Questions tagged [point-particles]
The point-particles tag has no usage guidance.
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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
$$\delta S=-mc\...
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What is the correct gravitational potential energy of a single particle in an $N$-body system?
I am aware that the total gravitational potential energy of a system of $N$ particles is given by pairwise interactions, i.e., you start with a single particle in the system, and then calculate the ...
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General solution to point mass bouncing between sliding walls
My question is about problem #7 from the 2021 AAPT Olympiad F=ma exam. It's a point mass bouncing horizontally back and forth between a stationary wall and a wall that is sliding toward the other ...
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A problem about relativistic particle actions [closed]
I have a problem of a course in General Relativity which I don’t know to start solving, and I was wondering if someone could give me some indications or ideas on how to figure it out. It is the ...
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Relativistic Particle Path Integral by Faddeev Popov
In evaluating the path integral for a relativistic point particle in the einbein formulation, it is common to see the following
$$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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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
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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?
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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 ...
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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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Why does the electron not spin? [duplicate]
The goto answer to that question is that the electron is a pointlike particle and cannot spin.
The electron is not pointlike though. It is described by a wavefunction. One can prepare the wavefunction ...
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Deriving the energy-momentum tensor of a point particle
I am trying to connect two different representations of the energy-momentum-tensor, which I found in different books.
In Weinberg's Gravitation one finds for the energy-momentum-tensor of a point ...
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Charge distribution on two charged bodies connected by a wire
A question specifies two identical conducting spheres, both of negligible radius (I take this to mean they're to be treated as point charges), and with charges of opposite sign. They're separated by ...
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How is the action for a point particle defined in general relativity? [duplicate]
In classical physics, the action $S$ is defined as the time integral of the Lagrangian $L$, i.e.
$$
S = \int_{t_0}^{t_1} L\, dt.
$$
What is the relation between the action, for a point particle, and ...
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Why are electrons inherently magnetic? [duplicate]
I read that permanent magnetism is caused by electrons orbiting in a way which produces a net magnetic field. but how can a particle with no dimensions have a magnetic dipole? also I read that photons ...
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Is muon a point particle? [duplicate]
Im just a beginner in particle physics. As I have understand, electrons are considered as a point particle whose spin has nothing to do with original rotation around own axis but an intrinsic quantum ...
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Modify Newton's gravity to cure the action at a distance
Take a bunch of particles (can be point particles) at ${\bf{x}}_i(t)$ and of mass $m_i>0$.
The gravitational field is defined by the Poisson equation
$$
\nabla^2 \Phi({\bf{x}},t) = 4 \pi G \rho({\...
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Action for massless particles in GR [duplicate]
Relativistic action for a massive point particle is defined to be
$$S=-mc\int d\sigma \sqrt{-g_{\mu \nu}(x)\dot{x}^{\mu}\dot{x}^{\nu}}.$$
In David Tong's lecture notes on GR
If all we want to do is ...
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Do charges have spatial dimension? [duplicate]
I don't know much about anything in physics. I hope you can bear with that. Let me start with my question do charges have any dimension, by this I mean physical dimension like length, breadth, height ...
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Do electron-electron collisions have an associated scattering cross section?
Various texts (1,2) state that electrons are point particles, but if this is the case then when two electrons collide, one of them knows the others position with exact certainty (treating one as an ...
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Inverse-square laws and point particles [closed]
It's my understanding that many inverse-square laws can be explained as a central point emitting "interaction rays" in all directions equally. And that when another object with some area is &...
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A photon scatters an electron at an angle... Does it imply electron having an area greater then the photon's?
Even we don't know much about scattering areas of photons and electrons does the fact that a photon scattering an electron at an angle mean that the photon cross-section area hits only a small lateral ...
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Relationship between stress-energy tensor for a point particle and its Lagrangian
The Lagrangian for a (relativistic) point particle with rest mass $m$ and velocity $v$ is:
$$L=-\frac{m}{\gamma (v)}$$
(using $c=1$). Over on Wikipedia we can find the Stress-energy tensor for said ...
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Lagrangian mechanics formulation of a simple free motion of two masses in uniform gravity field
As a part of larger project, I decided to test my Lagrangian formulation of simple system of two rigidly connected point masses as indicated below.
I introduce the generalized coordinates vector $\...
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Extended SUSY and superspace
I am trying to understand how to construct an action using the superspace formalism for $\mathcal N>1$. I have read that this is quite difficult to do, so let's consider a simple example. Suppose I ...
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Actions for relativistic point-particles of higher spin
To describe the behavior of a relativistic point-particle, we have the standard action
$$S=\int d\tau \bigg[\frac{1}{e} \dot X^\mu\dot X_\mu +m^2 e\bigg], $$
where $e$ is the worldline einbein. Then, ...
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General Relativity at Microscopic Scale
If we consider a particle to be point-like, wouldn't it produce a Schwarzschild spacetime in it's vicinity?
What does spacetime look-like in the vicinity of point particles? What experiments have been ...
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Why the use of proper time as a parameter to describe the worldline only works for *massive* particle?
In Hobson et al, General Relativity: An Introduction for Physicists (pg. 15), it was said that it is natural to describe the worldline of a massive particle by giving the four coordinates $(t,x,y,z)$...
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Is there a code for Ewald Summation for Dipoles?
Does anybody know if there exists a code that calculates the potential energy for a system with both point charges and point dipoles using Ewald summation?
This would be a great help to my Master ...
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Can elementary particles be explained adequately by a wave-only model?
I have been watching quantum mechanics documentaries and reading a layman's book called "The Quantum Universe". I believe I understand why the double slit experiments exclude a particle only model. ...
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