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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Arbitrarity of $i$ in the propagator
My question is simple: how arbitrary can the factor in front of the propagator be?
What I mean by that is, if we call the wave operator $K$ and the propagator $G$, I've seen different books use ...
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Sign Convention in Ray Optics
While solving questions on Refraction due to 2 spherical surfaces the sign of the image formed after the first refraction (here at '$A$') depends whether the image formed is towards left or right side ...
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What is parity useful for in physics?
What do we gain by defining the parity of different objects in physics? I can learn that $L$ (angular momentum) has the opposite parity as $p$ (linear momentum) or $B$ (magnetic field) hass opposite ...
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What is a rigorous and general definition of the parity operator?
Is there a rigorous definition of the parity operator?
I see parity come up in the context of angular momentum, magnetic fields, quantum spin/particles. It is also related to the Levi-Civita symbol vs ...
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Why are most solar panel rated at 12 volts or 24 volts? [closed]
Most solar panel come in 12 volts or 24 volts, why?
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Fourier Transform of a Wave Packet [closed]
In the analysis of coherence and interference, I encountered the following expression:
$$F(t)=\Re\int_0^\infty\mathrm d\omega e^{-i\omega t}H(\omega)$$, where $\Re$ denotes the real part of the ...
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Why does the Strange Quark have Strangeness -1?
I have been trying to find an explanation for the strange quarks negative strangeness value, I understand the term strangeness predates the quark model, but I'm unsure if terminology carry over is the ...
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Lower vs Upper indices in stress energy tensor
In Goldstein Classical Mechanics, chapter 13 page 56, equations 13.30, the canonical stress energy tensor $T_\mu^{\,\,\,\nu}$ is defiend as:
$$T_\mu^{\,\,\,\nu}=\frac{\partial\mathcal{L}}{\partial \...
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Problem with derivation of the Dirac Hamiltonian
I'm having son trouble when obtaining the Dirac equation. I am working in (1+1)-dimensional Minkowski spacetime with signature $(-, +)$ in coordinates $(t, x)\equiv(1, 2)$. I can think of two ways to ...
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What is a signature of pp-wave metric?
pp-wave spacetime metric is defined in Brinkmann coordinates as $$ds^2 = H(u,x,y)du^2 + 2 du dv + dx^2 + dy^2.$$ Since it's lorentzian (https://en.wikipedia.org/wiki/Pp-wave_spacetime), I wonder what ...
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In stress-strain diagrams, why is the dependent axis ($y$) used to represent stress and the independent axis ($x$) to represent strain?
why this convention is used
despite the fact that strain is influenced by stress (cause -> stress, effect -> strain)
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The definition of Time and second
From the book "University of Physics 15th edition", in chapter 1, they talk about the fundamental units. They stated that the definition of unit of time is based on an atomic clock, where 1s ...
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Conventions Consistency For the Dirac Field
I am writting a text and I try to be consistent with my definitions. I have expanded my fields in modes in the following way
$$\psi(x)=\int\frac{d^3\vec{p}}{(2\pi)^3\sqrt{2p^0}}\sum_s\bigg(u_s(\vec{p})...
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Covariant vs. contravariant definition of the Energy-Momentum tensor
I have a question regarding the definition of the energy-momentum tensor.
I've seen it defined as a (2,0) tensor, so it has 2 upper indices $T^{ab}$, but many times it is written as a (0,2) tensor ...
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When defining a coordinate system, does it matter if it is right- or left-handed?
When you are defining a coordinate system when solving a problem, do the coordinates need to be right-handed to obtain a correct solution? I feel like the answer is no because the directions of ...
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Noether/Hilbert energy-momentum tensor
In chapter 4 of Carroll's book Spacetime and geometry he finds using the Hilbert action that the energy-momentum tensor for a scalar field is (see eq. (4.79))
$$T_{\mu\nu}^{\phi}=\nabla_\mu\phi\nabla_\...
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Does the expression "$𝑑𝑠^2$..." mean the same thing as "$\Delta 𝑠^2$... "?
I reviewed this question but sometimes I'm unsure about delta versus differential notation.
Does the expression "$ds^2=-c^2dt^2+a^2(t)[dr^2 + S_k^2(r)d\Omega^2 ]$" mean the same thing as
&...
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When or why to use the $\equiv$ symbol in place of the $=$ symbol?
In literature, I read the following:
A typical relationship*, often appearing in the literature, is:
$$|-\nabla(\bar p+\rho g z)|\equiv \rho g J=q(\mu w+\rho Bq^m)$$
The nomenclature does not define ...
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Negative sign on Coriolis acceleration not necessary?
Why is the Coriolis acceleration often written as $-2({\bf \Omega \times v})$, (for example Wikipedia)? Why is it not written $2({\bf v \times \Omega)}$ which means the negative sign is not needed? ...
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The direction of turn of a coil
I'm confused about how the coil is turned. If the magnet is brought closer to the coil then the first coil at A should become North ( if viewed from magnet's side). But to find direction of current I ...
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Is there a name for this type of wavevector?
When we say wavevector we often mean a vector $\mathbf k$ that is related to the direction and wavelength of a plane wave, given by $e^{i\,\mathbf k\cdot\mathbf x}$. I have to write something about ...
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Particle on a sphere, it's solution having extra $(-1)^m$ term
To solve a particle on a sphere problem in quantum mechanics we get the below equation :$\left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right)-\frac{m^{2}}{\sin ^{2}...
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What is the meaning of external work in electric potential?
We learned that $$-Work = \Delta U = q(Va-Vb).$$ However, we write that $$W = q(Va-Vb)$$ in this question. Why don't we write the minus sign in the equation? How does external work affect the minus ...
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Different result when deriving electric force as $dW/dr$ and $-dU/dr$
Work done by electric field, $W$ is the negative of the change in electric potential energy, $U_r$.
$$W=-\Delta U$$
By considering an infinitesimal change in EPE, we can deduce that electric force, $...
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Complex valued Grassmann variables $(\theta \eta)^* $, $(\theta \eta)^T$ and $(\theta \eta)^\dagger$
Since hermitian conjugation and complex conjugation are serious issues in a QFT lagrangian with Grassmann variables, see here and here. Let us try to go to the bottom.
We start by accepting the ...
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Is $\bar{\psi} \psi$ its own complex (*)? transpose ($T$)? hermitian conjugate ($\dagger$)?
Related to this earlier A common standard model Lagrangian mistake?
Here I am treating Dirac equation of Dirac field as QFT.
You may want to consider the quantized version or the classical version.
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About Einstein's sum rule and Dirac equation
I am studying the Dirac equation and I'm having some trouble about something that I think should be trivial. I'm working in a (1+1)-dimensional Minkowski spacetime with signature $(+, -)$, i.e., $ds^2=...
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Intuition for the negative sign of gravitational potential energy
The gravitational potential energy is introduced to us as $U = mgy$. We usually set $U = 0$ on ground level and hence, for an object at height $y$, we have a potential energy equal to $U = mgy$.
I ...
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Vector subtraction coordinates in rotated axes
I'm going through Anthony Zee's Einstein Gravity in a Nutshell and got confused on one of his points that seems to be a more general confusion about rotating axes.
Zee first defines the rotation of ...
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Variations of thin lens formula [duplicate]
I came across the thin lens formula online as:
$$\frac 1f = \frac 1v + \frac 1u $$
where f = focal length, v = distance of image, and u = distance of object
However, I noticed that the formula was ...
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Signature of the Minkowski metric tensor
In special relativity, events happen in the Minkowski spacetime, with signature $(3,1)$ or $(1,3)$. I was wondering about the need of different sign for temporal and spatial coordinates. Looking ...
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Why do we have the negative on the RHS of $\Delta \mathscr{l} E_{t1} - \Delta \mathscr{l} E_{t2} = -\Delta \mathscr{l} M_s$?
I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Section Fields at a General Material Interface of chapter 1.3 FIELDS IN MEDIA AND BOUNDARY CONDITIONS says ...
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Can current also flow from low potential to high potential?
I understand that current flows from high potential to low potential.
As you can see in the picture, the top of the circuit has a potential 2V higher than the bottom.
However, since the current is ...
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Conservation of Energy For Electrostatics
Starting from Newton's second law, I am trying to show that energy is not conserved with an applied external force when moving a positive charge from $r_b$ to $r_a$ (see image). I'm not sure where I'm ...
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What is the relationship between work done and potential energy in Newtonian graviational field?
I am taking a first year physics course, my calculus is really rusty and I am having a very hard time with (Potential) Gravitational Energy.
Let's consider a body of mass $m_1$ located at $r_1$ from ...
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Alternative expression for Riemann curvature tensor
There is the usual expression for the Riemann tensor
$$R_{abcd}=\partial_c\Gamma_{adb}-\partial_d\Gamma_{acb}+\Gamma_{ace}{\Gamma^e}_{db}-\Gamma_{ade}{\Gamma^e}_{cb}.$$
However, in the last page of ...
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Notation used to denote the unit $\rm mm^3$
For example, to denote the volume of a cube with the sides $1mm$ we write $1mm^3$. But I think it should be written as $1 (mm)^3$ because the prefix $m$ denote the factor $10^{-3}$ hence $$[1mm^3=10^{-...
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Energy Momentum Tensor for massive Real Scalar Field in GR with metric signature (+ - - -) [duplicate]
I wanted to calculate the Energy Momentum Tensor for the massive real scalar field in Kerr Background. But instead of the usual (- + + +) metric signature, I have to use the (+ - - -) signature for ...
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Why electrical current is base quantity instead of electrical charge? [duplicate]
I thought base quantities are defined as independent quantity.
But I realized Electrical Current which usually notated as I for ...
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Is my book drawing a vector wrongly?
My book's drawing:
According to my book, $\underline{u}=\vec{AB}$. However, my book hasn't put the arrow at the end of the line segment $AB$, but rather my book has put the arrow at the middle of $AB$...
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Why were electrons chosen to be negatively charged? [duplicate]
Wouldn't it make more sense to call electrons positively charged because when they move they make electricity?
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Vector symbols confusion: A vs |Ā| when it comes to representation of magnitude of vectors
My teacher said that $\vec{A} = \left| \vec{A} \right| \hat{A}$ , where $\left| \vec{A} \right|$ is the magnitude and  is the direction of the vector.
In this homework question, what exactly do you ...
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Where does the (-) sign come from in $\nabla \cdot \vec{J} + \frac{d \rho_v}{dt} = 0$?
Where does the (-) sign come from in $$\nabla \cdot \vec{J} = - \frac{d \rho_v}{dt}~?$$
Starting from $$I = \int_s \vec{J} \cdot d\vec{s} = \int_s \rho\vec{u} \cdot d\vec{s}$$
$$= \rho_v \int_s \vec{u}...
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What is the precision of number 4.03100?
Trailing 0s occurring after decimal are significant. Like 0.302000.
Suppose I got the measurement reading of 4.03100, with clearly 6 significant digits.What's the precision of my measurement? Isn't it ...
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If $\underline{u}$ is a vector, does $u$ indicate its magnitude?
If $\underline{u}$ is a vector, does $u$ indicate its magnitude? $|\underline{u}|$ also indicates the magnitude, doesn't it?
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Meaning of big $O$ notation with 2 values separated by a comma
I'm reading Classical Electrodynamics 3e by Jackson. In section 1.7 he performs a proof of the Poisson equation in the context of the electric potential. Near the end of the proof, he writes
$$
\...
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Is $\Delta$ notation commonly used for the difference in a quantity between two objects? [closed]
In a standard Atwood machine, the acceleration is
$$a = g\dfrac{m_1 - m_2}{m_1+m_2}.$$
Would writing this as
$$a = g \dfrac{\Delta m}{M}$$
where $M$ is the total mass be an abuse of notation to most ...
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Why is the Fermi Constant sometimes listed in units of 'joule metre$^3$'? How is that related to its normal units of GeV$^{-2}$ or J$^{-2}$?
Normally, the Fermi Constant is valued as $1.1663787\times10^{-5}$ GeV$^{-2}$ or its equivalent in Joules. But on Rampfesthudson and Oxford Reference, it says,
$1.435\times10^{-36}$ joule metre$^3$
I ...
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Why am I getting negative current on the right loop of the Kirchhoff's circuit?
I have the above circuit and I calculated that the:
left loop = I1(Rc+4) - I2(Rc)=12
right loop = I1(Rc) - I2(Rc+3) = 5
I then generated numbers from 0 to 5 ohms with stepsize 0.1.
After replacing ...
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Would paradoxes arise if the one-way speed of light weren't $c$?
Introduction
Let me start by saying that this is not a question about how to measure the one-way speed of light (OWSOL). It's about the physical implications of the idea that this speed is merely ...
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