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 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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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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46 views

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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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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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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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
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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29 views

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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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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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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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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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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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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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
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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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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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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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 ...
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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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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. $\partial_{\mu}$...
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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 ...
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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 $...
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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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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 ...
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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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88 views

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 ...
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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
94 views

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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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)+\...
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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 ...
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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
40 views

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 ...

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