Questions tagged [conventions]
A convention is a set of agreed, stipulated, or generally accepted norms. It typically helps common efficiency or understanding but is not required, as opposed to a strict standard or protocol.
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Why didn't we change the conventional direction of current after discovering electrons? [closed]
The direction of current is taken to be opposite to that of the flow of electrons, due to the established convention that current is in the direction of the flow of positive charges. My question is ...
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1answer
109 views
Is the speed of light exactly 299792458 m/s?
I want to know if there is any uncertainty in the measurement of the speed of light. If yes, please mention the uncertainty.
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1answer
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Normalization of $U(1)$ gauge fields
In G. W. Moore, “Introduction to Chern-Simons theories.” 2019 TASI School. [Online]. Available: https://www.physics.rutgers.edu/~gmoore/TASI-ChernSimons-StudentNotes.pdf the $U(1)$ gauge field has a ...
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42 views
Deriving the Yang-Mills equation from the formal definition
We assume the curvature as a $\mathfrak{g}$-valued 2-form on a principal bundle, $F \in \Omega^2(P,\mathfrak{g})$. For the curvature it holds
\begin{equation}
D_A F=dF+\rho_*(A) \wedge F
\end{equation}...
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0answers
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Unequal forms of the Yang-Mills equation in local coordinates
I found three different expressions for the Yang-Mills equation in local coordinates:
In 1: $\square A^{\beta}-\partial^{\beta}\left(\partial_{\alpha} A^{\alpha}\right)+\partial_{\alpha}\left[A^{\...
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2answers
107 views
Do MIT students omit square braces of SI unit? [closed]
$$ v:=\text{symbol which represents a speed } $$
As concrete value of $ v$ is specified, at least the below 2 notations can be done.
$$ \text{notation 1} \rightarrow v=10 \left[ \frac{ \text{m} ...
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2answers
47 views
Doubt concerning the definition of $p$ and $-p$ in quantum field theory
We can define the field in term of the ladder operators as:
$$
\phi(\vec{x}) \propto \int d^3p \left( a_{\vec{p}}e^{i\vec{p}\cdot\vec{x}} + a^\dagger_{\vec{p}}e^{-i\vec{p}\cdot\vec{x}} \right)
$$
...
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1answer
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Curvature 2-forms: missing factor 1/2 in (14.21) and (14.22) of Misner, Thorne and Wheeler?
It seems that the correct version of (14.21) is
$$
\frac{1}{2}\,\langle d\alpha,u\wedge v\rangle=\partial_u\langle\alpha,v\rangle-\partial_v\langle\alpha,u\rangle-\langle\alpha,[u,v]\rangle
$$
where $\...
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0answers
15 views
Coefficient of Performance and Sign Convention
I am using the sign convention: Heat absorbed by the system is positive and heat left the system is negative. Work done on the system is positive and work done by the system is negative. It was super ...
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1answer
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Conventions for graded wedge product in supergeometry
There are two conventions for the graded exterior product on superspace (see https://ncatlab.org/nlab/show/signs+in+supergeometry):
$$\alpha \wedge \beta = (-1)^{pq+|\alpha||\beta|}\beta\wedge\alpha \;...
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2answers
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Why electric field due to a positive charge points radially outward? [duplicate]
We have always been taught and my book also says that electric field due to a positive charge points radially outwards.On the other hand for a negative charge the electric field points radially ...
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1answer
31 views
Negative Sign in Potential Energy Expression [duplicate]
The potential energy can be mathematically expressed as:
$$U=-\int \vec F \cdot d\vec x$$
I do understand the negative sign is basically to adjust in the relation
$$K_1+U_1=K_2+U_2$$
What is the ...
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0answers
28 views
Why do we add an error of 0.1 to a measurement by an instrument of least count 0.1
If the measuremnt comes between 2.3 and 2.4 why do we write as 2.3 ± 0.1. Why can't we write it as 2.35 ± 0.05. I understand this gives a wrong idea about precision, but why not create a new ...
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2answers
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How to add these in accordance with the rules of significant figures?
$2300$ has 2 significant figures (2,3). Thus $2300+123 = 2423$. However, we can also write this as $100\cdot(23+1.23) = 100\cdot( 24.23 )$ since 23 has no decimals, 24.23 is rounded to 24. The answer ...
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2answers
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Why are centimetres still in use? [closed]
When SI units were adopted in the UK old, imperial, units were dropped but with a few exceptions for very specific purposes eg pints for beer, pounds and ounces for babies birth weight and feet and ...
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0answers
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Feynman Vol-I 33-6 The intensity of reflected light. Are the given reflection coefficients the squares of what are typically used?
From https://www.feynmanlectures.caltech.edu/I_33.html#Ch33-S6
We have assumed unit amplitudes for the incident waves, so that $\left|B\right|^2/1^2$ is the reflection coefficient for waves polarized ...
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0answers
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(Non-)Hermiticity of Dirac operator
I have a Dirac operator given by
\begin{equation}
D\!\!\!/[A, A^{5}]=\gamma^\mu D_\mu=\gamma^\mu (\partial_{\mu} - {\rm i} A_{\mu} - {\rm i} \gamma_{5} A_{\mu}^{5}),
\end{equation}
where $A_{\mu}$ ...
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3answers
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How does the number of significant figures change when a unit is added?
This (foolish) doubt on significant figures is giving me sleepless nights.
Say, A given number is 20000 I would say it has 1 significant digit right?
But Now, Say The value given is 20000 m (metres) , ...
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0answers
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Can we interchange the quantities involved in Fleming's left hand rule?
Fleming's left hand rule states that If we stretch the thumb and first two fingers of left hand in mutually perpendicular directions such that forefinger points along B (Magnetic field vector) and ...
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1answer
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Can we use the equations $-AωSin(ωt+φ)$ and $AωSin(ωt+φ)$ interchangably?
My book says that,
For a simple harmonic motion,
velocity of the particle
= -AωSin(ωt+φ)
Now, assuming φ to be π/2, in the next sentence, they say that,
maximum velocity = Aω.
Why have they simply ...
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2answers
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Understanding the notion of “difference” in Voltage [closed]
Ok I'm having some hard time to grasp the concept of "Voltage". I'm going to refer to 2 videos I watched, although I watched more and read about it, but these two pretty much summarize what ...
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Why are there two different naming system to describe the shells and sub shells of an atom?
I know that the shells and sub shells in the atom are named as 1,2,3 and so on for shells and 0,1,2 ... (n-1) for a subshell but at the same time they are also represented by K,L,M,N and so on and s,p,...
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2answers
49 views
Work done to bring a mass from an infinite distance away
In the notes I received from high school teacher, it says:
How much work is done by the gravitational field of the planet in bringing a satellite from an infinite distance to a position $r$ away?
In ...
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2answers
66 views
Particle Charge
Simple question that I've never heard a satisfactory answer for from a physics teacher: what exactly is a 'charge' of a particle?
Most teachers I've heard from define charge in one of two ways:
In ...
2
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5answers
117 views
Gravitational potential energy at $r = \infty$
At $r = \infty$, the gravitational potential energy of an object due to Earth’s gravitational field is at a maximum value of $0$. I understood this to mean that an object will have maximum potential ...
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0answers
20 views
Flipped sign in solution of Dirac bispinor
I’ve been following David Tong’s lecture notes on QFT, and I came across something that I couldn’t work out for the general solution of the Dirac Spinors. On page 100 in the link here Tong Notes Part ...
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2answers
45 views
Forces on an oscillating skateboard
A half pipe of a skateboard park consists of a concrete trough with a semicircular section of radius 5m, I hold a frictionless skateboard on the side of the trough, pointing down toward the bottom and ...
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2answers
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Why is least count error like this?
For a measurement of 4.6 (between 4.6 and 4.7 ) with a least count of 0.1 we write the measurement as 4.6 ± 0.1 . Why can't we write it as 4.65 ± 0.05. My guess is this gives a false sense of ...
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0answers
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Energy-momentum tensor of a fluid for scalar fields
I know that the energy-momentum tensor for a perfect fluid in General Relativity is given by
$$T_{\alpha \beta} = (\rho +p)u_{\alpha}u_{\beta}-p\,g_{\alpha \beta}, $$
where $\rho$ is the density, $p$ ...
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2answers
52 views
Sign Confusion Electric Potential
I was solving a question and trying to find the potential difference between two points and got confused with the signs . We know $$dV = -E.dr .$$ In this equation there is dot product between E and ...
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1answer
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Facing problem in rounding off [closed]
I have few questions assigned by my tutor about rounding off digits up to two significant figures. I can't solve one of them even after searching up the web I can't understand the problem.
So the ...
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2answers
390 views
Adding a constant term to potential in Schrödinger's Equation
If we add a constant term $k$ to the potential function in time-independent Schrödinger's equation, $V(x) \rightarrow V(x)+k$, then how does it affect the solution, and what is its significance? ...
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1answer
54 views
Does $\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}\mathbb1$ determine the hermiticity of the gamma matrices?
If I remember correctly, the derivation of the Dirac equation requires that $\gamma^0$ is Hermitian while $\gamma^i$ for $i=1,2,3$ is anti-Hermitian. This is clearly true for the standard Dirac ...
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0answers
29 views
Why does $\textbf{F}=- \boldsymbol{\nabla} V$? [duplicate]
From the question I asked just now, I now know that the plus or minus doesn't matter for $ \boldsymbol{\nabla} V$ in math (since the opposite vector field $\vec{-F}$) must be conservative as well.
$$ \...
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1answer
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Can anyone tell me how does conservative forces work? Confused
From vector calculus, I'd learnt that a conservative vector field satisfies
$$
\textbf{F} = \boldsymbol{\nabla} g
$$
which $\textbf{F}$ is the gradient of some scalar-valued function, and $g$ is the ...
2
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1answer
70 views
Conservation of momentum for a 3-point amplitude
When talking about 3-point amplitudes (e.g. three gluons) I`ve come across the fact,
that if we have three lightlike 4-momenta $p_1,p_2$ and $p_3$ they should satisfy
$$p_1^{\mu} + p_2^{\mu} + p_3^{\...
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3answers
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Dirac equation more natural in $O(1,3)$ than $O(3,1)$?
In physics, the Lorentz group $O(1,3)$ is of central importance, being the setting for electromagnetism and special relativity.
According to Wikipedia:
Some texts use $O(3,1)$ for the Lorentz group; ...
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1answer
41 views
Expression of $\not{p}$ in Dirac equation
In scattering amplitudes, page 9, equation (2.6), (2.7), $\not{p}$ (in the Dirac equation (2.4)) is as follows:
\begin{align}
\not{p} = \left( \begin{matrix} 0 & p_{a\dot{b}} \\ p^{\dot{a}b} & ...
2
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1answer
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Einstein notation and writing down the geodesic equation - a misunderstanding?
if one wants to write down the geodesic equation to describe the movement of the planets (for i=1 in the following context) one uses the metric tensor $g_{ik}$ for spherical symmetric coordinates.
One ...
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3answers
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Why many equations of potential of integration omit a symbol of constant of integartion and some other equations don't omit it?
In some problem, an equation of potential which is gained from an integration does not has a symbol of constant of integration however some other problem has constant of integration. What are the ...
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1answer
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Different signatures of the metric in Einstein field equations
Throughout the GR lectures, we have always used (- , + , + , +) signature for the metric tensor but in some chapters it was switched to (+ , - , - , -) and immediately after that Einstein field ...
2
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1answer
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Sign error when deriving Weyl spinor transformation laws (3.37) in Peskin Schroesder
I am having some trouble deriving the transormation laws for the weyl spinors, equation (3.37) in the Peskin Schroesder book on quantum field theory.
Beginning with the relation $\psi\to(1-\frac{i}{2}\...
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0answers
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What does it mean for $2\pi = 1$ in a “private system of units”?
I saw the following image of an excerpt from Robert Mill's Tutorial on Infinities in QED, floating about the internet:
The book is available here, however I don't think I have access to it, unless ...
2
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1answer
116 views
What is wrong with this proof that $h^\vee$ the dual Coxeter number is always 1?
(Not putting this in the math stack exchange because this is all about structure constants which are more familiar to physicists.)
Say we have the basis of a Lie algebra $\mathfrak{g}$ with dimension $...
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3answers
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Is displacement of wave $y=A\sin(\omega t-kx)$ or $y=A\sin(\omega t+kx)$?
I have read online that $\sin(\omega t-kx)$ represents a wave traveling in the positive $x$ direction, and $\sin(\omega t+kx)$ represents a wave traveling in the negative direction. Can someone ...
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2answers
72 views
Is the definition $\left(\mathcal{K}_{l}\right)_{mn}=\epsilon_{lmn}$ for the generators of $SO(3)$ in Misner, Thorne and Wheeler correct?
Note: I do not believe this is simply a matter of convention regarding what is considered a positive angle, handedness of the coordinates, nor the ordering of matrix multiplication for vector ...
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3answers
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Does everything have potential energy? + Question about mechanical energy
I'm currently learning about potential energy, kinetic energy, and mechanical energy, and I have a few questions:
Does everything have potential energy? If yes, how so? For example, does a book ...
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2answers
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Why there is a negative sign on the gravitation formula?
It all started when I was coding some simulation of the Newton's Law of Gravitation and Culomb's Law.
When I was seeking information on the internet, I found out that some people wrote this formulas ...
4
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0answers
69 views
Error of $-i$ factor in light cone indices in conformal field theory in Becker's book
In Becker's book of String theory Ch-$3$ I'm getting an error of factor $-i$ in the definition of lightcone indicies after Wick rotation. The convention of the book is following $\sigma_{\pm}=\tau\pm\...
0
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0answers
79 views
Are there several conventions (source or receiver) for the *Jones vector*? What about the one of particle physics?
There are several conventions for defining the polarisations left and right: from the source and from the receiver. See for example:
https://en.wikipedia.org/wiki/Circular_polarization#...
