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.

Filter by
Sorted by
Tagged with
0
votes
1answer
27 views

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 ...
1
vote
2answers
18 views

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 ...
0
votes
1answer
27 views

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, ...
-2
votes
0answers
36 views

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 ...
1
vote
2answers
78 views

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(...
2
votes
1answer
43 views

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 ...
2
votes
2answers
54 views

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 ...
0
votes
0answers
24 views

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 ...
0
votes
0answers
30 views

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 ...
0
votes
2answers
91 views

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=\...
1
vote
0answers
75 views

“$10^{\mathrm{th}}$” 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 $10^{th}$ ...
0
votes
1answer
39 views

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 ...
0
votes
1answer
37 views

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 ...
0
votes
0answers
41 views

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 ...
0
votes
0answers
68 views

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 $$M' = \Lambda M \Lambda^{T}$$....
2
votes
1answer
36 views

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 ...
4
votes
1answer
96 views

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 ...
1
vote
1answer
36 views

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: ...
3
votes
1answer
40 views

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 $...
2
votes
2answers
55 views

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 ...
4
votes
2answers
218 views

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 ...
0
votes
1answer
28 views

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 ...
-1
votes
1answer
22 views

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
1
vote
1answer
38 views

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)...
0
votes
2answers
43 views

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 ...
1
vote
2answers
43 views

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 ...
1
vote
2answers
88 views

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. ...
0
votes
0answers
14 views

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 ...
0
votes
1answer
20 views

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 ...
1
vote
1answer
86 views

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 ...
0
votes
1answer
41 views

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 ...
0
votes
0answers
19 views

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),\...
2
votes
2answers
75 views

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 ...
1
vote
1answer
50 views

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 ...
1
vote
2answers
67 views

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 \...
0
votes
3answers
98 views

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 ...
1
vote
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 Schrödinger equation for a spinless particle of mass $m$ alone in space, with no forces acting on it, ...
0
votes
0answers
26 views

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 ...
0
votes
0answers
34 views

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(\...
1
vote
0answers
62 views

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 ...
1
vote
1answer
53 views

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 ]...
0
votes
1answer
41 views

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?
0
votes
3answers
38 views

Can we set an arbitrary reference level of elastic potential energy

$$ΔE_e=\frac{1}{2}k(x_f^2-x_i^2)$$ 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 ...
0
votes
1answer
22 views

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 ...
0
votes
1answer
38 views

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 ...
0
votes
1answer
64 views

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 ...
2
votes
1answer
67 views

$d$-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}...
0
votes
2answers
44 views

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 ...
2
votes
2answers
95 views

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}{\...
0
votes
0answers
44 views

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 ...

1
2 3 4 5
24