arXiv subjects

Pavel Spirin

Publications and source records attributed to Pavel Spirin.

15 recordsLinked to original sources

arXiv2024

Vacuum Polarization Effects of Pointlike Impurity

We develop precise formulation for the effects of vacuum polarization near a pointlike source with a zero-range ($δ$-like) potential in three spatial dimensions. There are different ways of introducing $δ$-interaction in the framework of quantum theory. We discuss the approach based on the concept of self-adjoint extensions of densely defined symmetric operators. Within this approach we consider the real massive scalar field in three-dimensional Euclidean space with a single extracted point. Appropriate boundary conditions imposed at this point enable one to consider all self-adjoint extensions of $- Δ$ as operators which can describe a pointlike source with a zero-range potential. In this framework we compute the renormalized vacuum expectation value of the field square $\langle ϕ^{ 2}(x)\rangle_{\rm ren}$ and the renormalized vacuum average of the scalar-field's energy-momentum tensor $\langle T_{μν}(x)\rangle_{\rm ren}$. Asymptotic cases are discussed in detail.

hep-th↗

arXiv2023

Casimir interaction of finite-width strings

Within the trln-formalism we investigate the vacuum interaction of cosmic strings and the influence of strings width on this effect. For the massless real scalar field we compute the Casimir contribution into the total vacuum energy. The dimensional-regularization technique is used. It is shown that the regularized Casimir term contains neither the UV-divergences, nor the divergences related with the non-integrability of the renormalized vacuum mean of the energy-momentum tensor.

hep-th↗

arXiv2017

Piercing of domain walls: new mechanism of gravitational radiation

Domain wall (DW) moving in media undergoes the friction force due to particle scattering. However certain particles are not scattered, but perforate the wall. As a result, the wall gets excited in the form of the branon wave, while the particle experiences an acceleration jump. This gives rise to generation of gravitational waves which we call "piercing gravitational radiation" (PGR). Though this effect is of higher order in the gravitational constant than the quadrupole radiation from the collapsing DWs, its amplitude is enhanced in the case of relativistic particles or photons because of absence of the velocity factor which is present in the quadrupole formula. We derive the spectral-angular distribution of PGR within the simplified model of the weakly gravitating particle-wall system in Minkowski space-time of arbitrary dimensions. Within this model the radiation amplitude is obtained analytically. The spectral-angular distribution of PGR in such an approach suffers from infrared and ultraviolet divergences as well as from collinear divergence in the case of a massless perforating particle. Different cut-off schemes appropriate in various dimensions are discussed. Our results are applicable both to cosmological DWs and to the braneworld models.

hep-th↗

arXiv2016

Vacuum polarization and classical self-action near higher-dimensional defects

We analyze the gravity-induced effects associated with a massless scalar field in a higher-dimensional spacetime being the tensor product of $(d-n)$-dimensional Minkowski space and $n$-dimensional spherically/cylindrically-symmetric space with a solid/planar angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole (if \mbox{$n\geqslant 3$}) or cosmic string (if $n=2$) with $(d-n-1)$ flat extra dimensions. Thus, we refer to them as conical backgrounds. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green's function, valid for any $d\geqslant 3$ and $2\leqslant n\leqslant d-1$, and compute it to the leading order. With the use of this Green's function we compute the renormalized vacuum expectation value of the field square $\langle ϕ^{2}(x)\rangle_{\mathrm{ren}}$ and the renormalized vacuum averaged of the scalar-field's energy-momentum tensor $\langle T_{M N}(x)\rangle_{\mathrm{ren}}$ for arbitrary $d$ and $n$ from the interval mentioned above and arbitrary coupling constant to the curvature $ξ$. In particular, we revisit the computation of the vacuum polarization effects for a non-minimally coupled massless scalar field in the spacetime of a straight cosmic string. The same Green's function enables to consider the old purely classical problem of the gravity-induced self-action of a classical pointlike scalar or electric charge, placed at rest at some fixed point of the space under consideration. To deal with divergences, which appear in consideration of the both problems, we apply the dimensional-regularization technique, widely used in quantum field theory (QFT). The explicit dependence of the results upon the dimensionalities of both the bulk and conical submanifold, is discussed.

hep-th↗

arXiv2016

Branestrahlung: radiation in the particle-brane collision

We calculate the radiation accompanying gravitational collision of the domain wall and the point particle in five-dimensional spacetime. This process, which can be regarded as brane-particle bremsstrahlung, here called {\it branestrahlung}, has unusual features. Since the brane has intrinsic dynamics, it gets excited in the course of collision, and, in particular, at the moment of perforation the shock branon wave is generated, which then expands with the velocity of light. Therefore, apart from the time-like source, whose radiation can be computed in a standard way, the total radiation source contains a light-like part whose retarded field is quite non-trivial, exhibiting interesting retardation and memory effects. We analyze this field in detail, showing that, contrary to the claims that the light-like sources should not radiate at all, the radiation is non-zero and has classically divergent spectrum. We estimate the total radiation power introducing appropriate cutoffs. In passing, we explain how the sum of the non-local (with the support inside the light cone) and the local (supported on the cone) singular parts of the Green's function of the five-dimensional d'Alembert equation together define a regular functional.

hep-th↗

arXiv2015

Gravitational Bremsstrahlung from Massless-particle Collisions

The angular and frequency characteristics of the gravitational radiation emitted in collisions of massless particles is studied perturbatively in the context of classical General Relativity for small values of the ratio $α= 2 r_S/b$ of the Schwarzschild radius over the impact parameter. The particles are described with their trajectories, while the contribution of the leading nonlinear terms of the gravitational action is also taken into account. The old quantum results are reproduced in the zero frequency limit $ω\ll 1/b$. The radiation efficiency $ε\equiv E_{\rm rad}/2E$ outside a narrow cone of angle $α$ in the forward and backward directions with respect to the initial particle trajectories is given by $ε\sim α^2$ and is dominated by radiation with characteristic frequency $ω\sim {\mathcal O}(1/r_S)$. The comparison with previous works and the known literature is presented.

hep-th↗

arXiv2015

Gravitational radiation in massless-particle collisions

The angular and frequency characteristics of the gravitational radiation emitted in collisions of massless particles is studied perturbatively in the context of classical General Relativity for small values of the ratio $α\equiv 2 r_S/b$ of the Schwarzschild radius over the impact parameter. The particles are described with their trajectories, while the contribution of the leading nonlinear terms of the gravitational action is also taken into account. The old quantum results are reproduced in the zero frequency limit $ω\ll 1/b$. The radiation efficiency $ε\equiv E_{\rm rad}/2E$ outside a narrow cone of angle $α$ in the forward and backward directions with respect to the initial particle trajectories is given by $ε\sim α^2$ and is dominated by radiation with characteristic frequency $ω\sim {\mathcal O}(1/r_S)$.

hep-th↗

arXiv2013

Vector Bremsstrahlung by Ultrarelativistic Collisions in Higher Dimensions

A classical computation of vector bremsstrahlung in ultrarelativistic gravitational-force collisions of massive point particles is presented in an arbitrary number d of extra dimensions. Our method adapts the post-linear formalism of General Relativity to the multidimensional case. The total emitted energy, as well as its angular and frequency distribution and characteristic values, are discussed in detail. For an electromagnetic mediation propagated in the bulk, the emitted energy $E_{em}$ of scattering with impact parameter b has magnitude $E_{em} \sim e^4 e'^2 γ^{d+2}/(m^2 b^{3d+3})$, with dominant frequency $ω_{em} \sim γ^2/b$. For the gravitational force the charge emits via vector field, propagated in the bulk, energy $E_{rad}\sim[G_D m' e]^2 γ^{d+2}/b^{3d+3}$ for $d \geq 2$, with dominant frequency $ω\simγ^2/b$ and energy $E_{rad}\sim[G_5 m' e]^2γ^{3}\ln γ/b^{6}$ for $d=1$, with most of the energy coming from a wide frequency region $ω\in [γ/b),γ^2/b] $. For the UED model with extra space volume $V=(2πR)^d$ the emitted energy is $E_{UED}\sim (b^{d}/V)^2 E_{rad}$. Finally, for the ADD model, including four dimensions, the electromagnetic field living on 3-brane, loses on emission the energy $E_{ADD}\sim[G_D m'e]^2γ^{3}/(V b^{2d+3})$, with characteristic frequency $ω_{ADD}\simγ/b$. The contribution of the low frequency part of the radiation (soft photons) to the total radiated energy is shown to be negligible for all values of d. The domain of validity of the classical result is discussed. The result is analyzed from the viewpoint of the deWitt - Brehme - Hobbs equation (and corresponding equations in higher dimensions).

hep-th↗

arXiv2012

Gravitational bremsstrahlung in ultra-planckian collisions

A classical computation of gravitational bremsstrahlung in ultra-planckian collisions of massive point particles is presented in an arbitrary number d of toroidal or non-compact extra dimensions. Our method generalizes the post-linear formalism of General Relativity to the multidimensional case. The total emitted energy, as well as its angular and frequency distribution are discussed in detail. In terms of the gravitational radius r_S of the collision energy, the impact parameter b and the Lorentz factor in the CM frame, the leading order radiation efficiency in the Lab frame is shown to be of order (r_S/b)^{3(d+1)} gamma_{cm} for d=0, 1 and of order (r_S/b)^{3(d+1)} gamma_{cm}^{2d-3} for d>1, up to a known d-dependent coefficient and a ln gamma_{cm} factor for d=2, while the characteristic frequency of the radiation is gamma/b. The contribution of the low frequency part of the radiation (soft gravitons) to the total radiated energy is shown to be negligible for all values of d. The domain of validity of the classical result is discussed. Finally, it is shown that within the region of validity of our approach the efficiency can obtain unnatural values greater than one, which is interpreted to mean that the peripheral ultra-planckian collisions should be strongly radiation damped.

hep-th↗

arXiv2011

Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions

Classical bremsstrahlung of a massless scalar field $Φ$ is studied in gravity mediated ultra-relativistic collisions with impact parameter $b$ of two massive point particles in the presence of $d$ non-compact or toroidal extra dimensions. The spectral and angular distribution of the scalar radiation are analyzed, while the total emitted $Φ-$energy is found to be strongly enhanced by a $d-$dependent power of the Lorentz factor $γ$. The direct radiation amplitude from the accelerated particles is shown to interfere destructively (in the first two leading ultra-relativistic orders) with the one due to the $Φ-Φ-graviton$ interaction in the frequency regime $γ/b\lesssim ω\lesssim γ^2/b$ in all dimensions.

hep-th↗

arXiv2010

Transplanckian bremsstrahlung and black hole production

Classical gravitational bremsstrahlung in particle collisions at transplanckian energies is studied in ${\mathcal M}_4\times {\mathcal T}^d$. The radiation efficiency $ε\equiv E_{\rm rad}/E_{\rm initial}$ is computed in terms of the Schwarzschild radius $r_S(\sqrt{s})$, the impact parameter $b$ and the Lorentz factor $γ_{\rm cm}$ and found to be $ε=C_d (r_S/b)^{3d+3} γ_{\rm cm}^{2d+1}$, larger than previous estimates by many powers of $γ_{\rm cm}\gg 1$. The result is reliable for impact parameters in the overlap of $r_S λ_C$, with $b_c$ marking (for $d\neq 0$) the loss of the notion of classical trajectories and $λ_C\equiv \hbar/mc$ the Compton length of the scattered particles. The condition on $s$ and $m$ for extreme radiation damping and (presumably) no black hole production is also derived.

hep-ph↗

arXiv2010

Radiation reaction in curved even-dimensional spacetime

We develop a new method of computing radiation reaction for a point particle interacting with massless scalar and vector fields in curved space-time. It is based on the analysis of field Green's functions with both points lying on the particle world-line and does not require integration of the field stresses outside the world line as was used in the DeWitt-Brehme approach, thus leading to a substantial simplification of the problem. We start with space-time of an arbitrary dimension and show that the Hadamard expansion of the massless scalar and vector Green's functions contain only integer inverse powers of the Synge world function in even dimensions and only half-integer in the odd dimensions. The even-dimensional case then is treated in detail. We analyze divergencies, calculate higher-derivative counterterms, and find a recurrent formula for the local parts of the reaction force in neighboring dimensions. Higher-dimensional curved space counterterms are not simply the covariant generalizations of the flat ones, but contain additional curvature-dependent terms. We illustrate our formalism in four and six dimensions. In the first case we rederive the results of DeWitt-Brehme-Hobbs in a simpler way, in the second case we give a covariant generalization of the Kosyakov equation. The local part of the reaction force is found to contain a term proportional to the Riemann tensor which is absent in four dimensions.

gr-qc↗

arXiv2009

Classical ultra-relativistic scattering in ADD

The classical differential cross-section is calculated for high-energy small-angle gravitational scattering in the factorizable model with toroidal extra dimensions. The three main features of the classical computation are: (a) It involves summation over the infinite Kaluza-Klein towers but, contrary to the Born amplitude, it is finite with no need of an ultraviolet cutoff. (b) It is shown to correspond to the non-perturbative saddle-point approximation of the eikonal amplitude, obtained by the summation of an infinite number of ladder graphs of the quantum theory. (c) In the absence of extra dimensions it reproduces all previously known results.

hep-ph↗

arXiv2006

Radiation reaction in curved space-time: local method

Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the procedure of integration of the field momentum over the tube surrounding the world-line. To avoid these problems we suggest a purely local derivation dealing with the field quantities defined only {\em on the world-line}. We consider point particle interacting with scalar, vector (electromagnetic) and linearized gravitational fields in the (generally non-vacuum) curved space-time. To properly renormalize the self-action in the gravitational case, we use a manifestly reparameterization-invariant formulation of the theory. Scalar and vector divergences are shown to cancel for a certain ratio of the corresponding charges. We also report on a modest progress in extending the results for the gravitational radiation reaction to the case of non-vacuum background.

gr-qc↗

arXiv2004

Radiation reaction reexamined: bound momentum and Schott term

We review and compare two different approaches to radiation reaction in classical electrodynamics of point charges: a local calculation of the self-force using the charge equation of motion and a global calculation consisting in integration of the electromagnetic energy-momentum flux through a hypersurface encircling the world-line. Both approaches are complementary and, being combined together, give rise to an identity relating the locally and globally computed forces. From this identity it follows that the Schott terms in the Abraham force should arise from the bound field momentum and can not be introduced by hand as an additional term in the mechanical momentum of an accelerated charge. This is in perfect agreement with the results of Dirac and Teitelboim, but disagrees with the recent calculation of the bound momentum in the retarded coordinates. We perform an independent calculation of the bound electromagnetic momentum and verify explicitly that the Schott term is the derivative of the finite part of the bound momentum indeed. The failure to obtain the same result using the method of retarded coordinates tentatively lies in an inappropriate choice of the integration surface. We also discuss the definition of the delta-function on the semi-axis involved in the local calculation of the radiation reaction force and demonstrate inconsistency of one recent proposal.

hep-th↗