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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183 views

How can electric flux be negative?

If electric flux is the number of field lines, then how can it be negative?
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2answers
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Does the quadratic mass term $\phi^2$ belong to the free Lagrangian or is it an interaction term?

$$L = -\frac{1}{2}\partial_\mu\phi\partial^\mu\phi - \frac{m^2}{2}\phi^2.$$ Why is the $\phi^2$ term in the scalar Lagrangian not considered a self-interaction?
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Sign of work against an electrostatic field

I think I'm slightly confused with the signs. The work needed in order to bring point charges $q_i$ from infinity to a distance $r$ from some shape of charge $Q(r)$ with a varying charge (because we ...
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2answers
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Can we assume a force to already be negative before knowing the value of it? [closed]

Let me make my question clear by the following example:- Let’s take a case of an individual who is in an elevator accelerating downward with some acceleration ‘ a ‘ such that ‘a’ < g . Let’s take ...
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1answer
35 views

Regarding sign of energy stored in springs

A block of mass $m$ is at natural length initially.It is attached to two springs having spring constant $k1$ and $k2$. It is attached in such a way that when one elongates ,the other compresses.Using ...
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1answer
47 views

Regarding the signs in the Clebsch-Gordan coefficients

Let's take, for example, the $\frac{1}{2}$ $\frac{1}{2}$ spin case. We have, for $J = 1, M = 0$ $$|1,0\rangle=\frac{1}{\sqrt{2}}(|-1 / 2,1 / 2\rangle+|1 / 2,-1 / 2\rangle),$$ and, if we follow the ...
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35 views

Euler beam equation sign confusion

Euler beam equation is defined as follows: $$M=-EI{\frac {d^{2}w}{dx^{2}}}$$ There is a negative sign, so if the second derivative of the deflection is negative, the moment is positive. When the ...
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0answers
87 views

Can an affine first-order polynomial system be chaotic?

While studying chaos theory, one of the basic principles presented to me was that chaos only occurs in deterministic nonlinear systems. This pointed me to learn more about the differences between ...
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Which way of integrating the quaternion representation of orientation is correct?

I am wondering how to integrate a measurement of angular velocity into an orientation quaternion. Suppose I have measurements of the rotation rate about the three principal axes of a body. I would ...
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4answers
69 views

If Gravitational potential energy increase with height then why it is 0 at infinity?

Due to MGH relation, if we increase height then potential energy increases. Then why it is zero at infinity?
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1answer
50 views

Sign of effective action of bosonic string?

I've been looking at David Tong's Lectures on String Theory. He states that the low-energy effective action of the bosonic string is given by $$S=\frac{1}{2k_0^2}\int d^{26}X\sqrt{-G}e^{-2\Phi}\Big(\...
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1answer
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Time-like coordinate vs space-like coordinates in GR

I know the definition of space-like and time-like coordinates in simple geometric, basically, we got: $$ds^2=dt^2-dx^2-dy^2-dz^2$$ so the coordinate with a positive contribution to the $ds^2$ is the ...
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2answers
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What's the justification for the sign in the formula for work?

In case of electric potential at a point (P) the derivation says that it is equal to the external work done to bring a unit positive charge from infinity to point P without acceleration i.e with ...
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Sign Problem When Dealing With Quadratic Air Resistance and Gravity [closed]

While dealing with an object falling vertically, and subject to quadratic air resistance, an equation of motion that is often presented is \begin{equation*} m\dot{v} =mg-cv^{2} \end{equation*} In ...
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1answer
137 views

Gauss' Law in 2D?

At first I thought it was $$∮E.dl=Q/ϵ.$$ So i've read through some sources here and on the internet and most of them said that $$∮E.dl=2πq.$$ But I'm confused. Can anyone explain where does the $...
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Why is the work term negative in the 1st law of thermodynamics using constant pressure specific heat?

From the first law, we have that $$dq = c_v dT+pd\alpha\tag{1},$$ that is, the total energy (by unit mass, where $\alpha$ is the specific volume) equals the variation in internal energy plus the work ...
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1answer
27 views

Sign convention for Maxwell's model of viscoelastic material

Maxwell's equation for viscoelastic body is $\dot{\varepsilon}(t)=\frac{\dot{\sigma}}{E}(t)+\frac{\sigma}{\eta}(t)$, where $\varepsilon=\frac{dl}{l}$ is strain and $\sigma$ is stress. I am a little ...
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Conservative Force and Energy [closed]

When a charge is moved from infinity to $r$, its electric potential energy is equal to the negative work done by the field. In this argument, is it also true that there is positive work done by the ...
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Regarding number of degrees of freedom of a dynamical system (as well as it's relation to number of equations of motion)

I would like to know why in the context of vibrating systems, we define degrees of freedom in terms of number of independent coordinates (by coordinates I mean the numbers which specify the components ...
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1answer
38 views

Why does positive net energy mean energy loss and negative energy gain? [closed]

To my knowledge Work is defined as $W=-\int{\vec{F}\cdot d\vec{s}}$, or in the context of vectorfields as $F=-q\nabla\Phi$ ($q=m$ in the case of gravity). Recently I have been wondering whether there ...
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Why does the S matrix always contain a factor of $(2\pi)^4?$

In quantum field theory, one usually defines the scattering amplitude as $$S-1=(2\pi)^4\delta(p_{out}-p_{in})M_{Scattering Amplitude}$$ Where S is the S matrix element for any scattering process. It's ...
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Origin of the factor of $i$ in the photon propagator

I'm following Peskin and Schroeder and am having trouble tracking down a particular factor of i that is persistently used in the definition of Green's functions. For example, equation 9.52 states that ...
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4answers
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Why is the electric potential at infinity zero?

As per net results, the potential at infinity is considered to be zero. Apart from considering this as a physics law, is there any proper reason why we consider potential at infinity to be zero?
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1answer
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What is the old (50's) convention on Dirac gamma matrices?

What were the standard relations for gamma matrices in the mid 50's, when 4-vectors where represented by $(x_1, x_2, x_3, ict)$? In particular the values of $\gamma^\mu\gamma^\nu$ , the definition of $...
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1answer
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Choice of metric [duplicate]

We have the metric given by a matrix $g_{\mu\nu}$, however, some textbooks define it as: $$g_{\mu\nu} = \begin{pmatrix} -1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & ...
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1answer
67 views

Dirac's equation, boosts and rotations

If we consider Dirac's equation in two different frames of reference $$\left(i\gamma^{\mu} \partial_{\mu}-m c\right) \psi(x)=0,$$ $$\left(i\gamma^{\mu} \partial_{\mu}^{\prime}-m c\right) \psi^{\prime}\...
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2answers
132 views

Why we write the constant in front of the Einstein-Hilbert Action?

Why we write the constant? $$S_{EH}=\frac{c^4}{16\pi G}\int \sqrt{-g}R d^4x$$
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2answers
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I'm having trouble understanding the formula of Potencial Difference (or Voltage) in Electrostatics

For example, my textbook clearly says that the Potencial Difference between points A and B is given by $$ V_{AB} \equiv V_A-V_B = \int_A^B \vec E\cdot d\vec l $$ but I've seen, in other textbooks, ...
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How do I know the sign convention for $W$ and $Q$ in thermodynamics? [duplicate]

Can someone correct me if I am wrong. For example, 43 kJ work energy has been done on the system, sign convention is +43kJ, because work is entering into the system 62 kJ work energy has been ...
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1answer
102 views

Quantization of the Klein-Gordon equation, sign problem

In Peskin and Schroeder, they quantize the Klein-Gordon field in the following way. They write the Fourier transform of $\phi(x,t)$ $$ \phi(x,t)=\int \frac{d^3 p}{(2\pi)^3}e^{ipx}\phi(p,t) $$ after ...
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1answer
29 views

Torque cross product

Torque is the cross product of force and distance. Almost all the resources I find online have the formula as $\vec\tau=\vec d\times \vec F$, yet my professor (and I've seen some other sources do ...
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1answer
42 views

Is it a convention to take the dipole moment vector $\vec p$ in the direction opposite to the electric field?

Is it a convention to take the dipole moment vector $\vec p$ in the direction opposite to the electric field? Or it is proved by mathematics
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3answers
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What's the difference between flemming's left hand rule and the right hand rule of magnetism?

In flemming's left hand rule, thumb represents the direction of motion/ magnetic force, index is magnetic field and middle finger is current while in right hand rule of magnetism, thumb represents ...
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2answers
61 views

Why is the scaling factor in the Robertson-Walker metric squared?

Not much to add beyond the title. The Robertson-Walker metric solution to the field equations has the form $$g_{\mu\nu}dx^\mu dx^\nu=-dt^2+a^2(t)\biggl(\frac{dr^2}{1-Kr^2}+r^2(d\theta^2+sin^2\theta \...
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0answers
41 views

Complex notation convention for time variation

In describing plane wave EM variation, some textbooks use the complex notation $\exp(i\omega t)$, while others use $\exp(-i\omega t)$. Is there a motivation for chosing one or the other convention, ...
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2answers
65 views

Tensor ordering in index lowering operation

If we take two vectors and want to contract them with the metric tensor to find some frame invariant quantity: $$A^a B^b g_{ab}=\vec A\cdot \vec B$$ is there a convention on where the metric tensor ...
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1answer
43 views

Mathematical convention when using spatial indices: numerical $(1,2,3)$ versus Cartesian $(x,y,z)$ [closed]

When writing a document I find that I am switching back and forth between indicial notation for spatial coordinates. I would like to get your thoughts on the following examples accompanied with ...
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2answers
102 views

Is the labelling of $g_{\mu\nu}$ as “the metric” and $g^{\mu\nu}$ as “the inverse metric” arbitrary?

I understand the up and down indices change the way in which the metric transforms under basis changes, that's not what I'm getting at. My question is that since the metric is specifically an ...
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2answers
83 views

Not understanding the minus sign in the torque equation for a simple pendulum

The pic above is from Introduction to mechanics by Kleppner. In the torque equation they justified the minus sign because the torque has a clockwise sense. This makes sense to me if I pick the y axis ...
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1answer
87 views

Hermitian Conjugation in 2D CFT

When we take the hermitian conjugate of an operator in D dimensions we have: $$ \mathcal{O}_{flat}(r,\vec{n})^\dagger=\frac{1}{r^{2\Delta}}\mathcal{O}_{flat}\left(\frac{1}{r},\vec{n}\right) $$ where $\...
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1answer
67 views

Euler-Lagrange equations in QFT and metric signs

I'm having a probably dumb problem with the Euler-Lagrange equations and the dot-product in Minkowski spacetime. I know that some objects are defined naturally with lower-indexes, e.g. $\partial_{\mu}$...
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1answer
31 views

Change sign for response function

There is a argument about response function: according to the Kramers-Kronig relation$$G(\omega)=\int_{-\infty}^{+\infty}d\omega' \frac{A(\omega')}{\omega+i0_+-\omega'}$$ response function will change ...
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1answer
68 views

What is the electric potential in free space? [closed]

What is the electric potential in free space? Is it not zero, since there is no charge around?
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4answers
125 views

Clean link between electromotive force and difference of potential: potential difference around a resistor or inductance

I would like to clarify some aspects of EM that I never realized before: proper link between voltage in electric circuit and electromotive force. Electrical vision of electric circuit: In almost all ...
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1answer
29 views

Epsilon Tensor Changing Sign

I am trying to solve a commutator relation containing an epsilon tensor. The expression has the following form: $\epsilon_{3kj} \sigma_{j} x_{k}$. Because of an other solution, this should be ...
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3answers
200 views

Voltage difference between two points [closed]

I want to know how to find the voltage difference between two points A and B which is $V_{ab}$ by Kirchhoff's law ... Also what does it mean if the value is negative? What is the difference between $...
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1answer
41 views

Determining Signs when Deriving Voltage

In my intro E&M class, we were given an example problem to determine the voltage within a cylindrical capacitor as a function of radius. A diagram of such a cylindrical capacitor is below. The ...
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1answer
180 views

$(\psi_L^\dagger \psi_R)^\dagger \neq (\psi_R^\dagger \psi_L)^\dagger$ ? What is the transpose for spinors?

The dirac mass term in terms of Weyl spinors is $$\psi_L^\dagger \psi_R + \psi_R^\dagger \psi_L.$$ My understanding is that both terms are necessary to form a hermitian term. Naively, if you take ...
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1answer
61 views

Understanding Electrostatic Work

$$W=-\int_\infty^\textbf{r}\textbf{F}\cdot\textbf{dl} =-Q\int_\infty^\textbf{r}\textbf{E}\cdot\textbf{dl} = Q(V(\textbf{r})-V(\infty)) =QV(\textbf{r})$$ I'm trying to understand how this definition ...
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2answers
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Changing sign of Lagrangian & Hamiltonian: how to interpret energies then?

In Lagrangian mechanics, it is possible to multiply the Lagrangian by a constant $a$. Let's assume I take $a=-1$. Then, the Hamiltonian will have its sign changed as well. And it will represent the ...

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