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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Sign conundrum while deriving electrostatic potential
Consider a fixed, positive Point charge $q1$, kept at the origin. Another (positive) charge, $q2$, is being brought from $\infty$ to the point $(r,0)$, by an external agent slowly. We wish to ...
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Problem with the formula for electric intensity due to a charged sheet
The formula for the electric field due to a charged sheet is $\LARGE\frac{\sigma}{2\epsilon_0}$. Now, if I want to find the electric intensity of a point between two equally and oppositely charged ...
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How is the reference point of potential energy defined in electric fields?
Consider the diagram below of a positive charge and three points marked in the field X, Y and Z.
I understand that for a gravitational field, we define the potential energy as being always negative, ...
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The exact nature of the spacetime interval
The book I will reference here is (specifically page XXXV of) The Geometry of Physics by Frankel.
I asked this question a long time ago when I was a complete newcomer to general relativity. There was ...
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Why use two spacetime indices to label Lorentz generators?
I've seen (e.g. in Srednicki) the following notation for the connection between a Lorentz transformation $\Lambda$ and the Lorentz generators $M^{\mu\nu}$:
\begin{equation}
{\Lambda^\mu}_\nu = {\left(...
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Showing that the Wess-Zumino Lagrangian is invariant under a SUSY transformation
I want to show that the free Wess-Zumino Lagrangian is invariant under a SUSY transformation, e.g. following this reference (section 3.1).
However, I have a hard time understanding the daggers and ...
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2answers
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In relativity, why does spacetime diagram have position on $x$-axis and time on $y$-axis?
In regular Newtonian physics, we use $ x(t) - t$ graph to under position of a particle but why is it that in special relativity that we switch up the axis notation? I was seeing the lecture by Leonard ...
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How to calibrate potential function?
The original question:
Given sphere with radius $ R $ and charge $ Q $, and an infinite wire that goes through the center of the sphere with charge density $ \lambda $.
Find an expression for the ...
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Direction of Integration of Electrostatic force over a circular arc, direction of the resultant force changing with interchange in limits?
Problem:
A uniformly charged circular arc with linear charge density $m$ subtends angle $\theta$, find the net force acting on a charge placed at its center if total charge of the arc is $Q$ and the ...
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Question regarding the general form of four-vectors in particle physics
Consider the decay of a particle $X$ to two particles $c$ and $d$ in the rest frame of $X$.
Using energy and momentum (4-vector) conservation, show that the energy of particle
$c$ is given by:
$$E_c=\...
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“$10^{\mathrm{th}}$” Index skipped in M-theory
Why is it that in M-theory, the 11-dimensional vectors are labelled with indices $0 \dots 9,11$. For example, the spatial momentum components are $p_{1}, \dots, p_{9}, p_{11}$. Why is the $10^{th}$ ...
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What is the convention for tensor indices for matrices?
The Lorenz-Transformation of the EM-Tensor F is given by the equation
$$ F'^{\mu \nu} = \Lambda^{\mu}_{\ \ \rho} \Lambda^\nu_{\ \ \sigma} F^{\rho \sigma}$$
Then it says that this is equivalent to the ...
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What is the number of significant figures in $6*(7.203)**2$?
My textbook says:
"In multiplication or division, the final
result should retain as many significant
figures as are there in the original number
with the least significant figures."
but it ...
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Which basis 2-form elements represent positive traversals in Minkowski 4-space?
I'm certain some of this relies on arbitrary choice, for even in Euclidean 3-space, there is no a priori preferred choice of left versus right hand coordinates. In fact according to Einstein:
There ...
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Contravariant rank-2 tensor transformation in index notation
I'm slightly confused about the placement of upper and lower indices for the transformation of a rank-2 contravariant tensor.
A contravariant rank-2 tensor transforms as $$M' = \Lambda M \Lambda^{T}$$....
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Confusion even over such a simple application of the Right-hand rule to determine direction of magnetic field
After reading this question on this site I learned that the direction of the magnetic field is given by $\boldsymbol{B}=\frac{1}{\omega}\boldsymbol{k}\times \boldsymbol{E}$
The left diagram below is a ...
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1answer
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Why do different quantum field theory books have different conventions regarding the normalization? [closed]
Why are there several different versions of the scalar field solution, with a different coefficient in front of the exponential in the solution? Why don't all the authors use the same convention? I ...
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How can multiplication rule in sigfigs make sense?
I've been going through significant figures video on khan academy and it says the product of two numbers cannot have more significant digits than the significant digits in any of the inputs.
Example:
...
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1answer
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Normalization of overcomplete coherent states as basis
In a complete orthonormal basis $|x\rangle$, we often use the completeness relation:
$$\sum_{n=0}^\infty | x \rangle \langle x | = \mathbb{I}$$
if the basis is continuous we use the natural extension
$...
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2answers
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Does “adding a constant to the potential energy” imply “adding a total time derivative to the Lagrangian.”
I am trying to understand why Taylor says in his Classical Mechanics text, "we can always subtract a constant from the potential without effecting any physics."
I assume "doesn't effect ...
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2answers
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Tensor and Matrices
Suppose that we are dealing with the following matrix:
$$A=\begin{bmatrix}a_{00} & a_{01} \\ a_{10} & a_{11}\end{bmatrix}$$
but I don't want to use matrix notation, insted I want to use tensor ...
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Reference Point and Change in Potential Energy
Okay so I am VERY confused. Everything online is telling me that I can choose any reference point for potential being zero and still get a consistent result for potential difference HOWEVER I have ...
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1answer
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Negative test charge Electrostatics
Will there be any significant change (if any) in the formulas of electrostatics, if we use a negative test charge in the derivation. thanks for the help appreciate
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Sign of pair of Dirac spinor bilinear
I don't understand the following statement: Any pair of Dirac spinors verifies $(\bar{\Psi}_1\Psi_2)^\dagger=\bar{\Psi}_2\Psi_1$ and it is valid for both commuting and anti-commuting (Grassmann-valued)...
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Why do electrons flow in the opposite direction of the electric field?
I was taught that the potential decreases in direction of electric field but when we place a positive charge in between it's electric field is too in that same direction but the negative charge has ...
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2answers
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Why do we normalize the radial and the angular parts of a spherical wavefunction separately?
I'm trying to revise the Quantum Mechanical model of the Hydrogen atom, and I understand all the methods involved, including separating the wavefunction into its radial and angular parts, solving all ...
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2answers
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Why is the electric potential at a distance of $R$ from a point charge $q$ equal to $\frac{-q}{4\pi\varepsilon_0 R}$
My textbook mentions that the electric potential at distance of $R$ from a point charge $q$ will be given by $\dfrac{-q}{4\pi\varepsilon_0 R}$. I don't understand why the negative symbol appears here.
...
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Sign of reflection coefficient $E_r/E_i$ at normal incidence! [duplicate]
At normal incidence the plane of incidence is not defined! So how do we will understand that whether the reflection coefficient is positive or negative; because according to frensel equation for E ...
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Can we make uniformity in marking zero potential? Say it at earths surface or at infinity from earths surface?
The gravitational potential energy at infinity os supposed to be zero. Since body always moves towards lower potential, the gravitational potential is taken as negative so that gravitational potential ...
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1answer
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Are the Lowering and Raising Operators of QM the same as those of QFT?
We know that the lowering and raising operators in quantum mechanics are defined as
\begin{array}{l}
a =\frac{1}{\sqrt{2}}(X+i P) \\
a^{\dagger} =\frac{1}{\sqrt{2}}(X-i P),
\end{array}
respectively.
I ...
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Please help me understand Bird's transport phenomena tensor sign convention
im having difficulty understanding the criteria of signs settled down by BSL transport phenomena in the derivation of Stokes law in chapter 2
at the page 59 it takes the molecular momentum-flux tensor ...
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Is there a convention for left / right-chiral Weyl spinors?
In order to distinguish the representations of the Lorentz group, we can combine the generators for rotations ($J$) and boosts ($K$) into linear combinations,
$$ A_i = \tfrac{1}{2}(J_i + \text{i}K_i),\...
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2answers
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A confusion about the direction of the current density
I'm contradicting my premise again and again and I have no idea what I'm doing wrong. Say there is a given current density in a charged infinite cylinder, $J$ in the $\hat{z}$ direction. It follows ...
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1answer
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How to decide which way are the limits of an integral?
So, I'm trying to calculate the electric field at a point $r$ distance away on the perpendicular bisector of a finite line charge having uniform charge density $\lambda$
I arrive at the following ...
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2answers
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Why isn't the work done by gravity positive in this situation?
I want to find the work done by the force of gravity to move an object of mass $m$ from infinity to a point $P$ at distance $r_p$ from a body of mass $M$ (that I assume fixed). The formula should be
\...
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3answers
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The form of gauge invariance
When imposing local gauge invariance for a simple lagrangian describing a free Dirac fermion field:
$$\mathcal{L}=\bar{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi$$
Is there a particular ...
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2answers
80 views
Addition of a constant potential in the Schrodinger equation
A really elementary question:
Solutions of the single particle, non-relativistic, time-dependent Schrƶdinger equation for a spinless particle of mass $m$ alone in space, with no forces acting on it, ...
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Changing the convention of positive and negative charge holders in an atom
Would there be any specific change in the physical/chemical laws if one day we changed the convention that electrons are negatively charged to the one that electrons are positively charged and vice ...
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Substitution of frequation in Fourier transform of the signal $\hat x(f)$ to $\hat x(\omega)$
In wikipedia of ESD and PSD, there is a pair of equations, one is
$$\hat x(f) = \int_{-\infty}^\infty e^{-2\pi ift}x(t){\rm d}t$$
We know $\omega= 2\pi f$. How can we obtain then the other
$$\hat x(\...
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Conceptual Question on Maxwell's 3rd Equation in Integral Form
$$
\oint_C \vec{E} \cdot d \vec{l} = -\frac{d}{dt} \oint_S \vec{B} \cdot d \vec{A}
$$
where $S$ is a surface and $C$ is its boundary.
Why is there no negative sign in front of the left-hand side? I ...
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1answer
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Lorentz transformation of Weyl fields
In the Srednicki's textbook, Chapter 35, the author states (Equation 35.28):
$$
U(\Lambda)^{-1}[\psi^\dagger \bar\sigma^\mu \chi ] U(\Lambda) = \Lambda^\mu_{\,\,\nu} [\psi^\dagger \bar\sigma^\nu \chi ]...
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1answer
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What is the sign of Weinberg angle?
One has $\cos{\theta_W}=m_W/m_Z$, and $\sin^2{\theta_W}=1-(m_W/m_Z)^2$
Is the sign of the Weinberg angle defined or an important quantity?
If yes, are there constraints?
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Can we set an arbitrary reference level of elastic potential energy
$$ĪE_e=\frac{1}{2}k(x_f^2-x_i^2)$$
Where $k$ is the spring constant and $x$ is the displacement from equilibrium position.
Are we allowed to select an arbitrary reference level of elastic potential ...
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Why does taking sign convention in Ray optics generalize the formulas?
I have read a lot about why sign conventions are used in ray optics. It is because the formulas are different for different lens and object.
My teacher also said that sign conventions are like the ...
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Is the sign convention necessary in solving kinematics?
I have started with kinematics and I have a really basic question of following sign convention i.e taking up and right positive and down and left negative. Is such a convention necessary when I can ...
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1answer
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Why is the annihilation operator associated with the positive frequency solutions?
I am looking for a qualitative explanation, if possible, of the following passage from Peskin & Schroeder, bottom of page 26, concerning the quantised real Klein-Gordon field:
A positive ...
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1answer
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$d$-dimensional Einstein equations
I am reading this paper https://arxiv.org/abs/2002.02577. On page 13, it is written that the $d$-dimensional Einstein equations are
$$G_{\mu\nu}+\frac{(d-1)(d-2)}{6}\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}...
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2answers
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Where does the infinity in the definition of electric potential lie?
Electric potential at a point is defined as the amount of work done in bringing a test charge from infinity to that point..my question is that if we don't know where this point of infinity lies then ...
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How does the transformation of 4-derivative into a 4-momentum actually happen in a derivative coupling?
Consider a derivative coupling with $$\mathcal{L}_{int} = \lambda \phi_1 (\partial_\mu \phi_2) (\partial_\mu \phi_3),\tag{7.101}$$ and a scalar field
$$ \phi(x) = \int \frac{d^4p}{(2\pi)^3} \frac{1}{\...
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Is force always the negative change in potential energy with respect to position?
For example, In the non-inertial rotating reference frame of a turntable that has a tether ball pole rotating on top of it, the ball at the end instantly starts rotating and then eventually moves up ...
