Questions tagged [point-particles]

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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^{-\...
2 votes
2 answers
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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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3 answers
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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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2 answers
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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 ...
2 votes
1 answer
118 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 ...
3 votes
3 answers
138 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 ...
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7 answers
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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 ...
3 votes
2 answers
113 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 ...
1 vote
1 answer
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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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8 answers
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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 ...
2 votes
2 answers
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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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4 answers
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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 ...
1 vote
0 answers
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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 ...
1 vote
5 answers
258 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 ...
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1 answer
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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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1 answer
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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 ...
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6 votes
2 answers
243 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 ...
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8 votes
4 answers
898 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?
1 vote
1 answer
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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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6 votes
6 answers
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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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7 votes
2 answers
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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 ...
2 votes
1 answer
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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 ...
1 vote
0 answers
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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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0 answers
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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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0 answers
71 views

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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3 votes
1 answer
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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 ...
1 vote
2 answers
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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 ...
1 vote
1 answer
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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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2 votes
2 answers
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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 ...
4 votes
1 answer
979 views

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 ...
2 votes
2 answers
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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 $\...
1 vote
0 answers
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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 ...
4 votes
0 answers
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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, ...
4 votes
3 answers
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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 ...
3 votes
3 answers
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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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1 answer
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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 ...
15 votes
6 answers
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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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1 answer
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Action for extended objects

Take a spacetime $M$, with some $k$-manifold embedding $$X : \Sigma \to M$$ The image of $X$ represents some extended object (a $k$-brane as the string theory people say). If we only care about the ...
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Is this a sufficient condition for a stable equilibrium point?

My question is based on thinking about a point particle in electromagnetic fields, but the idea should apply to other problems. The point $\mathbf x_0$ is an equilibrium point of the force field $\...
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3 votes
1 answer
381 views

Deriving the 4-momentum of a free particle moving in curved spacetime

Consider a free particle with rest mass $m$ moving along a geodesic in some curved spacetime with metric $g_{\mu\nu}$: $$S=-m\int d\tau=-m\int\Big(\frac{d\tau}{d\lambda}\Big)d\lambda=\int L\ d\lambda\...
2 votes
3 answers
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Relative size of electrons and quarks

Today, we consider quarks and electrons (leptons) as point-like or fundamental (structureless). Is there any way to indirectly probe quark/lepton substructure and guess if they are composite of ...
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In QED why is the electron a point particle? [duplicate]

I read Feynman's book but this still unclear to me.
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1 answer
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Does the electron have size? [duplicate]

Can we ascertain the size of the electron? If it really is zero radius, then it can't be matter because it doesn't occupy space? Definition of matter (Google): physical substance in general, as ...
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1 vote
1 answer
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How to theoretically/experimentally prove that spin can not be treated as a classical (rotational) motion? [closed]

As well known, spin could not be thought of as a rotational motion in classical mechanics, i.e. it's an intrinsic property. But how to prove it? i.e. how to mathematically/experimentally show that ...