higher spatial derivatives, and the renormalizable couplings, due to the time-space anisotropic scaling, present in the Lifshitz setting are extremely important in fulfilling the physical constraints in order to this vacuum process to happen. We evaluate in details the instantaneous rate of energy loss for a charge, and also analyze the emission of very soft photons in this framework.
A new relation between two-dimensional conformal field theories and three-dimensional topologically massive gauge theories is found, where the dynamical nature of the 3d theory is ultimately important. It is shown that the those primary states in CFT which have non-unitary descendants correspond in the 3d theory to supercritical charges and cause vacuum instability. It is also shown that logarithmic operators separating the unitary sector from a non-unitary one correspond to an exact zero energy ground state in which case the 3d Hamiltonian naturally has a Jordan structure.
For the example of the logarithmic triplet theory at c=-2 the chiral vacuum torus amplitudes are analysed. It is found that the space of these torus amplitudes is spanned by the characters of the irreducible representations, as well as a function that can be associated to the logarithmic extension of the vacuum representation. A few implications and generalisations of this result are discussed.
We propose a model of a spinless electrical charge as a self-consistent field configuration of the electromagnetic (EM) field interacting with a physical vacuum effectively described by the logarithmic quantum Bose liquid. We show that, in contrast to the EM field propagating in a trivial vacuum, a regular solution does exist, and both its mass and spatial extent emerge naturally from dynamics. It is demonstrated that the charge and energy density distribution acquire Gaussian-like form. The solution in the logarithmic model is stable and energetically favourable, unlike that obtained in a mod…
We introduce p-1 pseudocharacters in the space of (1,p) model vacuum torus amplitudes to complete the distinguished basis in the 2p-dimensional fusion algebra to a basis in the whole (3p-1)-dimensional space of torus amplitudes, and the structure constants in this basis are integer numbers. We obtain a generalized Verlinde-formula that gives these structure constants. In the context of theories with boundaries, we identify the space of vacuum torus amplitudes with the space of Ishibashi states. Then, we propose 3p-1 boundary states satisfying the Cardy condition.
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra governed by this non-linear correction. It turns out that such time parametrization is essentially energy-dependent and becomes global only asymptotically - when the energies get very small comparing to the effective quantum gravity scale. Similar thing happens to the Lorentz invariance - in the resulting theory it becomes an asymptotic low-energy phenomeno…
We argue that if the velocity of electromagnetic waves in vacuum, \cem, is different from the limiting velocity for massive particles, \cst, then, a proton moving with velocity $\cem < v < \cst$ would radiate Cherenkov radiation. Because we have seen protons with energy $\sim 10^{19}$ eV coming from a distance of order more than 1 Mpc, we can put a constraint on $Δ:= (\cst - \cem)/\cst$: $Δ< 10^{-27}$.
Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the fundamental Bose-Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativistic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic postulates, Mach's princip…
If one analyzes the effects of electromagnetic vacuum fluctuations upon an electron interference pattern in an approximation in which the electrons follow classical trajectories, an ultraviolet divergence results. It is shown that this divergence is an artifact of the classical trajectory approximation, and is absent when the finite sizes of electron wavepackets are accounted for. It is shown that the vacuum fluctuation effect has a logarithmic dependence upon the wavepacket size. However, at least in one model geometry, this dependence cancels when one includes both vacuum fluctuation and pho…
We study the competing effects of gluon self-coupling and their interactions with quarks in a baryon, using the very simple setting of a hermitian 1-matrix model with action tr A^4 - log det(nu + A^2). The logarithmic term comes from integrating out N quarks. The model is a caricature of 2d QCD coupled to adjoint scalars, which are the transversely polarized gluons in a dimensional reduction. nu is a dimensionless ratio of quark mass to coupling constant. The model interpolates between gluons in the vacuum (nu=infinity), gluons weakly coupled to heavy quarks (large nu) and strongly coupled to …
We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional ${\mathcal{M}} P$-product. The method is to analyze regularization tails with a power-law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multi-layer structure of the fermionic projector near the light cone. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed.
We review some aspects of logarithmic conformal field theories which might shed some light on the geometrical meaning of logarithmic operators. We consider an approach, put forward by V. Knizhnik, where computation of correlation functions on higher genus Riemann surfaces can be replaced by computations on the sphere under certain circumstances. We show that this proposal naturally leads to logarithmic conformal field theories, when the additional vertex operator insertions, which simulate the branch points of a ramified covering of the sphere, are viewed as dynamical objects in the theory. We…
The effects of vacuum polarization arising from loops of massive scalar particles on graviton propagation in curved space are considered. Physically, they are due to curvature induced tidal forces acting on the cloud of virtual scalar particles surrounding the graviton. The effects are tractable in a WKB and large mass limit and the results can be written as an effective refractive index for the graviton modes with both a real and imaginary part. The imaginary part of the refractive index is a curvature induced contribution to the wavefunction renormalization of the graviton in real affine tim…
A new model of nonlinear electrodynamics named as \emph{"double-logarithmic"} is introduced and investigated. The theory carries one dimensionful parameter of the $β$ as Born-Infeld electrodynamics. It is shown that the dual symmetry and dilatation (scale) symmetry are broken in the proposed model. The electric field of a point-like charge is derived for this model and it becomes non-singular at the origin and by use of this electric field the static electric energy of a point like charge is calculated. In the presence of an external magnetic field the theory shows the phenomenon known as vacu…
Using the logarithmic superfluid model of physical vacuum, one can formulate a quantum theory, which successfully recovers Einstein's theory of relativity in low-momenta limit, but otherwise has different foundations and predictions. We present an analytical example of the dispersion relation and argue that it should have a Landau "roton" form which ensures the suppression of dissipative fluctuations. We show that at small momenta, a dispersion relation becomes relativistic with small deformations, such that a photon acquires effective mass, but a much more complex picture arises at large mome…
In the present paper we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantit…
We consider the universal logarithmic divergent term in the entanglement entropy of gauge fields in the Minkowski vacuum with an entangling sphere. Employing the mapping in arXiv:1102.0440, we analyze the corresponding thermal entropy on open Einstein universe and on the static patch of de Sitter. Using the heat kernel of the vector Laplacian we resolve a discrepancy between the free field calculation and the expected Euler conformal anomaly. The resolution suggests a modification of the well known formulas for the vacuum expectation value of the spin-1 energy-momentum tensor on conformally fl…
The self-gravitational correction of the ultraviolet-divergent second- order "vacuum polarization" radiative correction insertion Feynman diagram is carried out using full, self-consistent Einstein equation propagation of the intermediate virtual gravitons, which takes into account their important non-linear interactions with each other. (As a by-product, the subsequent perturbative treatment of these non-linearities is avoided, which eliminates the source of the ultraviolet divergences of the second- quantized gravity theory itself.) The corrected diagram is finite, makes no contribution to c…
Two different approaches to calculate the fusion rules of the c_{p,1} series of logarithmic conformal field theories are discussed. Both are based on the modular transformation properties of a basis of chiral vacuum torus amplitudes, which contains the characters of the irreducible representations. One of these is an extension, which we develop here for a non-semisimple generalisation of the Verlinde formula introduced by Fuchs et al., to include fusion products with indecomposable representations. The other uses the Verlinde formula in its usual form and gets the fusion coefficients in the li…
In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2,2p-1,2p-1,2p-1) series of triplet algebras and a bit logarithmic extensions of the minimal Virasoro models. Since in all known examples of logarithmic conformal field theories the vacuum representation of the maximally extended chiral symmetry algebra is an irreducible submodule of a larger, indecomposable module, its character provides a lot of non-trivial information about the theory such…
