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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Are there several conventions (source or receiver) for the *Jones vector*? What about the one of particle physics?

There are several conventions for defining the polarisations left and right: from the source and from the receiver. See for example: https://en.wikipedia.org/wiki/Circular_polarization#...
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Missing sign in Dirac equation

This is very trivial, but it's really bugging me. The ansatz for the Dirac equation in terms of $\boldsymbol\alpha$ and $\beta$ matrices is $$ [i(\partial_t+\boldsymbol\alpha\cdot\boldsymbol\nabla)-\...
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Why is the decimal system a more convenient system? [closed]

Can you give reasons as to why decimal system is a more convenient system? I got this in the chapter Units and Dimensions.
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55 views

Notation confusion for differential volume

Can anyone help me with an explanation of the following notation. I am a bit confused: Lets say we have some type of integral and in the end we write different differential, such as: $$d\vec r ,\quad ...
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Different versions of Schwinger parameterization

One common used trick when calculating loop integral is Schwinger parameterization .And I have see two versions among wiki,arxiv and lecture notes. $$\frac{1}{A}=\int_0^{\infty} dte^{-tA}$$ or, $$\...
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179 views

Integration path with opposite direction from the unit vector

The task is to calculate the voltage between points $M$ and $N$ if the electric field vector is known to be $\vec{E}=\frac{V_0\cdot x^2}{a^3} \cdot \vec{i} + \frac{V_0 \cdot y}{a^2} \cdot \vec{j}$, ...
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When and why are units measured in degree?

I was always under the impression that a unit is measured in degree if it is a relative unit. While this is true for temperatures and angles, I cannot find any reference to this definition or any ...
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Symbol of quintal

Depending on the source, I have come across the symbol of quintal as 'q', 'qt'and 'qtl'. Is there a standard symbol for quintal. If yes what is it?
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Can we speak of an absolute voltage without a convention?

In most practical cases I have seen, voltage was regarded as a difference in electric potential, save the odd change of magnetic flux over time which, as a form of change, also conveys the notion of a ...
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Time convention vs time domain, what is the difference?

I really think those are the same thing, but couldn't be so sure. Is there any difference between time convention and time domain? For example: "wave propagates along x direction with $e^{jwt}$ ...
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Confused regarding sign convention of silvered plano convex lens

I'm totally confused while finding the sign convention of a silvered plano convex lens. I know that equivalent power of such a system can be found by adding the power of the mirror and twice the power ...
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Possible Error in Marion and Thornton's Classical Dynamics of Particles and Systems

so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3 The rotation matrix associated with 1.2a and ...
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Sigma Significance in Particle Physics and Beyond [closed]

Why is a 5 sigma confidence level enough to solidify an experimental result as not being a statistical fluke in particle physics? Other branches of science have different sigma values for which they ...
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Does swapping “$i$” with “$-i$” change a physical theory?

Mathematically speaking, "$i$" and "$-i$" are the two roots of the equation $x^2+1=0$ and it seems to me at least that there is no obvious way of distinguishing between them. Thus, ...
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What is the difference between positive negative potential and positive, negative work done?

if work is done along the direction of force,then the work is regarded as positive work and if work is done in a direction opposite to the direction of force then it's regarded as negative work....
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Why not $\frac{x}{c}$ instead of $ct$?

The moral of the parable in special relativity is that: The same units should be used for all distances. The (squared) distance is invariant. Different frames are related by rotations. Now what we ...
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Cylindrical/Spherical Capacitor derivation sign issues

In deriving the capacitance for a cylindrical and spherical capacitors, I keep obtaining the incorrect sign on V. I completely understand the problem besides one step. First we start with Gauss' law:...
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Spacetime translation in QFT

I have a question about the field under the spacetime translation. For example, in page 26 of Peskin's textbook, they give the translation properties of the field. So consider the space translation, ...
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300 views

Derivation of the Electromagnetic Stress-Energy Tensor in Flat Space-time

I am working on deriving the electromagnetic stress energy tensor using the electromagnetic tensor in the $(-, +, +, +)$ sign convention. However, I have hit a snag and cannot figure out where I have ...
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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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Chasing down minus sign in the expression $p_\mu - e A_\mu$ for the momentum

In his Quantum Field Theory book, Folland says that the prescription for incorporating a 4-potential $A$ into the Dirac equation $(i \gamma^{\mu} \partial_\mu - m)\psi = 0$ is to replace $i\partial_\...
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Different definitions of the electric potential

While studying electrostatics, my professor wrote the following definition for the electric potential: $V(P)=V(P_{0})+ \int_{P}^{P_{0}} \vec{E} \cdot \vec{dl}$ ($P_{0}$ is the reference point) and I'...
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The Electromagetic Tensor and Minkowski Metric Sign Convention

I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$. For the convention of (+, -,...
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Isn't the work done on a spring-mass system zero, so that there is be no change in potential energy?

So far what I had understood about potential energy is that it is defined for a system of particles (at least two particles) with forces acted by the particles on each other of same magnitude and ...
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Reference point in Laplace's equation

I have been learning about how we go about solving Laplace's equation when we want to find the potential for some region with no charge. My question is, is it implicitly considered here that the ...
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Why is $\Delta V = - \int E \cdot dr$ when charge is moving from lower potential to higher potential?

In a parallel plate capacitor, charge $q$ is travelling from negative to positive plate. Why is $\Delta V$ negative? Every book explains it by saying $\Delta U = -W$, but this equation came when we ...
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Transpose of a 2x2 Tensor

This question arises after reading through several Stack Exchange posts and after a long chat with another user in a previous question I asked about this topic. The following "contradiction" ...
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64 views

Negative or positive newtons [closed]

Do we write A car needs 6000N of force to be stopped or A car needs -6000N of force to be stopped
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Confusion in Signs when formulation mathematical equations for physics problems

One of the common confusion I face when writing and solving mathematical equations for physical problems is regarding signs. Consider this problem; A ball is dropped from rest from top of the building,...
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58 views

Find the density of the sphere, $\rho(r)$

If the field vector $\hat{g}$ is independent of the radial distance withing the sphere, find the function describing the density $\rho$ of the sphere, $\rho(r)$. In spherical coordinates, the ...
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39 views

How many significant figures should be used in an answer?

For an answer to a problem in significant figures, should the number of significant figures in the answer be based on the term with the least number of significant figures in the prompt? Just as an ...
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131 views

Issue with understanding the Weinberg's proof of the Goldstone boson theorem

To prove Goldstone's theorem Weinberg (in volume II, page 170, equation 19.2.18) starts with the expectation value over the vacuum of the commutator between one field $\phi_n(x)$ and the conserved ...
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51 views

Problem with the sign of work

I have been stuck in a conceptual problem about the sign of the work. For example, suppose that we have a mass $m$ on a spring such that the equilibrium position is at $x=0$, and we stretch the spring ...
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28 views

Phasor transformation to sinus or cosinus?

In my EM waves lecture, our lecturer somehow explained the way we make phasor transformation of a particular function such as $$A\cos(\omega t-( \alpha +\beta z))u_{y}$$ converted into phasor form of $...
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Potential sign question

Let's consider a positive test charge $q$ and a positive source charge $q_o$ If we take direction of $\vec{r}$ from $q_o$ to $q$, then potential energy of $q_o$ due to $q$ will be: $$P=k\dfrac{q_oq}{r}...
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227 views

Sign convention in optic problems

Note: The convention used in our physics textbook and the mentioned question is Cartesion Convention Today in our physics test, we were given the following question:- A mirror has focal length 20 cm ...
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38 views

Definition for Fourier transform for physically representing field in frequency domain

If I have a time-dependent electric field $E(t)$ and want to calculate the spectrum of this field by $$A_0\cdot|E(\omega)|^2\,$$ where $A_0$ is some constant factor. My questions is which definition ...
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Significant figures in textbooks

I know that there are a plenty of questions similiar to this one, but none of them was able to definitely give an answer, at least in my point of view. In so many Physics textbooks (Tipler, Halliday, ...
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64 views

Wedge Product Convention

In Wald’s General Relativity textbook he defines the wedge product as: $$(w \wedge u)_{a_1 ... a_p b_1 ... b_q}= \frac{(p+q)!}{p!q!} w_{[a_1 ... a_p}u_{b_1 ... b_q]}$$ My question is relatively simple:...
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Where must one use $x=A \cos \omega t$ and $x=A \sin \omega t$? [duplicate]

Consider the following example: A particle oscillates with simple harmonic motion in a straight line. In the first $t$ seconds, it travels a distance $a$. In the next $t$ seconds, it travels an ...
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How do we Wick rotate the Maxwell $U(1)$ gauge theory's field strength $F$?

How do we Wick rotate the Maxwell $U(1)$ gauge theory's field strength, say in 3 space and 1 time dimensions? Suppose we start with a Lorentz signature with coordinates $(x_0, x_1, x_2, x_3)$, then we ...
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74 views

$\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki

The theta angle due to the chiral gamma^5 rotation of chiral fermion results in the phase alpha(x) that has different + or - sign for (1) Peskin&Schroeder, (2) Weinberg or (3) Srednicki. Here ...
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140 views

How to figure out if the vector product of force and displacement is $-\mathbf fd\mathbf x$ or $\mathbf fd\mathbf x$?

Consider the force due to a point charged particle at the origin and the particle which we move to also be charged with the same charge. When we move a particle from point $\mathbf{x}$(position vector)...
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81 views

How to remove the $\exp(-i(p^0+q^0)x^0)$ term in the canonical commutation?

Using the convention A Modern Introduction to Quantum Field Theory by Michele Maggiore Eq. 4.2 or equivalently the quantum theory of fields by Steven Weinberg Eq.1.2.63. $\phi(x)=\int \frac{d^3p}{(2\...
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48 views

Symmetric infinite well potential

Assume we have the following potential : $$ V\left(x\right)=\begin{cases} 0 & -\frac{L}{2}\leq x\leq\frac{L}{2}\\ \infty & else \end{cases} $$ The wave function for a particle in this well ...
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625 views

Limits of Integration Trig, Mag Field Infinite Length Wire

I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it. Here's the set up: ...
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245 views

Sign of counterterm vertex factor (Srednicki)?

My question is about a mere minus sign which, although irrelevant in my specific problem (as will be shown), I fear may bite me later on. In Srednicki chapter 14, the author is computing the 1-loop ...
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145 views

Confusion on kinetic energy quadratic forms and eigenfrequencies

I am new to the idea of expressing kinetic energy in terms of the quadratic form. I noticed that online, people often express the kinetic energy as: $$T = \frac{1}{2} \dot q^T M \dot q \tag{1}$$ ...
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174 views

QFT: Higgs mechanisms covariant derivative under gauge transformation

So we have a Maxwell field coupled to a complex $\Phi(x)$ (charged) scalar field with mass and self-interaction terms: $$L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+D_{\mu}\Phi^*D^{\mu}\Phi-m^2\Phi^*\Phi-\...
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Density of states, Solid state physics

Im reading about Somerfeld's model, and under the assumptions of periodic boundary conditions for a particle in a box, the density of states in my book defined to be $$ g\left(\varepsilon\right)=\frac{...

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