Questions tagged [point-particles]
The point-particles tag has no usage guidance.
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Equation of motion for $X^{\mu}$ (geodesic equation)
The action for a relativistic particle of mass $m$ in a curved $D$-dimensional is $$\tilde{S}_0=\frac{1}{2}\int d\tau (\dot{X}^2-m^2)$$ for particular gauge and $\dot{X}^2=g_{\mu\nu}(X)\dot{X}^{\mu}\...
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The size of elementary particles [duplicate]
There is no evidence that particles like electrons have inner structure.
The question is, when people say that electrons are point-like do they mean:
If we measure an electron to be localized to ...
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How do I compute the stress-energy tensor for a simple system of $N$ point particles?
I haven't been able to find a simple self-contained definition of the stress-energy tensor as used in the Einstein field equations.
Suppose I have $N$ classical (not quantum) point particles with ...
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Average distance travelled by particle points placed uniformly at random in a sphere with speed $||v||$ and direction uniformly random?
I would like to compute the average distance travelled by particle points at constant speed $v>0$ with uniformly-distributed directions and placed uniformly at random inside a hollow sphere of ...
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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. ...
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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 ...
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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 ...
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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 ...
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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
$$
S[\vec{r}]=\int dt L(\vec{r}(t),\dot{\...
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Finding the equipotential surface of a system of two unequal oppositely charged point charges [closed]
We have a system of two unequal opposite point charges, of which $q_2$ is smaller and $d$ is the distance between charges. There is an equipotential spherical surface of potential $V=0$ that encloses ...
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Does classical electrodynamics have a Lagrangian that gives both the Lorentz force and Maxwell equations?
There is a Lagrangian for a particle of mass $m$ and charge $q$
$$\mathcal{L}_1 = \mathcal{L}_k(m, \vec{v}) - q\phi + q\vec{v}\cdot\vec{A}$$
where $\mathcal{L}_k(m, \vec{v})$ is either $\frac{1}{2}m\...
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Derivation by Zee of a relativistic point particle action in a EM field in curved space
In Einstein Gravity in a Nutshell by Zee, in section IV.1 page 241, he tries to write down the action for electromagnetism and gravity in an intuitive and patchwork way,
Starting from the relativistic ...
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Constraints Generating Gauge Transformations and BRST
Given a gauge-invariant point particle action with first class primary constraints $\phi_a$ of the form ([1], eq. (2.36))
$$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
$$
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How to determine whether an object is a point object?
I know that we can consider an object as point object, if its size is negligible as compared to distance traveled by it in reasonable amount of time. But in my book Ncert there is questions which asks ...
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2D newtonian gravitational flux not the same for centered/offset point mass? [closed]
$\alpha*r$" />
I am having trouble comparing the 2-dimensional gravitational flux, due to a point mass $M$ located at the origin of the gaussian circle (in green) at point O, versus a point mass ...
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How does normal force act on ring with a point mass on it? [closed]
I have been thinking about this situation, I have no idea how the normal force act of such a body.
Here I have taken the point mass and ring of same mass m but please provide a general solution.
So I ...
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Sign convention for the Lagrangian of a free massive point particle in general relativity
As far as I understand, the Lagrangian of a massive free particle in the context of general relativity is the following:
$$L=-mc\sqrt{g_{\mu\nu}\dfrac{dx^\mu}{dt}\dfrac{dx^\nu}{dt}}.$$
But is this the ...
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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(\...
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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 ...
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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 ...
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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)) \...
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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....
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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 (...
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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 (...
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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$ ...
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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\...
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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 ...
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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 ...
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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
$$Z = N\int_{x(t_1) = x_1}^{x(t_2) = x_2}\mathcal{D}e\mathcal{D}x\,e^{-\...
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Solving EOMs for massless particle in a potential
As discussed here and within, the Lagrangian for a massless particle, using the $(-,+,+,+)$ metric signature, is
$$L = \frac{\dot{x}_\mu \dot{x}^\mu}{2e} - V,\tag{1}$$
where $\dot{x}^\mu := \frac{dx^\...
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Clarifications on Susskind's argument for relativistic laws of motion [closed]
I am reading Special Relativity and Classical Field Theory by Susskind. Lecture 3 is about relativistic laws of motion, and I had a few questions about Susskind's arguments here.
He says that, if we ...
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Is the force at the origin of electromagnetic fields infinite?
We know that the electromagnetic force created by its field from an charged particle, e.g. a electron gets weaker at larger and larger distances from that electron. Electrons are treated as points ...
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What is the stress-energy tensor in this case?
In case of static point mass we have the following stress energy tensor
$$T_{00}=m\delta^3(\vec{r})$$
And other components are zero.
What are the components of this tensor in case of moving point mass ...
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Relativistic Euler-Lagrange equation
I am confused from the equation 6, why we get Euler-Lagrange equation from equation 8 but not from equation 6?
Why we need to use $\zeta$ as invariant parameter in equation 8 even we already have ...
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Derivation of gravitational dynamics using Lagrangian?
The standard textbook approach in Newtonian gravitational dynamics is to derive the particle dynamics using the particle Lagrangian:
$$L = T-V = \frac 1 2 m \dot x_u \dot x_u -m\phi(x_u)\tag{1}$$
With ...
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When we say a rigid body is a system of particles, what exactly are 'particles' here?
In Newtonian mechanics, a particle (in my knowledge) is a point-like mass with no shape and size, deformation, rotation and internal movements, which is an idealized model of an object which does have ...
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Why does the trajectory of a relativistic particle "minimises its Minkowski distance"?
The action of a relativistic free particle is
$$\mathcal{S}=\int^{t_{1}}_{t_{0}} L dt\tag{1},$$
for
$$L=-\frac{mc^{2}}{\gamma}.\tag{2}$$
I understand that a particle will follow the trajectory of ...
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Variational operator confusion
Let $L=L(X, \dot X)$ such that the first variation of $L$ is given by $$\delta L=\frac{\partial L}{\partial X}\delta X+\frac{\partial L}{\partial \dot X}\delta \dot X.\tag{1}$$ This is pretty standard ...
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How can an electron be a point particle but also a wavefunction?
A point particle is a point in space of a fixed co-ordinate. However, the wavefunction must always be spread out in space to be normalizable to unity.
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Mathematical Definition of Point Source
Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating".
The usual definition in Physics describes it just as a source whose ...
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Confused about relativistic point particle action in MTW
In MTW page 179 exercise 7.2 they give the following action for an particle in an electromagnetic potential.
$$I = -\frac{1}{16 \pi} \int F_{\mu \nu} F^{\mu \nu} d^4x + \frac{1}{2}m \int \frac{dz^{\mu}...
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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?
...
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Why is the action integral of relativity particles $S = -mc\int ds$? [duplicate]
In my classical mechanic course material, it states that
(In context of relativity) The path of a particle is called its "world line". Each world line can be noted mathematically using the ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
user311753
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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 ...
user311653