Questions tagged [point-particles]

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Quantization of charge implying charge exist in the form of point particles

The statement for quantization of charge says that total charge of a body is constant. Now the word " body " seems vague. We may consider any part of space which we want and call it a body. ...
User51's user avatar
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Can a point charge be asymmetric?

The derivation of Coulombs law from Maxwell's first equation for a point charge assumes that the field is symmetric along a sphere. What happens if this assumption is removed? Could there be other ...
Kids Free's user avatar
3 votes
4 answers
181 views

Lagrangian for a free antimatter particle

Context The Lagrangian, $L$, of a free particle is derived many places including in Section 8 of Landau's Theory of Classical Fields. The well-known result for a free material particle of mass $m$ and ...
Michael Levy's user avatar
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What do we learn from quantizing the relativistic point particle?

In many textbooks on string theory, some time is spend on quantizing the relativistic point particle as a warming-up for quantizing the Nambu-Goto action for relativistic strings. However, I have not ...
Fraxinian's user avatar
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Is there a Lorentz invariant action for a free multi-particle system?

I want to write down a Lorentz-invariant action of free multi-particle systems. I know that a Lorentz-invariant action for each particle might be expressed as $$ S[\vec{r}]=\int dt L(\vec{r}(t),\dot{\...
watahoo's user avatar
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Finding the kinetic energy without exactly knowing the motion [closed]

let $P$ be a point particle of mass $m$ simultaneously subjected to elastic force $ \overrightarrow{F_1}= -k \overrightarrow{e_r}$ and the Newtonian $ \overrightarrow{F_2}= -\frac{\gamma}{r^2}$ ...
Massimiliano Messina's user avatar
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1 answer
64 views

Finding the equipotential surface of a system of two unequal oppositely charged point charges [closed]

We have a system of two unequal opposite point charges, of which $q_2$ is smaller and $d$ is the distance between charges. There is an equipotential spherical surface of potential $V=0$ that encloses ...
Mirza Beglerović Raven's user avatar
13 votes
6 answers
8k views

Does classical electrodynamics have a Lagrangian that gives both the Lorentz force and Maxwell equations?

There is a Lagrangian for a particle of mass $m$ and charge $q$ $$\mathcal{L}_1 = \mathcal{L}_k(m, \vec{v}) - q\phi + q\vec{v}\cdot\vec{A}$$ where $\mathcal{L}_k(m, \vec{v})$ is either $\frac{1}{2}m\...
Chad K's user avatar
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2 votes
1 answer
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Derivation by Zee of a relativistic point particle action in a EM field in curved space

In Einstein Gravity in a Nutshell by Zee, in section IV.1 page 241, he tries to write down the action for electromagnetism and gravity in an intuitive and patchwork way, Starting from the relativistic ...
mathemania's user avatar
9 votes
1 answer
512 views

Constraints Generating Gauge Transformations and BRST

Given a gauge-invariant point particle action with first class primary constraints $\phi_a$ of the form ([1], eq. (2.36)) $$S = \int d \tau[p_I \dot{q}^I - u^a \phi_a]\tag{1}$$ we know immediately, ...
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Continuity equation in curved space-time: a point particle

Let us consider the action describing a point particle with charge $e$. The interaction term is equal to $$ S_{int} = e\int A_{\mu}\dfrac{d{x}_e^{\mu}}{d\tau}d\tau = e\int A_{\mu}\dot{x}_e^{\mu}dt $$ ...
K. Pull's user avatar
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6 answers
106 views

How to determine whether an object is a point object?

I know that we can consider an object as point object, if its size is negligible as compared to distance traveled by it in reasonable amount of time. But in my book Ncert there is questions which asks ...
S K's user avatar
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1 answer
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2D newtonian gravitational flux not the same for centered/offset point mass? [closed]

$\alpha*r$" /> I am having trouble comparing the 2-dimensional gravitational flux, due to a point mass $M$ located at the origin of the gaussian circle (in green) at point O, versus a point mass ...
Ne612we's user avatar
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1 answer
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How does normal force act on ring with a point mass on it? [closed]

I have been thinking about this situation, I have no idea how the normal force act of such a body. Here I have taken the point mass and ring of same mass m but please provide a general solution. So I ...
SAM4RTH's user avatar
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1 answer
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Sign convention for the Lagrangian of a free massive point particle in general relativity

As far as I understand, the Lagrangian of a massive free particle in the context of general relativity is the following: $$L=-mc\sqrt{g_{\mu\nu}\dfrac{dx^\mu}{dt}\dfrac{dx^\nu}{dt}}.$$ But is this the ...
Wild Feather's user avatar
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Notation: Proper time as a parameter of a curve versus as a functional

I am trying to figure out some notation issues (or at least that what I assume this is). I assume the "proper time" could refer to a "proper time functional" of a timelike path $P(\...
qwerty's user avatar
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1 answer
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Is there a shape associated to point charge? [duplicate]

This is puzzling to me because I have learnt that a charged sphere has the same electric field and electric potential at a point beyond its surface. So does it mean that a point charge is also ...
Sanskar Benjwal's user avatar
1 vote
3 answers
951 views

Is an electron a point charge? [closed]

Doesn't electron capture imply an electron is not a point charge? It needs to have a radius that overlaps with the proton. If it was a point charge, no matter how close it got to the proton, the ...
talanum1's user avatar
3 votes
1 answer
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Massive vs. massless relativistic point particle in einbein form: Difference in the gauge structure?

The action for the relativistic point particle with mass $m \geq 0$ in a curved background is given by: \begin{equation} S[X] = \int_{\tau_0}^{\tau_1} d\tau \left[ e(\tau)^{-1} g_{\mu \nu}(X(\tau)) \...
warpfel's user avatar
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Roundness of electrons [duplicate]

I have seen articles online discussing the roundness of electrons. This goes a bit against my understanding of electrons as elementary point like particles. How can a point have a shape? What does ...
Tjommen's user avatar
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6 answers
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Why do we insist that the electron be a point particle when calculation shows it creates an electrostatic field of infinite energy?

I've heard compelling reasons to think that it is one although why do we assert this in light of the calculation which shows a point particle creates an electrostatic field of infinite energy (see e.g....
greatscissors's user avatar
2 votes
1 answer
141 views

Relationship between Lagrangians describing a particle interacting with a scalar field

In Susskind's Particles and Fields lecture, he considered the Lagrangian obtained by considering a particle and the effects of a scalar field $\phi(t, x)$ with coupling constant $g$ on the particle (...
Prajith Velicheti's user avatar
1 vote
3 answers
238 views

Additional electric field due to changing magnetic field around a moving charge

Imagine a point charge moving along x-axis in empty space at a constant velocity $v$. Since the charge is moving, the electric and magnetic field around it should be surmisable from this image (...
Kraken's user avatar
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1 answer
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Constraint in BRST quantization of point particle

On page 130 of Joe Polchinski's String Theory volume 1 book, the Constraint or the missing equation of motion for point particle after gauge fixing is $H = 0$, and the BRST operator is the ghost $c$ ...
Roy's user avatar
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1 answer
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Variational Principle for Relativistic Action

I'm going through p. 27 in Landau & Lifshitz Classical Field Theory (vol 2), and I'm confused as to why only the contravariant part of the proper time is varied? They start with $$\delta S=-mc\...
Redcrazyguy's user avatar
1 vote
3 answers
293 views

What is the correct gravitational potential energy of a single particle in an $N$-body system?

I am aware that the total gravitational potential energy of a system of $N$ particles is given by pairwise interactions, i.e., you start with a single particle in the system, and then calculate the ...
Gregor Hartl Watters's user avatar
1 vote
0 answers
49 views

A problem about relativistic particle actions [closed]

I have a problem of a course in General Relativity which I don’t know to start solving, and I was wondering if someone could give me some indications or ideas on how to figure it out. It is the ...
cut's user avatar
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Relativistic Particle Path Integral by Faddeev Popov

In evaluating the path integral for a relativistic point particle in the einbein formulation, it is common to see the following $$Z = N\int_{x(t_1) = x_1}^{x(t_2) = x_2}\mathcal{D}e\mathcal{D}x\,e^{-\...
anon123456789's user avatar
2 votes
2 answers
173 views

Solving EOMs for massless particle in a potential

As discussed here and within, the Lagrangian for a massless particle, using the $(-,+,+,+)$ metric signature, is $$L = \frac{\dot{x}_\mu \dot{x}^\mu}{2e} - V,\tag{1}$$ where $\dot{x}^\mu := \frac{dx^\...
tomdodd4598's user avatar
0 votes
1 answer
113 views

Clarifications on Susskind's argument for relativistic laws of motion [closed]

I am reading Special Relativity and Classical Field Theory by Susskind. Lecture 3 is about relativistic laws of motion, and I had a few questions about Susskind's arguments here. He says that, if we ...
Relativisticcucumber's user avatar
0 votes
3 answers
90 views

Is the force at the origin of electromagnetic fields infinite?

We know that the electromagnetic force created by its field from an charged particle, e.g. a electron gets weaker at larger and larger distances from that electron. Electrons are treated as points ...
Anon's user avatar
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4 votes
2 answers
509 views

What is the stress-energy tensor in this case?

In case of static point mass we have the following stress energy tensor $$T_{00}=m\delta^3(\vec{r})$$ And other components are zero. What are the components of this tensor in case of moving point mass ...
JavaGamesJAR's user avatar
2 votes
1 answer
272 views

Relativistic Euler-Lagrange equation

I am confused from the equation 6, why we get Euler-Lagrange equation from equation 8 but not from equation 6? Why we need to use $\zeta$ as invariant parameter in equation 8 even we already have ...
Sabi Shrestha's user avatar
3 votes
3 answers
750 views

Derivation of gravitational dynamics using Lagrangian?

The standard textbook approach in Newtonian gravitational dynamics is to derive the particle dynamics using the particle Lagrangian: $$L = T-V = \frac 1 2 m \dot x_u \dot x_u -m\phi(x_u)\tag{1}$$ With ...
David's user avatar
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4 votes
7 answers
3k views

When we say a rigid body is a system of particles, what exactly are 'particles' here?

In Newtonian mechanics, a particle (in my knowledge) is a point-like mass with no shape and size, deformation, rotation and internal movements, which is an idealized model of an object which does have ...
Harshit Rajput's user avatar
3 votes
2 answers
212 views

Why does the trajectory of a relativistic particle "minimises its Minkowski distance"?

The action of a relativistic free particle is $$\mathcal{S}=\int^{t_{1}}_{t_{0}} L dt\tag{1},$$ for $$L=-\frac{mc^{2}}{\gamma}.\tag{2}$$ I understand that a particle will follow the trajectory of ...
Adrien Amour's user avatar
1 vote
1 answer
203 views

Variational operator confusion

Let $L=L(X, \dot X)$ such that the first variation of $L$ is given by $$\delta L=\frac{\partial L}{\partial X}\delta X+\frac{\partial L}{\partial \dot X}\delta \dot X.\tag{1}$$ This is pretty standard ...
aygx's user avatar
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10 votes
8 answers
3k views

How can an electron be a point particle but also a wavefunction?

A point particle is a point in space of a fixed co-ordinate. However, the wavefunction must always be spread out in space to be normalizable to unity.
Egg Man's user avatar
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1 vote
3 answers
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Mathematical Definition of Point Source

Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating". The usual definition in Physics describes it just as a source whose ...
Johann Wagner's user avatar
2 votes
2 answers
305 views

Confused about relativistic point particle action in MTW

In MTW page 179 exercise 7.2 they give the following action for an particle in an electromagnetic potential. $$I = -\frac{1}{16 \pi} \int F_{\mu \nu} F^{\mu \nu} d^4x + \frac{1}{2}m \int \frac{dz^{\mu}...
Jeff's user avatar
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Definition of a point in physics [closed]

What exactly is a point in physics? I understand that in geometry this is unambiguous, but how does it relate to the real world? Is a point particle an object? Is a point in space a volume in space? ...
Ahmed Samir's user avatar
0 votes
4 answers
456 views

Concept of a point particle in physics

How is mechanics, which deals with theoretical point particles, applied to real objects? For example, a force acting on a point particle is reasonable, but for an extended object, how is it natural to ...
Ahmed Samir's user avatar
1 vote
0 answers
53 views

Size of electron? [duplicate]

It is claimed that the electron has a size less than $10^{-19}$m. I presume this is based on high-energy scattering experiments. But isn’t this apparent size simply a function of the high energy of ...
John Eastmond's user avatar
1 vote
5 answers
363 views

Is the electron a pointlike particle? And if yes, how is that possible, because the energy then would diverge, wouldn't it?

My problem is that I read (besides others in this post Why are electrons and quarks 0-dimensional?) that the electron is a point-like particle. My question is on the one hand whether that is true and ...
Luis's user avatar
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-1 votes
1 answer
154 views

How can a point particle have orientation? [duplicate]

I always thought that a point particle would have spherical symmetry. This is the case for the intrinsic electric field from an electron. However, the intrinsic magnetic field of an electron has ...
Juan Perez's user avatar
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2 votes
1 answer
198 views

Are Point particles real or just used for simplicity?

Wikipedia says A point particle is an idealization of particles heavily used in physics. Also In philosophy of science, idealization is the process by which scientific models assume facts about the ...
user avatar
7 votes
2 answers
288 views

How to treat pointlike objects in General Relativity?

In general relativity we usually treat falling bodies and most small objects as pointlike. It is then enough to solve the geodesic equation in order to predict their motion. However, it appears to me ...
user avatar
8 votes
4 answers
1k views

When can the bob of a physical pendulum be approximated as a point particle?

Suppose you have a cylindrical mass you used as a pendulum bob. When is it possible to approximate the cylinder as a point particle?
user942283's user avatar
1 vote
1 answer
302 views

Lagrangian of massless particle in a potential

There are a few questions about a Lagrangian for massless relativistic particles, notably here, here and here, regarding free particles in particular. In the case of the square-root Lagrangian for ...
tomdodd4598's user avatar
2 votes
0 answers
176 views

Deriving einbein action from Polyakov $p$-brane action

In this paper the author derives a "Polyakov style" $p$-brane action which is given by \begin{equation} S_{p}=-\frac{T_{p}}{2} \int d^{p+1} \xi \sqrt{-g}\left(g^{A B} h_{A B}-(p-1)\right) \...
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