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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questions
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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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3answers
50 views
Conservative Force and Energy
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 (positions & velocities) required to specify the motion ...
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1answer
35 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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2answers
81 views
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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0answers
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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 ...
2
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4answers
58 views
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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Gamma matrix commutator relation
I just saw this relation in my Quantum Field Theory textbook $$\varepsilon_{\mu \nu \alpha \beta} \sigma^{\alpha \beta}=-2 i \sigma_{\mu \nu} \gamma_{5}=\gamma_{5}\left[\gamma_{\mu}, \gamma_{\nu}\...
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1answer
41 views
What is the old (50's) convention on Dirac gamma matrices?
What were the standard relations for gamma matrices in the mid 50's, when 4-vectors where represented by $(x_1, x_2, x_3, ict)$? In particular the values of $\gamma^\mu\gamma^\nu$
, the definition of $...
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0answers
32 views
Proof regarding gamma matrices [closed]
How do I prove this?
$$\gamma^{\alpha}\gamma^{\beta}\gamma_5 - \gamma^{\beta}\gamma^{\alpha}\gamma_5 = \epsilon^{\alpha \beta \theta \lambda} g_{\theta \delta} g_{\lambda \rho} \sigma^{\delta \rho},$$
...
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1answer
19 views
Choice of metric [duplicate]
We have the metric given by a matrix $g_{\mu\nu}$, however, some textbooks define it as:
$$g_{\mu\nu} = \begin{pmatrix}
-1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 1 & ...
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1answer
50 views
Dirac's equation, boosts and rotations
If we consider Dirac's equation in two different frames of reference $$\left(i\gamma^{\mu} \partial_{\mu}-m c\right) \psi(x)=0,$$ $$\left(i\gamma^{\mu} \partial_{\mu}^{\prime}-m c\right) \psi^{\prime}\...
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2answers
114 views
Why we write the constant in front of the Einstein-Hilbert Action?
Why we write the constant?
$$S_{EH}=\frac{c^4}{16\pi G}\int \sqrt{-g}R d^4x$$
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2answers
43 views
I'm having trouble understanding the formula of Potencial Difference (or Voltage) in Electrostatics
For example, my textbook clearly says that the Potencial Difference between points A and B is given by $$ V_{AB} \equiv V_A-V_B = \int_A^B \vec E\cdot d\vec l $$
but I've seen, in other textbooks, ...
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29 views
How do I know the sign convention for $W$ and $Q$ in thermodynamics? [duplicate]
Can someone correct me if I am wrong.
For example,
43 kJ work energy has been done on the system, sign convention is +43kJ, because work is entering into the system
62 kJ work energy has been ...
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1answer
86 views
Quantization of the Klein-Gordon equation, sign problem
In Peskin and Schroeder, they quantize the Klein-Gordon field in the following way. They write the Fourier transform of $\phi(x,t)$
$$
\phi(x,t)=\int \frac{d^3 p}{(2\pi)^3}e^{ipx}\phi(p,t)
$$
after ...
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1answer
23 views
Torque cross product
Torque is the cross product of force and distance. Almost all the resources I find online have the formula as $\vec\tau=\vec d\times \vec F$, yet my professor (and I've seen some other sources do ...
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1answer
38 views
Is it a convention to take the dipole moment vector $\vec p$ in the direction opposite to the electric field?
Is it a convention to take the dipole moment vector $\vec p$ in the direction opposite to the electric field? Or it is proved by mathematics
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3answers
44 views
What's the difference between flemming's left hand rule and the right hand rule of magnetism?
In flemming's left hand rule, thumb represents the direction of motion/ magnetic force, index is magnetic field and middle finger is current while in right hand rule of magnetism, thumb represents ...
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2answers
58 views
Why is the scaling factor in the Robertson-Walker metric squared?
Not much to add beyond the title. The Robertson-Walker metric solution to the field equations has the form
$$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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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
58 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 ...
0
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1answer
41 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
100 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
56 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
68 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
53 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. $\partial_{\mu}$...
1
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1answer
29 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
51 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
110 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
27 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 ...
0
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3answers
76 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 $...
0
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1answer
38 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
164 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
58 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
84 views
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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0answers
23 views
Commercial Radio Bandwidths around the world
I'm a liberal arts person who has more than a passing interest in radio but it has taken years for this to dawn on me, so be kind if it is obvious.
I was out of the US recently, and I saw a radio in ...
2
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1answer
104 views
Derivation of combination of lenses using different sign conventions
In the following derivation of combination of thin lenses, why no sign convention is applied? For the first step, image distance, $u=+v_e$, but shouldn't it be $-v_e$ as the object is to the left of ...
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3answers
69 views
1st Law of Thermodynamics, Newton's 3rd Law and the Work-Energy Theorem
I came across $ΔU=Q+W_o $ where $W_o$ represents the work done on the system.
I also came across the formula $ΔU=Q-W_B$ where $W_B$ represents the work done by the system (gas).
My question is, ...
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2answers
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The reference point of potential energy
In one dimension (I am not familiar with multivariable calculus), potential energy is defined as
$$E_p = -\int F \ dx$$
This is an indefinite integral, and the integration constant $C$ is involved ...
1
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1answer
61 views
Why does $\phi=\phi^*$ imposed on complex scalar field Lagrangian miss out $1/2$ factors?
If we require the reality condition $\phi=\phi^*$ on the Lagrangian for a complex scalar field is $$\mathcal{L}=(\partial^\mu\phi^*)(\partial_\mu\phi)-m^2(\phi^*\phi),$$ two degrees of freedom $\phi$ ...
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1answer
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Convert propagators from Euclidean to Minkowski spacetime
I'm looking for a rule to "convert" the propagators of a quantum field theory formulated in Euclidean spacetime into those of the same theory but in Minkowski spacetime (with the $\operatorname{diag}(-...
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5answers
65 views
What is the reason for work done by gravitational force being negative?
When a body is moved from $r=∞$ to say, $r=R$, work done by the gravitational force is $-(GMm)/R$.
Why is it negative even though the Force and the displacement of the body is in the same direction. ...
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2answers
42 views
Properly reporting instrument readings
As a first approximation, the uncertainty ($\delta X$) associated to a mensurand can be expressed as $\delta X= \Delta X / 2$ with $\Delta x$ being the resolution of the instrument.
There is also a ...
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0answers
27 views
Question on notation convention regarding partial derivatives
H.Risken's book "The Fokker-Planck Equation" contains the following formula for the general 1D Fokker-Planck equation:
$\frac{\partial W}{\partial t}=\left[-\frac{\partial}{\partial x}D^{(1)}(x)+\...
17
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3answers
4k views
Why is ampere still a base unit? [duplicate]
The ampere is still a base unit, according to the SI brochure. However, in my perception the recent redefinition of units effectively defines the Coulomb as e/(1.602 176 634 × 10^−19), and the ampere ...
0
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3answers
210 views
Position Operator Eigenvectors change with Space Displacement
I am working through Ch. 3 of Ballentine where he finds the commutator relationships between various operators.
He begins on p.78 with a space displacement
$$\mathbf{x'} = \mathbf{x} + \mathbf{a}$$
...
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1answer
53 views
Momentum operator in spacelike metric convention
What are the underlying principles for choosing signs for the momentum operators in QM/QFT?
Let's say, for the $(+,-,-,-)$ metric convention we have $\partial^\mu = (+\partial_0,-\nabla)$. Why not $\...
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0answers
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EM wave: Why do you take the imaginary part of complex $H(z,t)$?
The following is an electromagnetic wave traveling in +z direction:
$$\vec{E}(z,t) = 1.0~e^{-\alpha z} e^{j(2\pi f t - \beta z)}~\hat{y}$$
$$\vec{H}(z,t) = - (2.28\times 10^3)~ e^{-\alpha z}~e^{j(2\...
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3answers
44 views
Sign of gravitational acceleration
The gravitational potential energy comes from the formula $mgh$ where $g$ is always $>0$.
But when we get to choose it's sign? I figured out, it really depends on what you choose as positive axis ...
