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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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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596 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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4answers
2k views

Why is potential energy negative when orbiting in a gravitational field?

I had to do a problem, and part of it was to find the mechanical energy of satellite orbiting around mars, and I had all of the information I needed. I thought the total mechanical energy would be the ...
3
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1answer
81 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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2answers
92 views

Electric potential energy and signs

I know that electric potential is negative near a negative charge and positive near a positive charge. But does this mean a small positive 'test' charge has a negative electric potential energy near a ...
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1answer
33 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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2answers
53 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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1answer
65 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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1answer
5k views

Direction of Potential Gradient & Electric field

Potential gradient is the negative of the electric field. Does the negative (here) means that its direction is opposite to electric field? If it does mean this, How is the direction of the potential ...
2
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2answers
131 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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2answers
62 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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4answers
220 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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0answers
45 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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2answers
39 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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1answer
216 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the $z$-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to ...
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4answers
6k views

Why the direction of dipole moment is from negative charge to positive charge?

An electric dipole moment is defined as $p = q\times 2d$. How to understand it physically? Why the direction of the electric dipole moment is from negative charge to positive charge?
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1answer
64 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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39 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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1answer
47 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} ...
2
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2answers
598 views

Euler angle: space-fixed vs body-fixed axes

I am sooo confused!! Between active and passive, intrinsic and extrinsic, vectors and basis .... Stipulate that we stick to active rotations only. Then Standard derivation of $R(\alpha, ...
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2answers
72 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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1answer
70 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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2answers
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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2answers
92 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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0answers
11 views

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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1answer
59 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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3answers
2k views

When an object moves downward, is its height negative?

The question is: A ball is thrown directly downward with an initial speed of 8.00m/s from a height of 30.0m. After what time interval does it strike the ground. So I went through the problem ...
3
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0answers
32 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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3answers
11k views

Thermodynamics - Sign convention

I use the sign convention: Heat absorbed by the system = $q+$ (positive) Heat evolved by the system = $q-$ (negative) Work done on the system = $w +$ (positive) Work done by the system = $w -$ ...
3
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2answers
136 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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1answer
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?
3
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2answers
113 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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2answers
99 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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1answer
91 views

Gauge pressure clarification

Is gauge pressure always zero-referenced against ambient air pressure? Or is it referenced against the sum of all pressures acting on a fluid, which usually just happens to be ambient air pressure? ...
7
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1answer
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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1answer
57 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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4answers
419 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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2answers
63 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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7answers
12k views

Why is the charge naming convention wrong?

I recently came to know about the Conventional Current vs. Electron Flow issue. Doing some search I found that the reason for this is that Benjamin Franklin made a mistake when naming positive and ...
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5answers
5k views

Why do we test electric fields with positive charges and not negative ones?

Is there any difference between using a positive versus a negative charge to test an electric field?
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1answer
55 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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2answers
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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2answers
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Is negative 20 psi / 1.5 bar possible?

If I understand correctly, negative pressure usually means relative pressure: the difference between inside and outside. If outside is normal (1 bar, 15 psi, 100 kPa etc), how low can the (relative) ...
2
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1answer
93 views

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
133 views

Getting the Lagrangian from the action in curved spacetime

Suppose I have this action: $$ S = \int \mathrm d^4 x\sqrt{-g}\times \text{something}$$ where $g$ is the determinant of the metric. Should I take the Lagrangian to be: $$ \mathcal L = \sqrt{-g} ...
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2answers
220 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: ...
2
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1answer
295 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.