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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Doubt in negative sign of relative velocities of two objects in same directions and opposite directions
Consider the following examples.
case 1)Two objects traveling in same direction one A in the velocity say 50 mph and other B in the velocity 60 mph. If we calculate velocity of A with reference to B ...
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In Peskin & Schroeder's QFT book page 704, the definition of electric charge is opposite?
In Peskin's book Chapter 4, the QED Lagrangian in Eq.(4.3) which contains the interaction term $$\mathcal{L}_{\mathrm{int}}=-q\bar{\psi}\gamma^\mu\psi A_{\mu}\tag{4.3}.$$ From this Lagrangian we can ...
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Confusion in definition of Potential Energy
Potential energy is defined like this. $ΔP.E=-W_{AB}$. This means that the potential energy at point A minus potential energy at point B should equal the negative of the work done by a conservative ...
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Why is there no negative sign in the linear form calculation of voltage but there is a negative in the integral form? [closed]
The formula for voltage given $\vec{E}$ and $d$ is $$V = |\vec{E}| d.\tag{1}$$
However, the formula is also $$V = - \int \vec{E} \cdot dr. \tag{2}$$
Why does one of these formulas have a negative and ...
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Voltage Difference Across Capacitor Plates
If a parallel plate capacitor is connected to a 9V battery, what is the electric potential difference between the two plates? Is it 18V since the positive plate will have an electric potential of 9V ...
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Sign convention of work
I am studying about reversible steady-flow work, and the author of the book states that Taking the positive direction of work to be from the system (work output) the energy balance of a steady-flow ...
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Teacher told us we're not allowed to write negative vectors, is this correct or not?
The question is a bit vague, so I apologize for that.
To properly explain what I mean, I'll use an example.
Let's say we've got two forces going left and right. $F_1$ is $20 \, \text{N}$, and will be ...
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The equipartion theorem and degree of freedom in case of vibration
I have been taught in chemistry that,
the energy of a vibrational freedom is $RT$ (ie, twice that of rotational/translational)
The degree of freedom which I found in chemistry, for the vibrational ...
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Changing the basis from $p$-basis to $k$-basis in standard quantum mechanics
if $$\hat p = \int dp |p\rangle p \langle p|$$ and I want to chage the basis to $|k\rangle$ it is correct to say that $\hat p$ is therefore equal to:
$$
\hat p = \hbar^2 \int dk |k\rangle k \langle k|
...
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Confusion on the signs in the complex scalar field [closed]
I saw there are different ways we can write down the complex scalar field. For example, in most textbooks I can find, this is defined as
$$\phi(x) =\int \dfrac{d^3p}{(2\pi)^3}\dfrac{1}{\sqrt{2E_p}}\...
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Confusion related to creation and annihilation operators
I'm studying QFT from Peskin and from the book by Ashok Das, and there seems to be a disagreement between the creation and annihilation operators, for the scalar Klein Gordon field theory.
In Das, we ...
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Factor in Gaussian filter
Why do Gaussian filter kernels commonly used in turbulence studies often have a factor of 6?
$$
G_{\ell}(|x|) = \left( \frac{6}{\pi \ell^2} \right)^{n/2} \exp \left( -\frac{6}{\ell^2} |x|^2 \right)
$$
...
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A contradiction in the derivation of electrostatic potential energy? [closed]
I am a 12th grade high school student with no knowledge of vector calculus and more advanced physics.. so if possible, please try to refrain from using advanced concepts which I do not understand.
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${}$ Projectile motion
Basically we take the value of acceleration due to gravity as -ve ($-g$),when an object is thrown in the opposite direction of $g$. But in projectile motion the object first opposed the g and travels ...
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Use of sign convention two times in ray optics
In this particular derivation of refraction happening at a spherical surface in terms of its radius of curvature , image and object distance and refractive index is done by my book as shown
When we ...
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Equivalence notation Euler angles-angular momentum in Wigner $D$ matrix
In Wigner little-$d$ function the convention that I found in wikipedia https://en.wikipedia.org/wiki/Wigner_D-matrix is z-y-z as shown here.
A 3-dimensional rotation operator can be written as
$$R(\...
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Question about sign convention in electron-hole crystal momentum
I was trying to understand a toy model Raman scattering diagram from a paper on pressure tuned moire phonons, when I realized the standard electron hole pair creation diagram confuses me. By ...
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Definition of energy for a Lagrangian with constraints [duplicate]
Suppose I have the Lagrangian in spherical coordinates:
$$\mathcal{L} = T=\frac{1}{2}m (\dot{r}^2 + r^2 \sin^2 \theta \dot{\phi}^2 + r^2 \dot{\theta}^2)$$
Where $T$ is the kinetic energy.
Now suppose ...
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Expression for Potential energy of a hanging mass
If the acceleration due to gravity is $g$ and a mass $m$ is hanging from a fixed support with a thread of length $l$, then it's potential energy ($U$) is given by:
$$U = -mgl;$$
This was stated by my ...
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Contradiction in Thermodynamic Work and Mechanical work [duplicate]
The first law states that $ \Delta U = Q - W $ where W is the work the system does on the outside. If there is no heat added, the change in energy is equal to the work done. If the work is negative, i....
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Help understanding quote on theory and knowledge in Gravitation (Misner, Wheeler, & Thorne, 2017)
I came across an interesting discussion at the start of chapter 3 of MWT Gravitation. It reads:
Here and elsewhere in science, as stressed not least by Henri Poincare, that view is out of date which ...
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Understanding sign convection for entropy change
I recently solved a problem where I had to study the change of entropy for a lake that is freezing. It started off as being plain water at $0$ degrees, that then freezes to some negative temperature.
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Landau/Lifshitz Particle Disintegration
In Landau/Lifshitz "Mechanics", 3e., there is a problem which asks the reader to find the relation between the angles $\theta_1,\theta_2$ in the lab frame when a particle disintegrates into ...
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What does $\overset{\circ}{=}$ mean in the context of thermodynamics? [closed]
Few days ago I started thermodynamics and whilst talking about systems and its type of walls the professor, a part from this one, showed some diagrams including this equal sign. He was talking about ...
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Sign convention for the Lagrangian of a free massive point particle in general relativity
As far as I understand, the Lagrangian of a massive free particle in the context of general relativity is the following:
$$L=-mc\sqrt{g_{\mu\nu}\dfrac{dx^\mu}{dt}\dfrac{dx^\nu}{dt}}.$$
But is this the ...
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The energy-momentum tensor of a scalar field
In Carroll's Introduction to General Relativity: Spacetime and Geometry, I am going to express the components of the energy-momentum tensor of scalar field in three-
vector notation, using the ...
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Why can $ϕ(p)$ be Fourier expanded to $ψ(x)$ in quantum mechanics? [closed]
I know the Fourier transform is $$
F(\omega)=\int_{-\infty}^{\infty} f(x) e^{-i \omega x} \,d x
$$
$$
f(x)=\frac{1}{2 \pi} \int_{-\infty}^{\infty} F(\omega) e^{i \omega x} \,d \omega,
$$
but in ...
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Significant figures in simple calculations
I have the resistivity of a material $\rho = 7.4 \times 10^{-7}$ $\Omega\cdot$m and I want to compute its conductivity $\sigma = 1/\rho$.
Straight forward calculation gives (up to 3 decimals) $\sigma =...
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The Plus/Minus sign on Forces in a Cartesian coordinate system
I have been struggling with Forces in a Cartesian Coordinate System and whether to understand what signs to put on to solve simple problems in the view of mathematics.
Let's make a simple one ...
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Clarification on thermodynamics and mechanics
This is a follow-up question to an answer https://physics.stackexchange.com/a/746974/377012 on this topic. In that answer, what does $W$ refer to? Is it the work done ON the system, by forces OTHER ...
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Reference point of potential in case of a battery
When we define electric potential of a charge,we need to take a charged body as a reference and then we bring the test charge to calculate the electric potential. Now,electric potential energy is ...
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Minus sign in Force potential relation, a convention?
The usual defination of force in terms of potential energy is
$$\vec F=-\nabla U$$
This definition leads to
$$K_1+P_1=K_2+P_2\rightarrow \Delta K + \Delta P =0$$
Where $K$ and $P$ are kinetic and ...
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Sign ambiguity of two diagrams in Mahan's book
In Mahan's book 'Many-particle Physics' 3rd Ed., Eq. (3.213) on page 135 gives a sign rule for Matsubara Green's functions $$(-1)^{m+F}$$ where $F$ is the number of fermion loops and $m$ is the order, ...
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Work Done By vs Work Done On
Assuming right to be positive, in this question, is the work done by the boy positive or negative? I would think it is negative because the force that the boy exerts is towards the left while the ...
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Sign conventions pressure volume work
In the first law of thermodynamics, using the convention that work is done on the system by the surroundings,
$dU=Q+W$.
Usually it is written that pressure volume work is $W=-pdV$, where $p$ is ...
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Combinatorics in $\lambda \phi^4$ theory and critical exponents
I am trying to understand critical phenomena from the perspective of Statistical Mechanics.
The interacting term in the $\lambda \phi^4$ scalar theory is usually (but not always) multiplied by $\frac{...
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Why do we indicate current to be flowing against electrons in a electric circuit ? If it is a convention thenwhy do we draw it along studying it? [duplicate]
I believe that electric current is a kind of force (even when we consider it to be opposite to the flow of electrons). If it is so then what is the nature of this force ? And also tell me if there are ...
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Does change in metric signature affect the result of loop integrals in momentum space?
I was wondering whether the change in metric signature affect the standard results of loop integrals. Suppose a rank-4 tensor integral's result is known, does changing the metric signature for the ...
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System in thermal equilibrium with reservoir
Let's say I was trying to build Statistical Mechanics from scratch. I had studied the microcanonical ensemble and made the following definitions:
$$\frac{\partial S}{\partial E} = \frac{1}{T},$$
$$\...
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Embedding diagram in west coast signature
Assume you have a metric in (+,-,-,-) signature,
$$d s^2=e^{2 \Phi(r)} d t^2-\frac{d r^2}{1-\frac{b(r)}{r}}-r^2 d \Omega^2.$$
To embed it, we take $t=$Constant, $\theta=\pi/2$ slice,
$$d s^2=-\frac{d ...
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What is the significance of a reference point in calculating the potential?
The gravitational potential is given as $$U(r)=-\frac{GMm}{R}$$ where $G$ is the universal gravitational constant $M$ is the mass of the earth and $m$ is the mass of an arbitrary object and $R$ is the ...
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Confusion about the signs we use in Faraday's law for emf
While reading griffiths, I came accross the definition of emf, which is given by
$$ \epsilon = -\int_a^b \vec{E} \cdot d\vec{l} = \oint \vec{f} \cdot d \vec{l} $$
Here we use $\vec{E} + \vec{f} = 0$ ...
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Sign of reversible work done
Consider a piston such that it is in mechanical equilibrium with its surroundings. If I pull the piston (reversible work) then the work done by me would be positive. If I push the piston, again work ...
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Why does Dirac bilinear $\bar{\psi}\sigma^{\mu\nu}\psi$ is frequently written with a factor of $i$?
The tensor Dirac bilinear $\bar{\psi}\sigma^{\mu\nu}\psi$ has the matrix tensor $\sigma^{\mu\nu}=\frac{i}{2}\left[\gamma^\mu,\gamma^\nu\right]$.
I can understand that the factor of $\frac{1}{2}$ is a ...
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Lorentz Transformation - Intuitive way to determine when to use Inverse transformation
Any intuitive way to decide when to use Lorentz transformation and when to use its inverse relation?
For example: A particle is moving with respect to me with speed of 0.99C. If question is : What ...
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Correct way to reference to a percentage value's category/label
When a percentage is written as, for example: 20% of sold products were of product A and 80% product B. What is the correct concept / word to use to describe "product A"? Is it units?
As ...
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Minus sign for incoming antifermions
In his Diagrammatica, The Path to Feynman Diagrams (Cambridge University Press, 1994; §4.5 "Quantum Electrodynamics", p. 88), M. Veltman reports the following Feynman rule for incoming ...
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Jackson's Electrodynamics: Green's function prefactor
In Ch. 6 of Jackson's Classical Electrodynamics 3rd ed., the Helmholtz equation Green's function is written as satisfying the following inhomogeneous equation (Eqn. 6.36):
$$ (\nabla^2 + k^2)G(\mathbf{...
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Generators in the fundamental representation of $SU(2)$ are $\sigma_i/2$. Why? [duplicate]
In physics, the generators of the fundamental representation of $SU(2)$ are taken to be $\sigma_i/2$ instead of $\sigma_i$ where $\sigma_i$ denotes the $i$th Pauli matrix. This is because, as I ...
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What happens if we define the gravitational potential zero point at a finite distance? [duplicate]
Two questions.
Can we, and if so how do we define the gravitational potential of a mass (say the sun) to be zero at a finite distance (say 1 light year)?
How does this change the gravitational force ...
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