Radiation reaction and renormalization for a photon-like charged particle
A renormalization scheme which relies on energy-momentum and angular momentum balance equations is applied to the derivation of effective equation of motion for a massless point-like charge. Unlike the massive case, the rates of radiated energy-momentum and angular momentum tend to infinity whenever...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2007 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Radiation reaction and renormalization for a photon-like charged particle / Yu. Yaremko // Вопросы атомной науки и техники. — 2007. — № 3. — С. 225-229. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859641149947379712 |
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| author | Yaremko, Yu. |
| author_facet | Yaremko, Yu. |
| citation_txt | Radiation reaction and renormalization for a photon-like charged particle / Yu. Yaremko // Вопросы атомной науки и техники. — 2007. — № 3. — С. 225-229. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | A renormalization scheme which relies on energy-momentum and angular momentum balance equations is applied to the derivation of effective equation of motion for a massless point-like charge. Unlike the massive case, the rates of radiated energy-momentum and angular momentum tend to infinity whenever the massless source is accelerated. The external electromagnetic fields which do not change the velocity of the particle admit only its presence within the interaction area. The effective equation of motion is the equation on eigenvalues and eigenvectors of the electromagnetic tensor. The same solution arises in Rylov's model of magnetosphere of a rapidly rotating neutron star (pulsar).
Пораховані енергія-імпульс та момент кількості руху електромагнітного поля безмасового точкового заряду. На відміну від точкового джерела з ненульовою масою спокою, інтеграли руху, що переносяться полем прискореного безмасового заряду, необмежено зростають. Тому фотоноподібний заряд може існувати лише в такому зовнішньому полі, яке не змінює його швидкості. Ефективним рівнянням руху є рівняння на власні вектори та власні значення тензора напруженості зовнішнього електромагнітного поля. Таке ж рівняння виникає в запропонованій Риловим моделі магнетосфери пульсара.
Найдены енергия-импульс и момент количества движения электромагнитного поля безмассового точечного заряда. В отличии от точечного источника с ненулевой масссой покоя, излученные интегралы движения поля ускоренного безмассового заряда неограниченно возрастают. Вследствиe этого фотоноподобный заряд может существовать лишь в таком внешнем поле, которое не изменяет его скорости. Эффективным уравнением движения является уравнение на собственные векторы и собственные значения тензора напряжения внешнего электромагнитного поля. Такое же уравнение появляется в предложенной Рыловым модели магнитосферы пульсара.
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| first_indexed | 2025-12-07T13:22:25Z |
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| fulltext |
RADIATION REACTION AND RENORMALIZATION
FOR A PHOTON-LIKE CHARGED PARTICLE
Yu. Yaremko
Institute for Condensed Matter Physics of NASU, Lviv, Ukraine;
e-mail: yar@ph.icmp.lviv.ua
A renormalization scheme which relies on energy-momentum and angular momentum balance equations is ap-
plied to the derivation of effective equation of motion for a massless point-like charge. Unlike the massive case, the
rates of radiated energy-momentum and angular momentum tend to infinity whenever the massless source is accel-
erated. The external electromagnetic fields which do not change the velocity of the particle admit only its presence
within the interaction area. The effective equation of motion is the equation on eigenvalues and eigenvectors of the
electromagnetic tensor. The same solution arises in Rylov's model of magnetosphere of a rapidly rotating neutron
star (pulsar).
PACS: 03.50.De, 11.10.Gh, 97.60.Gb
1. INTRODUCTION
In the paper [1] massless charged particles of spin
one or larger are excluded in quantum electrodynamics
by the argument that masslessness, Lorentz invariance,
and electromagnetic coupling, are mutually incompati-
ble. Roughly speaking, the interaction with an external
electromagnetic field drastically changes incoming
massless particle state, so that outgoing state does not
describe a particle without rest mass. Further in Ref.[2]
the existence of massless charges is forbidden in general
by the condition that the energy of such particles in the
electromagnetic field has no lower bound. In the present
paper we consider the problem of reality of a massless
charge within the realm of classical field theory.
Since the concept of a "zero-mass interacting parti-
cle" is quite different in quantum and classical theories,
it would be more appropriate to obtain the equation of
motion as a limiting case of the well-known Lorentz-
Dirac equation [3]. (It defines the motion of point-like
charge with rest mass m under the influence of an ex-
ternal force as well as its own electromagnetic field, for
a modern review see [4,5].) In Ref.[6] the motion of
massive charged particles in a very strong electromag-
netic field is studied. The guiding center approximation
[7] is used in the Lorentz-Dirac equation. In this ap-
proximation the particle motion is described as a com-
bination of forward and oscillatory motions (the field
changes are small during a gyration period). If the gra-
dient of the field potential is much larger than the rest
mass of the particle, the strong radiation damping sup-
presses the particle gyration. It is shown [6] that the
particle velocity is directed along one of the eigenvec-
tors of the (external) electromagnetic tensor if m→0 in
the rewritten Lorentz-Dirac equation. The equation on
eigenvalues and eigenvectors of the electromagnetic
tensor governs the motion of charges in the massless
approximation.
According to Ref.[6], the effective equation of mo-
tion for this charge does not contain derivatives higher
than 1. This conclusion is in contradiction with that of
[8] where the 5-th order differential equation determines
the evolution of photon-like charge.
In the present paper we apply the regularization pro-
cedure based on Noether conservation laws to the prob-
lem of radiation reaction for a massless charge in re-
sponse to the electromagnetic field. The conservation
laws are an immovable fulcrum about which tips the
balance of truth regarding renormalization and radiation
reaction.
2. GENERAL SETTING
We consider a massless point-like particle which
carries an electric charge q and moves on a lightlike
world line γ: IR→IM4 described by functions zµ(τ), in
which τ is an arbitrary parameter. A tangent vector to
each point zµ(τ)∈γ lies on the future light cone with
vertex at this point:
02 =z . (1)
(We use an overdot on z to indicate differentiation with
respect to the evolution parameter τ.) We let
uα(τ)=dzα/dτ the 4-velocity, and aα(τ)=duα/dτ is the 4-
acceleration. Initially we take the world line to be arbi-
trary; our main goal is to find the particle's equation of
motion.
Following [8], we deal with an obvious generaliza-
tion of the standard variational principle for massive
charge
fieldparticle IIII ++= int , (2)
with
∫−= αβ
αβ
π
fxfI field
4d
16
1 , . (3) ∫= µ
µ jxAI 4
int d
The particle part of variational principle should be
consistent with the field and the interaction terms. So, if
we require that the renormalized mass be zero, a non-
zero bare mass is necessary to absorb a divergent self-
energy. Hence the world line of the bare particle should
be assumed time-like rather than lightlike. We may also
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2007, N3 (1), p. 225-229. 225
require that the world line be lightlike before renormali-
zation as well as after this procedure. To solve the di-
lemma we establish the structure of the bound and ra-
diative terms of energy-momentum and angular mo-
mentum carried by electromagnetic field of the photon-
like charge.
Having variated (3) with respect to potential Aµ we
obtain the Maxwell field equations [4]
□ , (4) )(4)( xjxA µµ π−=
where current density is zero everywhere, except at the
particle's position where it is infinite
∫ −= )]([)(d)( τδττ µµ zxuqxj , (5)
and □=ηαβ∂α∂β is the wave operator.
The components of the momentum 4-vector carried
by the electromagnetic field are [4,5]
∫Σ= µν
µ
ν στ Tpem d)( , (6)
where dσµ is the outward-directed surface element on an
arbitrary space-like hypersurface Σ. The angular mo-
mentum tensor of the electromagnetic field is written as
( )αµνανµ
α
µν στ TxTxM em −= ∫Σ d)( (7)
where
( )αβ
αβµνν
α
µαµν ηπ ffffT 4/14
1 −= (8)
is the electromagnetic field's stress-energy tensor.
3. ELECTROMAGNETIC FIELD
OF A PHOTON-LIKE CHARGE
Let the past light cone with vertex at an observation
point x is punctured by the particle's world line γ at point
z(s). The retarded Green function associated with the
d'Alembert operator □ and the charge-current density (5)
is valuable only. The components of the Liénard-
Wiechert potential Â=Aαdxα are
r
su
qA
)(α
α = , (9)
where is the retarded distance [4,5];
R
)( uRr ⋅−=
µ=xµ−zµ(s) is the null vector pointing from z(s) to x.
The 4-potential is not defined at points on the ray in the
direction of momentary 4-velocity u(s) by reason of the
isotropy condition (1).
Straightforward computation reveals that □A=0 eve-
rywhere, except at the particle's position.
Unlike the massive case, the photon-like charge gen-
erates the far electromagnetic field : Af d=
r
kukakaqf ∧⋅+∧
=
)( , (10)
where the symbol denotes the wedge product. Beca-
use of isotropy condition the retarded distance vanishes
on the ray in the direction of particle's 4-velocity taken
at the instant of emission. The field diverges at all the
points of this ray with vertex at the point of emission.
∧
To calculate the stress-energy tensor of the electro-
magnetic field we substitute the components (10) into
expression (8). Contrary to the massive case [5, eqs.(5.3)-
(5.5)], the "photon-like" Maxwell energy-momentum
density contains the radiative component only:
2
224
r
kkaqT
βα
αβπ = . (11)
Hence the divergent self-energy which is due to volume
integration of the bound part of the electromagnetic
field's stress-energy tensor [9] does not arise. Unlike the
massive case, the photon-like charge does not possess
an electromagnetic "cloud" permanently attached to it.
Fig. 1. In the particle's momentarily comoving
frame the massless charge is placed at the coordinate
origin; its 4-velocity is (1,0,0,1). The point C is linked to
the coordinate origin by a null ray characterized by the
angles (φ,θ). (The null vector n=(1,n) defines this direc-
tion.) For a given point C with coordinates xα′=(t-s)nα′
the retarded distance is x0′-x3′=(t-s)(1-cos θ)
4. ENERGY-MOMENTUM AND ANGULAR
MOMENTUM CARRIED
BY THE ELECTROMAGNETIC FIELD
Now we calculate the electromagnetic field momen-
tum (6) where an integration hypersurface Σt={x∈M4:
x0=t} is a surface of constant t. Volume integration of
the radiative energy-momentum density (11) over a
hyperplane Σt gives the amount of radiated energy-
momentum at fixed instant t. An appropriate coordinate
system is a very important for the integration. We intro-
duce the set of curvilinear coordinates for flat space-
time M4 involving the observation time t and the re-
tarded time s:
'
')()( αα
α
αα nstszx Ω−+= . (12)
The null vector n=(1,n) has the components
(1,cosφsinθ, sinφsinθ,cosθ); θ and φ are two polar an-
gles. Matrix space-time components are Ω0
µ= Ωµ
0=δ0
µ;
its space components Ωi
j constitute the orthogonal ma-
trix which rotates space axes of the laboratory Lorentz
frame until new z-axis is directed along three-vector v.
(Particle's 4-velocity has the form (1,vi), |v|=1, if pa-
rametrization of the world line γ is provided by a dis-
joint union of hyperplanes Σt.) In terms of curvilinear
coordinates (t,s,θ,φ) the retarded distance is as follows:
)cos1)(( θ−−= str . (13)
The situation is pictured in Fig. 1.
226
The surface element is given by dσ0=(-g)½dsdθdφ
where
)cos1(sin)( 2 θθ −−=− stg (14)
is the determinant of metric tensor of Minkowski space
viewed in curvilinear coordinates (12). In these coordi-
nates the components of the electromagnetic field's
stress-energy tensor (11) have the form:
42
2
200
)cos1()(
)(4
θ
π
−−
=
st
saqT ;
42
'
'
2
20
)cos1()(
)(4
θ
π
−−
Ω
=
st
nsaqT
ii
ii . (15)
The angular integration results the radiated energy-mo-
mentum:
∫
∞−
=
t
em ssaJqtp )(d2
1)( 2
0
20
∫
∞−
=
t
ii
em sssaJqtp )(v)(d2
1)( 2
1
2 , (16)
where factors J0 and J1 diverge:
20
0
)cos1(2
1lim
8
1
θθ −
+−=
→
J ;
−
−
−
−=
→ 20
1
)cos1(2
1
cos1
1lim
8
3
θθθ
J .
Similarly, the computation of the electromagnetic
field angular momentum (7) which flows across the
hyperplane Σt gives rise to the divergent quantities:
−
=
∫
∫
∞−
∞−
t
i
t
i
i
em
ssaJ
ssaJ
qtM
)((s)zd
)((s)svd
2
1)(
20
21
20 ;
[∫
∞−
−=
t
ijjiij
em zzssaJqtM vv)(d2
1)( 2
1
2 ]. (17)
The energy-momentum (16) and the angular mo-
mentum (17) of electromagnetic field generated by the
accelerated photon-like charge tend to infinity in the
direction of particle's velocity at the instant of emission.
The divergent terms are not bound terms which should
be absorbed by corresponding particle characteristics
within the renormalization procedure. Indeed, they do
not depend on the distance from the particle's world
line. Secondly, the energy-momentum and the angular
momentum accumulate with time at the observation
hyperplane Σt (see Fig.2). Hence the divergent Noether
quantities cannot be referred to an electromagnetic
"cloud" which is permanently attached to the charge and
is carried along with it.
As a consequence, the Brink-Di Vecchia-Howe ac-
tion term [10,eq.(2)]:
∫= 2)(d2
1 zeI particle ττ (18) ),( i
partp µ =
is consistent with the field and interaction terms (3).
Variation of (18) with respect to Lagrange multiplier
e(τ)≠0 yields the isotropy condition (1). The particle
part (18) of the total action (2) describes already renor-
malized massless charge.
Further in this paper we shall use a disjoint union of
hyperplanes Σt for parametrization of the particle world
line γ. We define vα(t)=dzα(t)/dt as the 4-velocity;
4-acceleration aα(t)=dvα(t)/dt looks as (0, ) in this
para-metrization.
iv
Changes in energy-momentum and angular momen-
tum radiated by accelerated charge should be balanced
by changes in already renormalized 4-momentum and
angular momentum of the particle. But the accelerated
photon-like charge emits infinite amounts of radiation
(see Fig. 2). To change the velocity of the massless
charge the energy is necessary which is too large to be
observed. Threfore, the effective equation of motion
should be supplemented with the condition of absence
of radiative damping.
Fig. 2. The bold circle pictures the trajectory of a
photon-like charge. The others are spherical wave
fronts viewed in the observation hyperplane Σt. The
circling photon-like charge radiates infinite rates of
energy-momentum and angular momentum in the direc-
tion of its velocity v at the instant of emission. The en-
ergy-momentum and angular momentum carried by
electromagnetic field of accelerated charge tend to in-
finity on the spiral curve
According to expression (10), non-accelerated pho-
ton-like charge itself does not generate the electromag-
netic field. The evolution of the particle beyond an in-
teraction area is determined by the Brink-Di Vecchia-
Howe Lagrangian. The particle's 4-momentum
does not change with time: ztep part )(=
0)()( =+ µµ ztezte . (19)
Since γ is degenerate (see eq.(1)), the 4-acceleration
vanishes in adapted parametrization. Since , the
Lagrange multiplier e=e
0≠z
0 does not depend on time. We
deal with a photon-like particle moving in the
v-direction with frequency ω0=e0, such that its energy-
momentum 4-vector can be written
. v00 ωω
227
5. MASSLESS CHARGE WITHIN
AN INTERACTION AREA
When considering the system under the influence of
an external device the change in particle's 4-momentum
should be balanced by an external force Fext:
µµ
extpart Fp = . (20)
This effective equation of motion is supplemented with
the condition of absence of radiative damping. In other
words, the external device admits a massless charge if
and only if the components of null vector of 4-velocity
do not change with time despite the influence of the
external field. The conclusion is similar to that of [1,2].
When the photon-like charged particle moves in the
external electromagnetic field , the Lorentz force
balances the change in its 4-momentum:
F
νµ
ν
µ vv qFe = . (21)
It is convenient to decompose into an electric
field E and a magnetic field B. Equation (21) is then
rewritten as
F
)v( ⋅= Eqe , . (22) ]v[v BqqEe ×+=
We have the following 4-th order algebraic equation
on eigenvalues e :
0)()( 2422224 =⋅−−+ EBqEBqee . (23)
In general, it possesses two real solutions [6,7]:
( ) 222 µ+−±=± BEqe , (24)
where
( ) 2222 )(4B EBE ⋅+−=µ . (25)
The field admits a photon-like charge if and only if cor-
responding eigenvectors
σ
κνλ )(][v BEBE +±×
=± , (26) )sgn( EB ⋅=κ
are of constant values. Here
2)( 22 µλ +−= BE , 2)( 22 µ+−= EBν ,
2)( 22 µσ ++= BE . (27)
The expression (26) is obtained in [11,eq.(2.3)] where
the model of magnetosphere of a rapidly rotating neu-
tron star (pulsar) is elaborated. It defines the velocity of
the massless charged particles which constitute the so-
called "dynamical phase" of the gas of ultrarelativistic
electrons and positrons moving in a very strong elec-
tromagnetic field of the pulsar. In Rylov's model [11]
the massless charges as a limiting case of massive ones
are considered. The reason is that the gradient of star's
potential is much larger than the particle's rest energy
mec2.
6. CONCLUSIONS
Our consideration is founded on the Maxwell equa-
tions with point-like source which governs the propaga-
tion of the electromagnetic field produced by a photon-
like charge. Unlike the massive case, it generates the
far electromagnetic field which does not yield to diver-
gent Coulomb-like self-energy. Hence the world line is
null before renormalization as well as after this proce-
dure. We choose Brink-Di Vecchia-Howe action [10]
for a bare particle moving on the world line which is
proclaimed then to be lightlike.
A surprising feature of the study of the radiation
back reaction in dynamics of the photon-like charge is
that the Larmor term (15) diverges whenever the charge
is accelerated. Since the emitted radiation detaches itself
from the charge and leads an independent existence, it
cannot be absorbed within a renormalization procedure.
Inspection of the energy-momentum and angular
momentum carried by the electromagnetic field of a
photon-like charge reveals the reason why it is not yet
detected (if it exists). Noninteracting massless charges
do manifest themselves in no way. Any external elec-
tromagnetic field (including that generated by a detect-
ing device) will attempt to change the velocity of the
charged particle. Whenever the effort will be successful,
the radiation reaction will increase extremely. In gen-
eral, this circumstance forbids the presence of the pho-
ton-like charges within the interaction area.
Nevertheless, there exists the electromagnetic fields
which do not change the velocities of the massless
charged particles. For example, superposition of plane
waves propagating along some base line admits the
massless charges moving analogously (see Appendix).
(But any disturbance annuls such a "loyalty".) It is
worth noting that the quantum mechanical results [1,2]
are in favour the conception that the external field dis-
tinguishes the directions of non-accelerating motions of
photon-like charges (if they exist).
To survive photon-like charges need an extremely
strong field of specific configuration, as that of the ro-
tating neutron star (pulsar). In [11] the model of the
pulsar magnetosphere is elaborated. It involves the so-
called dynamical phase which consists of the massless
charged particles moving with speed of light along
some base line determined by the electromagnetic field
of the star. (The massless approximation is meant where
the gradient of star's potential is much larger than elec-
tron's rest energy.) It is worth noting that the expression
for the particles' velocity [11,eq.(2.2)] coincides with
the solution (26) of the "massless" equations of motion
derived in the present paper.
Equation (21) on eigenvalues and eigenvectors of the
electromagnetic tensor governs the motion of charges in
zero-mass approximation. This conclusion is in contradic-
tion with that of [8] where the 5-th order differential
equation determines the evolution of photon-like charge.
The reason is that regularization approach to the radiation
back reaction (smoothing the behaviour of the Lorentz
force in the immediate vicinity of the particle's world
line), employed by Kazinski and Sharapov, is not valid in
the case of the photon-like charged particle and its field.
Indeed, the field diverges not only at point of world line
but at all points of the ray in the direction of particle's 4-
velocity taken at the instant of emission (see Fig. 2).
The ray singularity is stronger that δ-like singularity
of Green's function involved in [8] in the self-force ex-
pression. Hence integration over world line does not
yield a finite part of the self-force.
228
APPENDIX: MOTION OF MASSLESS CHARGES
IN A PLANE WAVE
In case of a plane wave with front moving in the
positive z-direction, the electric and magnetic fields are
related to each other as follows:
yx BE = , , . (A1) xy BE −= 0== zz BE
Since B2−E2 as well as the scalar product (B⋅E) van-
ish, the eigenvalues' equation (23) get simplified:
. The eigenvector corresponding to the fourthly
degenerate eigenvalue is defined by [6]
04 =e
0=e
zn
B
BE
=
×
=
2
][v . (A2)
Hence the plane wave admits massless charges moving
along z-line in the positive direction. Their frequencies
do not change with time.
REFERENCES
1. K.M. Case, S.G. Gasiorowicz. Can massless particles be
charged? //Phys.Rev. 1962, v. 125, p. 1055-1058.
2. G. Morchio, F. Strocchi. Confinement of massless
charged particles in QED4 and of charged particles
in QED3 //Ann.Physics. 1986, v. 172, p. 267-279.
3. P.A.M. Dirac. Classical theory of radiating electrons
//Proc.R.Soc. A. 1938, v. 167, p. 148-169.
4. F. Rohrlich. Classical Charged Particles. Redwood
City, CA: Addison-Wesley, 1990, 305 р.
5. E. Poisson. An introduction to the Lorentz-Dirac
equation . gr-qc/9912045, 1999, 14 p.
6. Yu.A. Rylov. The algebraical structure of the elec-
tromagnetic tensor and description of charged parti-
cles moving in the strong electromagnetic field
//J.Math.Phys. 1989, v. 30, p. 521-536.
7. D.M. Fradkin. Covariant electromagnetic projection
operators and a covariant description of charged par-
ticle guiding centre motion field //J.Phys.A:
Math.Gen. 1978, v. 11, p. 1069-1086.
8. P.O. Kazinski, A.A. Sharapov. Radiation reaction for a
massless charged particle //Class. Quantum Grav. 2003,
20, p. 2715-2725.
9. C. Teitelboim. Splitting of the Maxwell tensor: ra-
diation reaction without advanced fields
//Phys.Rev.D. 1970, v. 1, p. 1572-1582.
10. L. Brink, P. Di Vecchia, P. Howe. A locally super-
symmetric and reparametrization invariant action for
the spinning string //Phys.Lett.B. 1976, v. 65,
p. 471-474.
11. Yu.A. Rylov. The global structure of the pulsar
magnetospheres //Astrophys.Space Sci. 1989, v. 158,
p. 297-333.
ПЕРЕНОРМИРОВАНИЕ И РЕАКЦИЯ ИЗЛУЧЕНИЯ ФОТОНОПОДОБНОГО ЗАРЯДА
Ю.Г. Яремко
Найдены энергия-импульс и момент количества движения электромагнитного поля безмассового точеч-
ного заряда. В отличие от точечного источника с ненулевой массой покоя, излученные интегралы движения
поля ускоренного безмассового заряда неограниченно возрастают. Вследствиe этого фотоноподобный заряд
может существовать лишь в таком внешнем поле, которое не изменяет его скорости. Эффективным уравне-
нием движения является уравнение на собственные векторы и собственные значения тензора напряжения
внешнего электромагнитного поля. Такое же уравнение появляется в предложенной Рыловым модели маг-
нитосферы пульсара.
ПЕРЕНОРМУВАННЯ ТА РЕАКЦІЯ ВИПРОМІНЮВАННЯ ФОТОНОПОДІБНОГО ЗАРЯДУ
Ю.Г. Яремко
Пораховані енергія-імпульс та момент кількості руху електромагнітного поля безмасового точкового за-
ряду. На відміну від точкового джерела з ненульовою масою спокою, інтеграли руху, що переносяться по-
лем прискореного безмасового заряду, необмежено зростають. Тому фотоноподібний заряд може існувати
лише в такому зовнішньому полі, яке не змінює його швидкості. Ефективним рівнянням руху є рівняння на
власні вектори та власні значення тензора напруженості зовнішнього електромагнітного поля. Таке ж рів-
няння виникає в запропонованій Риловим моделі магнітосфери пульсара.
229
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| id | nasplib_isofts_kiev_ua-123456789-110963 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:22:25Z |
| publishDate | 2007 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Yaremko, Yu. 2017-01-07T15:03:20Z 2017-01-07T15:03:20Z 2007 Radiation reaction and renormalization for a photon-like charged particle / Yu. Yaremko // Вопросы атомной науки и техники. — 2007. — № 3. — С. 225-229. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 03.50.De, 11.10.Gh, 97.60.Gb https://nasplib.isofts.kiev.ua/handle/123456789/110963 A renormalization scheme which relies on energy-momentum and angular momentum balance equations is applied to the derivation of effective equation of motion for a massless point-like charge. Unlike the massive case, the rates of radiated energy-momentum and angular momentum tend to infinity whenever the massless source is accelerated. The external electromagnetic fields which do not change the velocity of the particle admit only its presence within the interaction area. The effective equation of motion is the equation on eigenvalues and eigenvectors of the electromagnetic tensor. The same solution arises in Rylov's model of magnetosphere of a rapidly rotating neutron star (pulsar). Пораховані енергія-імпульс та момент кількості руху електромагнітного поля безмасового точкового заряду. На відміну від точкового джерела з ненульовою масою спокою, інтеграли руху, що переносяться полем прискореного безмасового заряду, необмежено зростають. Тому фотоноподібний заряд може існувати лише в такому зовнішньому полі, яке не змінює його швидкості. Ефективним рівнянням руху є рівняння на власні вектори та власні значення тензора напруженості зовнішнього електромагнітного поля. Таке ж рівняння виникає в запропонованій Риловим моделі магнетосфери пульсара. Найдены енергия-импульс и момент количества движения электромагнитного поля безмассового точечного заряда. В отличии от точечного источника с ненулевой масссой покоя, излученные интегралы движения поля ускоренного безмассового заряда неограниченно возрастают. Вследствиe этого фотоноподобный заряд может существовать лишь в таком внешнем поле, которое не изменяет его скорости. Эффективным уравнением движения является уравнение на собственные векторы и собственные значения тензора напряжения внешнего электромагнитного поля. Такое же уравнение появляется в предложенной Рыловым модели магнитосферы пульсара. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники QED processes in strong fields Radiation reaction and renormalization for a photon-like charged particle Перенормування та реакція випромінювання фотоноподібного заряду Перенормирование и реакция излучения фотоноподобного заряда Article published earlier |
| spellingShingle | Radiation reaction and renormalization for a photon-like charged particle Yaremko, Yu. QED processes in strong fields |
| title | Radiation reaction and renormalization for a photon-like charged particle |
| title_alt | Перенормування та реакція випромінювання фотоноподібного заряду Перенормирование и реакция излучения фотоноподобного заряда |
| title_full | Radiation reaction and renormalization for a photon-like charged particle |
| title_fullStr | Radiation reaction and renormalization for a photon-like charged particle |
| title_full_unstemmed | Radiation reaction and renormalization for a photon-like charged particle |
| title_short | Radiation reaction and renormalization for a photon-like charged particle |
| title_sort | radiation reaction and renormalization for a photon-like charged particle |
| topic | QED processes in strong fields |
| topic_facet | QED processes in strong fields |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110963 |
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