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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I can make the mechanical energy 0 or in fact anything. Is this normal?

We let the rope fall with $\alpha = \pi/2$ (no initial velocity). if I choose the original of potential energy as the picture indicates there, this means that: $$E_m = E_{pe} + E_c = \frac12mv^2 ...
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Which number is bigger, -1 or -2? Discuss your answers by applying examples in Physics [closed]

Which number is bigger, -1 or -2? Discuss your answers by applying examples in Physics. My answer: -1 is bigger than -2. \begin{align*} \ 3.4 \cdot\ 10 ^{-1} = 0.34 \\ 3.4 \cdot\ 10 ^{-2} = 0.034 ...
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80 views

Can a discoverer give the name he wants to his finding? [migrated]

Let's assume that some scientist discovers a phenomenon that has never been noticed before. He wants to write a paper about it but he doesn't want to constantly write "effect of change of some ...
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91 views

What is the point of the reduced Planck's constant $\hbar$ (h-bar)? - Why don't we just have Planck's Constant $h$?

I know that $ħ$ is $h / 2π$ - and that $h$ is the Planck Constant ($6.62606957 × 10^{-34}$ $Js$). But why don't we just use $h$ - is it that $ħ$ is used in Angular Momentum Calculations?
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665 views

Symbols of derivatives

What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for ...
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1answer
84 views

Confusion about the Kronecker delta symbol

I am not sure I understand what the short-hand anti-symmetrization means. I.e. I know that $$\delta_{cd}^{[ab]} ~=~ \frac{1}{2}(\delta_{c}^{a}\delta_{d}^{b} - \delta_{c}^{b}\delta_{d}^{a})$$ but how ...
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40 views

Raising and lowering indices of the Levi-Civita epsilon symbol in two dimensions

In two dimensions, what is the relation between $\epsilon^a{}_b$ and $\epsilon_{ab}$ where $a, b$ take the values $\{1,2\}$? By that I mean, how does the sign change in that case? In four dimensions ...
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57 views

Why is the potential energy for a body raised up by a height negative?

I tried deriving the potential energy of a body when raised at a height $h$ above the earths surface, using the formula: $$PE = -W_\text{conservative}$$ where $W_\text{conservative}$ is the work ...
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2answers
136 views

Solar spectrum units

Why is intensity $I$ on a graph of the solar spectrum always showed in units of $[\mathrm{W/m^2/nm}]$ instead of simply $[\mathrm{W/m^2}]$? (The y-axis on the graph.) It is apparently shown as ...
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46 views

What is “above” and what is “below” the surface of a sphere?

When studying Electromagnetism using D.J. Griffith's Introduction to Electrodynamics, the boundary conditions for the electric potential across a surface charge density are expressed using the normal ...
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41 views

How are the components of the spin vector defined?

How do we distinguish between the $x$, $y$ and $z$ spin components? More precisely: how do we define the $z$ component? (according to what, it is the $z$?) for measuring the $x$ component how ...
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2answers
80 views

My total potential energy?

The potential energy in a uniformed gravitational field is $mg \cdot \Delta h$. This assumes of course that $g$ doesn't change and only gives the difference in potential energy for $\Delta h$. How ...
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1answer
68 views

Treating the spinors as Grassmann numbers or as c-number objects

In the literature on supersymmetry, the following spinor summation convention is often used (eg. Wess & Bagger's book Supersymmetry and Supergravity) $$ \psi\chi = \psi^{\alpha}\chi_{\alpha} = ...
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4answers
223 views

What is the right order of creation operators?

I started to learn some basics of second quantisation and specifically its use in quantum chemistry. Currently I'm reading this book by Péter R. Surján, and here is small excerpt from it. If one ...
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1answer
48 views

Scalar products in the spinor helicity formalism

In A. Zee's book Quantum Field Theory in a Nutshell (2nd edition), Chapter N.2, page 486, the momentum $p$ is written as a $2\times 2$ matrix: $$ p_{\alpha\dot{\alpha}} = p_{\mu} ...
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2answers
77 views

Is four-current a vector or a vector density?

According to MTW, $$F^{\alpha\beta}{}_{;\beta} = 4\pi J^\alpha$$ and we can infer that the four-current must be an ordinary vector field because the left side is tensorial. But Wikipedia says that ...
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47 views

What is the zero of potential?

A satellite of mass $m$ is travelling at a speed $v_0$ in a circular orbit of radius $r_0$ around a fixed mass at $O$. Taking the zero of potential at $r=\infty$, show that the total energy of the ...
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40 views

Transposition of spinors

Suppose we have two 4-components Dirac spinors, that is two non commuting objects, $\psi$ and $\chi$. We know that: $ \bar{\psi} \chi= - \chi \bar{\psi} $ $ \bar{\psi} = \psi^{+} \gamma_0 $ $+=T*$ ...
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Kármán Line Definition from “Aeronautical Flight” (Mass, Area, and Lift)

This question asks something very similar, and the single following answer says, in part, that the balance is achieved when: $$ \frac{2m}{\rho(r) A C_L r} = 1 $$ [...] I note that the mass ...
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33 views

What are the proposed realizations in the New SI for the kilogram, ampere, kelvin and mole?

The metrology world is currently in the middle of overhauling the definitions of the SI units to reflect the recent technological advances that enable us to get much more precise values for the ...
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61 views

Why do we have different signs before the delta on the Klein-Gordon and the Dirac Green's function equation?

Let's read equation (2.56) on Peskin & Schroeder $$(\partial^2+m^2)D_R(x-y)=-i\delta^4(x-y).$$ Let's look now to equation (3.118) $$(i\gamma^{\nu}\partial_{\nu}-m)S_R(x-y)=i\delta^4(x-y).$$ ...
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138 views

The force of gravity is $F_g=+mg$ or $F_g=-mg$?

I have noticed that in my classical mechanics course and in the textbook I read for it, seem to ignore the gravitational force's position. For example, if we were dealing with a system with a ball of ...
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1answer
48 views

Why is there not a delta here in this formula about temperature changes

I have been taught and have seen this formula many times $$Q=m\cdot c\cdot\Delta T$$ Where $Q$ is the internal energy, $m$ is the mass, $c$ is the specific heat and $\Delta T$ is the temperature. ...
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68 views

Yukawa potential, which is correct?

Sometimes I see Yukawa interaction term written as $$-g\bar{\psi} i \gamma^5 \phi \psi$$ and other times as $$-g \bar{ \psi} \gamma_5 \psi \phi $$ Which is the correct form?
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117 views

The definition of transpose of Lorentz transformation (as a mixed tensor)

In the appendix of the textbook of Group Theory in Physics by Wu-Ki Tung, the transpose of a matrix is defined as the following, Eq.(I.3-1) $${{A^T}_i}^j~=~{A^j}_i.$$ This is extremely confusing for ...
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102 views

How do you pronounce $\vec{A} \cdot \vec{B}$ and $\vec{A} \times \vec{B}$? [closed]

I'm French. I would like to know: How do you pronounce $\vec{A} \cdot \vec{B}$ : "A scalar B" or "A dot B" ? How do you pronounce $\vec{A} \times \vec{B}$ : "A vectorial B", "A vector B", "A cross ...
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94 views

Weinberg QFT Chapter 5: gamma matrices consistency

Currently reading through Weinberg's QFT book (Vol. 1) [readable in parts here]. In his derivation of the causal Dirac field in Ch. 5, he chooses his gamma matrices as (5.4.17) \begin{align} ...
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60 views

Defining creation and annihilation operators

Creation and annihilation operators can be defined in several different ways, some more general than others. We usually choose to denote by $a$ the annihilation operator and by $a^\dagger$ the ...
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187 views

Why is there $1/2\pi$ in $\int\frac{dp}{2\pi}|p\rangle\langle p|$?

I'm reading Richard MacKenzie's lectures on path integrals and on page 7 he derives the propagator for the free particle as follows: $$ \begin{align} K &= \langle q'|e^{-iHT}|q\rangle \\ &= ...
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4answers
456 views

When does acceleration due to gravity equal positive/negative? [closed]

For example a projectile is launched at an angle. What would $a$ in $y=vt +.5at^2$ be? Let's say I choose up to be positive. How do you not confuse yourself whether to use positive or negative $a$?
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1answer
66 views

Why have they chosen this direction for current in the RC circuit? Seems pretty artificial to me

The thing is, they use this direction for current flow to derive the equation $-iR-\frac{q}{c}=0$ and then derive the equation $q(t)=Q_o e^\frac{-t}{RC}$ from the differential equation ...
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64 views

How to understand whether potential energy increases or decreases?

I am confused by how to deal with the negative sign in the equation $U=-GMm/r^2$ in the following problem: If the distance between two masses is tripled, then the magnitude of the gravitational ...
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1answer
58 views

Why is the focal length of a convex mirror negative?

According to the Cartesian sign convention, the focal length should be positive since the convex mirror forms a virtual image to the right of mirror (positive direction) when light comes from left. ...
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51 views

Standard Usage of the word “per”

Math guy here. What is the usual meaning of "x per y per z?" Is this (ignoring details) (x/y)/z or x/(y/z)? Sorry to be mundane.
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1answer
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Is it okay to Wick rotate to give the negative of the Euclidean metric? Also, could we make the space-like coordinates imaginary instead?

There are 2 parts to my question: 1) Say we choose the metric signature to be (-+++), as in the Wikipedia page. Then the invariant interval in Minkowski space is written: $ds^{2} = -(dt^{2}) + ...
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2answers
235 views

Work done against gravity [closed]

The work done against gravity is $mgh$, well at least that's what my textbook says. I have a question: I can apply a force say 50N, so total work done = $mgh + mah$. Where $ma$ = Force. But the truth ...
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2answers
51 views

How to define a convex surface in case of refraction?

In an exam at high school level, it was said, "ray goes from optically denser to rarer medium through a convex surface. It forms a real image...." this was a part of the question. Now I thought that ...
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1answer
40 views

When to pull out a negative sign from a variable

I get confused about when there should be a negative sign in certain equations or not. I will give three short examples (that I will make long with explanation) that show my confusion. Example 1: ...
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1answer
296 views

Why isn't the quark charge taken as primitive?

Why are electrons taken implicitly to be the elementary charge? It would save a lot of fractions in particle physics problems.
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1answer
837 views

Derivation of formula of potential energy by a conservative force [duplicate]

the formula for potential energy by a conservative force is given by: $$ F = -\nabla U(r), $$ which in one dimension may be simplified to: $$ F = -\frac{dU}{dx} .$$ My question is how is it ...
2
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0answers
61 views

Question about Origins in Galilean transformation

I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, ...
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2answers
31 views

Direction of current in concentric cylinders

Example 7.2 in David Griffiths E & M book (3rd edition) has a side view of 2 concentric cylinders, with smaller radius $a$ and larger radius $b$. The region in between $a$ and $b$ has ...
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125 views

Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) ...
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112 views

Kinematic sign convention

For example, if I drop a ball from a $50$ meters building, then I will consider the ground is $0$ meter downward is positive ( which makes gravity positive, downward velocity positive, etc) so ...
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99 views

Is there a difference in handwritten nabla $\vec{\nabla}$ with an overset arrow and typeset nabla $\nabla$?

According to some physicist at KIT it is usual to write the following when using pen and paper: whereas in typeset texts you write $\nabla$. Is that true? Are there sources for this convention?
3
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1answer
51 views

Why is electric potential positive?

If there is a positive charge $q$ at the origin of a coordinate system, the electric potential $\phi$ at a distance $r$ from $q$ is (by definition, if we take the point of zero potential at infinity): ...
2
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1answer
101 views

Potential energy of a dipole in a uniform electric field convention?

When finding the potential energy of a dipole in a uniform electric field, I was told by my lecturer that the convention is that the potential energy is 0 when the dipole moment and electric field ...
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69 views

Sign error in calculating the electric field of point charge

I have to determine the electric field of a point charge, I get a true result except for a sign. Here is my passages. $$\nabla \cdot e = \frac{\rho}{\epsilon}$$ $$e = - \nabla u$$ $$\nabla^2 u = - ...
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Optics - Derivation of Linear Magnification of Lens without Sign Convention [duplicate]

In some posts in this forum I've read that sign convention in optics is useful for making formula memorizing easier, and that we have to use sign convention again while applying the formulae to ...
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83 views

Explanation for $M{\ddot{r}}=-\nabla \phi$

Could someone please explain this equation $$M\bf {\ddot{r}}=-\nabla \phi$$ Where $\bf r$ is a position vector and $\phi$ is the potential function. Could someone brief explain the potential function ...