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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Correlation function $\langle s_1(x, t)s_2(x', t')\rangle$ vs $\langle s_1(x, t)s_2(x', t')\rangle-\langle s_1(x, t)\rangle\langle s_2(x', t')\rangle$

The correlation function in statistical mechanics is defined in either of two ways $$g(\mathbf{x}-\mathbf{x}', t-t') = \left\langle s_1(\mathbf{x}, t)s_2(\mathbf{x}', t') \right\rangle$$ ...
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100 views

Two mass spring system

The equations of motion of the spring mass system with, m = 1 $ \ddot{y_1} = -k_1y_1 + k_1(y_2-y_1)$ $ \ddot{y_2} = -k(y_2-y_1) - ky_2$ My question is with the second term in the first equation. ...
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199 views

How should Christoffel symbols be written (in LaTeX)? [closed]

I'm writing a summary of a lecture on relativity, and we've recently introduced the Christoffel symbols. It seems that the upstairs indices are the "leftmost" and the downstairs indices are somewhat ...
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1answer
67 views

Problem arising from quantisation of e.m. field

In my studies on the quantisation of the electromagnetic field I've come across a small calculation that I wasn't able to reproduce. Remember the following: In the Gupta-Bleuler method to quantize ...
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28 views

The sign of a focal length

We know that for converging lens, $f>0$ , for diverging lens, $f<0$. But for many materials I have read so far, it says that: "the focal length of a concave lens is 8 cm." I thought that the ...
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2answers
100 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
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19 views

Conventions in defining spherical harmonics and associated Legendre polynomials

Relevant Background Spherical harmonics are defined with several different conventions: the definition used in quantum mechanics according to Wikipedia is $Y_l^{\,m}(\theta,\phi) = ...
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2answers
92 views

Momentum conservation in the one-loop contribution of the photon propagator

The lowest contribution to the photon self-energy is represented by the following diagram (Taken from F.Schwabl, Advanced quantum mechanics, p.365):: ($k$ is the momentum of the photon that decays in ...
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1answer
44 views

Velocity-time-distance problem

In my book the formula for the $y$-component of velocity during the upward projectile motion is given: $$V_y=V_{iy}-gt$$ and next to it the formula for $y$-component of velocity during the downward ...
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1answer
114 views

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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3answers
145 views

Complex scalar field theory

For the complex scalar field theory $$L = -\partial_{\mu}\phi^{*}\partial_{\mu}\phi - m^{2}\phi^{*}\phi + J\phi^{*}+J^{*}\phi,$$ Why is there no factor of 1/2 in the lagrangian like in the real ...
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37 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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2answers
137 views

Defining gravitational potential

I recently came across the definition of gravitational potential where ..... Suppose a particle of mass $m$ is taken from a point $A$ to $B$. Let $U(A)$ and $U(B)$ denote the gravitational ...
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1answer
68 views

Why do physicists use a positive sign for the Fourier kernel / outward propagating waves? [closed]

I am not a physicist but rather an engineer / mathematician, so I've always wondered why is it that physicists use the positive sign convention in the forward Fourier transform. That is, in all of my ...
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1answer
104 views

Maxwell equations in 2+1 D

I have a problem with the Maxwell equations in (2+1) dimensions using differential form. Following J. Baez "Gauge Fields, Knots and Gravity" page 93 (or any other book), the equations are ...
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83 views

What's the work done by a spring on a block when it moves from extreme to mean position?

I really don't know where am I doing it wrong, but block when it moves towards mean position displacement will be along the force right, so the force acting on block will be $+fxdx$ Integrating we ...
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1answer
69 views

Is the unit symbol written twice when using the +\- symbol?

When notating error using the $\pm$ symbol, are the units only ever included at the end? For example: 10.2 $\pm$ 3.2 m rather than 10.2 m $\pm$ 3.2 m This seems to be correct though I ...
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1answer
56 views

Why is a satellite's GPE negative? [duplicate]

Okay, so the formula for Gravitational Potential Energy (GPE) of satellites is: $$ U=-GmM/d$$ Mass and distance can't be negative, and $G$ is constant that is not negative. Why is a satellite's GPE ...
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57 views

Work done should be positive but it is coming out to be negative? [closed]

I have described a question in which this problem arises in the image below:
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2answers
93 views

Why specify the state of a particle in terms of position and momentum not velocity?

Often a particle's state is expressed in terms of position and momentum. Why not position and velocity? Momentum has a connection to the particle's mass which I wouldn't say is so important to the ...
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2answers
72 views

Complex conjugation of Weyl Spinors

Let $\chi$ be a left-handed Weyl spinor transforming as $$\delta\chi=\frac{1}{2}\omega_{\mu\nu}\sigma^{\mu\nu}\chi.$$ In my lecture notes it is explicitly stated that complex conjugation interchanges ...
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1answer
38 views

Non-linear pendulum (Whittaker's treatise on analytical dynamics of particles)

Reading through Whittaker's "treatise on the analytical dynamics of particles and rigid bodies" I have a question regarding his analysis of the simple nonlinear pendulum at chapter IV. At some point ...
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1answer
208 views

Gradient, divergence and curl with covariant derivatives

I am trying to do exercise 3.2 of Sean Carroll's Spacetime and geometry. I have to calculate the formulas for the gradient, the divergence and the curl of a vector field using covariant derivatives. ...
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2answers
64 views

What is time measured against? [duplicate]

Today I was observing a clock and its movement, every second is an exact second on every clock. I was making a comparison between a second and a meter. I know in France there is a metal stick one ...
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1answer
59 views

Definition of primary fields actually leads to a Witt algebra with a minus sign?

Let's take as an example Di Francesco et al. but every source I am aware of is doing the same. First of all, the Virasoro algebra is usually defined as $$[L_m,L_n] = (m - n)L_{m+n} + \frac{c}{12} m ...
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1answer
213 views

Electric field for concentric spheres

I have a couple clarifying questions: (A) in $E=kq/r^2$ for the area between a sphere inside another spherical shell, the sphere inside is considered a point charge. However, the sphere inside has a ...
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2answers
84 views

Why isn't the work minus the potential energy when bringing a charge in from infinity?

This is an example in my physics textbook, and there is just one step that I don't understand. Two point charges are located on the x-axis, $q_1 = -e$ at $x = 0$ and $q_2 = +e$ at $x=a$. Find ...
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2answers
120 views

How do you choose direction of moment of inertia?

If a car is accelerating forward from rest with no air resistance while weight and normal forces act on the wheels, in which direction is the moment of inertia? Is it positive, clockwise or anti ...
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2answers
324 views

Rule sign for concave and convex lens?

I am just totally confused about the rule sign of convex and concave lenses. The general formula: $1/v-1/u=1/f$ Is okay but when solving problem sums sometimes $v$ becomes negative sometimes $u$ and ...
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7answers
9k views

Why does public mains power use 50-60 Hz and 100-240 V?

Is there a physical reason behind the frequency and voltage in the mains electricity? I do not want to know why exactly a certain value was chosen; I am rather interested to know why that range/order ...
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2answers
121 views

Why is the charge of a proton positive? [duplicate]

Is there a reason that a proton has a positive charge while an electron has a negative charge? Are these just names that were given to the charges or was there a reason for making a proton have a ...
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75 views

Multiple Definition For Gravitational Potential Energy?

This may just be a simple Misconception Question, here goes: Definition for Gravitational Potential Energy: The work done by gravity to pull an object to the ground. ...
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1answer
47 views

Lower Voltage = Higher Potential?

I am doing problems from a textbook and one of the questions asks to determine where the higher potential is. (b) Find the potential difference between the points on the axis at and which of ...
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2answers
1k views

What's the difference between a positive and a negative current?

Say I have a wire, and I connect a current source on its left end, and a ground to its right end. Then using my power supply I source a positive current, does this mean that electrons will move from ...
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3answers
188 views

Should these be called “weights” or “masses”? [closed]

Yeah, those circular metal disks. Weights or masses? I call them weights because when I attach them to a spring I'm interested in their weight, but it feels odd saying a "Pick up the 100g weight". ...
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26 views

Index Placement for Spinors in Relativity

This may ultimately be a silly question, but a pedantic mind like mine gets tied into knots over differing notation. (Disclaimer: I'm a mathematician.) Let $\mathbb{W}$ be a complex two-dimensional ...
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1answer
94 views

What is meant by saying the work done by a conservative force is -(change in PE)?

I read through all related questions, and they are almost the same, but I still didn't understand this and so am asking again. What is meant when we say that the work done by conservative force is = ...
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1answer
170 views

How do you derive Fleming's left hand rule?

How do you derive Fleming's left hand rule? What is the theoretical explanation for the directions of the magnetic field, current and the force on the current for being oriented in that way relative ...
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33 views

Usage of delta operator [duplicate]

So I've always thought that "$\Delta$" when applied to an n-tuple or scalar was the change of that n-tuple or scalar relative to a previous state in time and proportional to the amount of time or ...
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1answer
48 views

What justifies adding phasors' vertical components

I learned that, when superimposing two waves on top of each other to calculate the resulting wave's amplitude, it's helpful to use phasors. From what I gathered, phasors are vectors originating at the ...
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1answer
367 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and ...
3
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2answers
185 views

Why in electrostatics is $dV=-E.dr$ but in electromagnetic induction, $EMF=+E.dS$?

In electrostatics we learned that $$dV=-E.dr$$. I understood the derivation which was used to derive this. Now when I have come to Electromagnetic Induction,I see that when there is a time varying ...
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3answers
347 views

Are quantum numbers always integers?

Quantum numbers are integers for lots of systems. For example, for a particle in an infinite well $$E_n = E_1 n^2 \text{ with } n = 1, 2, 3\ldots$$ for a quantum harmonic oscillator $$E_n = (n + ...
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1answer
46 views

Do I have some freedom when I define the quantum SHO ladder operators? [closed]

I tried to solve the quantum harmonic oscillator via the operator method. After doing it and looking up the solution I noticed that for some reason the ladder operators got an additional factor of (i) ...
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142 views

Schrodinger's equation with negative sign

In time dependent Schrodinger's equation as given in Schrodinger's lecture (Four Lectures on Wave mechanics, Blackie & Son, 1949, pg22) he arrives at $$\nabla^2\psi-\frac{4 \pi m ...
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General proof of formulas of geometric optics?

In most lf textbooks formulas of geometric optics like lens maker formula and base formula for that are proven (or rather verified from my point of view) by taking specific case (ray diagram) and ...
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105 views

Can the sign of metric change physics?

Consider the Lagrangian of a massless real scalar (classical field) in $\phi(\textbf{x},t)$: $$\mathcal{L}=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ The Hamiltonian density in two different ...
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Why is friction force negative in ice skater problem?

A 68.5 kg skater moving initially at 2.40m/s on rough horizontal ice comes to rest uniformly in 3.52s due to friction from the ice. What force does friction exert on the skater? I am not really ...
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1answer
33 views

Zero of Electric Potential Energy

When you have a positive charge and a negative charge, the line that cuts perpendicularly between their separation distance is an equipotential line of 0 volts. The math indicates that at that point, ...
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1answer
89 views

Rocket equation derivation, question about signs

My question is about signs in the derivation of the rocket equation. Considering a rocket of mass $m$, its momentum at time $t$ is $p(t)=mv$. At time $t+dt$ it ejects a quantity $dm$ so its momentum ...