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2
votes
1answer
26 views

Question about the expression of Witten Index

I am studying supersymmetry by myself. I do not understand the expression of Witten index, which is ${\rm Tr}(-1)^{F}$. What does it mean by writing $-1$ to the power of an operator $F$? Is this ...
1
vote
1answer
112 views

What does $L^2(S^1,\mu_H)$ mean?

It's a Hilbert space, $\mu_H$ stands for the Haar measure on $U(1)$, but what does $S^1$ mean? I found it in one of my quantum mechanics books which approaches from a very 'mathematical' way.
1
vote
4answers
51 views

Same equation, different meanings

I went into a physics classroom today and saw this equation written on the board: $$ E = \frac \sigma \epsilon $$ At first I thought it referred to the electric field $ E $ between 2 parallel plates ...
1
vote
2answers
32 views

Notation of complex valued atomic orbitals

Atomic orbitals are usually labeled $1s$, $2p_x$, $2p_x$, $2p_z$ and so on. These wave functions are defined to be real valued. The original wave functions are complex valued. The $2p_x$ orbital is ...
3
votes
2answers
61 views

Computational advantages of various notations for electromagnetism [closed]

Most undergraduate electromagnetism classes and textbooks use vector notation to describe Maxwell's equations. However, there are other notations like differential geometry and geometric calculus ...
1
vote
0answers
32 views

Basic Vector field question about notation [closed]

I am taking my first class in electrodynamics and the problem I am working on has a notation I have never seen before Consider a vector field of the form $V= f(x)y + g(y)x$ Is this essentially the ...
1
vote
3answers
133 views

Physical Explanation of Quantum Mechanics Notation? [closed]

CLARIFICATION: I just don't understand what the notations below mean and how to use them. ============= I just started taking QM, and the new notation is quite confusing. While the math makes a ...
5
votes
1answer
70 views

What do term symbols with a half-integer “$L$” like $^3[3/2]_{1/2}$ mean?

Atomic term symbols are used to notate the angular momentum content of the electronic states of an atom, and are normally written down as $$^{2S+1}L_J$$ where the state has total spin $S$, spin ...
1
vote
1answer
77 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 ...
4
votes
0answers
39 views

What is $\mathrm{U(1)}$ vector and axial?

In hadron physics we talked about $\mathrm{U(1)_V}$ (vector) and $\mathrm{U(1)_A}$ (axial) as well as $\mathrm{SU(3)_L}$ (left) and $\mathrm{SU(3)_R}$ (right). There are certain relations between them ...
1
vote
1answer
66 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 ...
3
votes
1answer
129 views

Repeated index in covariant derivative using abstract index notation

The same index showing up twice in the charge conservation law $\nabla_a j^a = 0$, as stated using abstract index notation, highly confuses me. If we chose a coordinate basis ...
-2
votes
1answer
82 views

Why does the symbol have an arrow? [closed]

What does the arrow in the symbol mean? Does it mean that it is a variable voltmeter and ammeter?
0
votes
1answer
21 views

Klein-Gordon equation probability density and current

After multiplying the K-G equation and its conjugate by the field, I have this equation $$\phi^*\frac{\partial^2 \phi}{\partial t^2}- \phi\frac{\partial^2 \phi^*}{\partial t^2}+\phi ...
1
vote
3answers
158 views

Difficulty in understanding ket vectors in quantum mechanics

$\newcommand{\k}[1]{\left | #1 \right\rangle }$ Dirac in his book The Principles of Quantum mechanics states that: To proceed with the mathematical formulation of the superposition principle we ...
0
votes
1answer
47 views

Euler-Lagrange for simple scalar field (Peskin & Shroeder)

I'm reading Peskin & Schroeder and they give as a simple example the Lagrangian $$\mathcal{L} = \frac{1}{2} (\partial_\mu \phi)^2$$ First of all, I'm guessing that $(\partial_\mu \phi)^2$ is ...
2
votes
0answers
23 views

What is the origin of the naming convention for the various branches in vibration-rotational spectroscopy?

In vibration-rotational spectroscopy, the different spectral lines are grouped into branches for different changes in the total angular momentum, i.e. $$ \begin{array}{rrrrrr} & \mathrm{O} & ...
0
votes
1answer
50 views

Calculus of Variations - Virtual displacements

I am currently reading "The Variational Principles of Mechanics - Cornelius Lanczos", in which the author talks about the variation of a function $F(q_1, q_2, \dots q_n)$ where $q_1, q_2, \dots q_n$ ...
3
votes
2answers
65 views

What exactly is an arbitrary parameter?

I was reading the article Turning Points: A meeting with Enrico Fermi by Freeman Dyson (available e.g. here), and I had a question about Dyson's use of the term 'arbitrary parameter'. More ...
1
vote
0answers
47 views

What visual methods Stephen Hawking developed for visualizing equations? [closed]

The Wikipedia page about Stephen Hawking states: As he slowly lost the ability to write, he developed compensatory visual methods, including seeing equations in terms of geometry. The physicist ...
1
vote
1answer
56 views

Is it right to write $\varepsilon_{ijk} \delta_{jl}=\varepsilon_{ilk}$? (indices notation)

Consider the $l$ component of vector position $\vec{r}$, $r_l$, and the $i$ component of angular momentum $\vec{L}$, $L_i$. We have that $$L_i=[r\times p]_{i}=\varepsilon_{ijk}r_jp_k$$ ...
0
votes
1answer
39 views

Expanding the Ricci tensor by summing over indices

I had an attempt at deriving the Schwarzschild metric. This is a 4-dimensional problem where the indices are being summed from 0 to 3. I got up to the part where I calculate the Ricci tensor which is ...
3
votes
1answer
48 views

What do variables with a numerical subscript mean in astronomy?

I am wondering if anyone can help me understand what a variable with a subscript on it means. The paper: B.F. Schutz, Nature 323, 310 (1986). The variable in question is this distance $r_{100}$ and ...
4
votes
3answers
277 views

Dirac notation - specific acting orientation for operators

I have this doubt: Imagine two operators $A$ and $B$ and the state $\psi$. I know that the following statement is true: $$\langle\psi| A|\psi\rangle^*=\langle\psi| A^\dagger|\psi\rangle$$ But ...
0
votes
1answer
47 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 ...
3
votes
1answer
118 views

What does a line above a commutator, e.g. $\overline{[x, H]}$ mean?

What does this notation mean in relation to quantum mechanics? $$\overline{[x,H]}\qquad\text{or}\qquad\overline{[p,H]}\tag{1}$$ I know $[x,H]$ is just the commutator e.g $xH-Hx$, and the ...
1
vote
1answer
114 views

Difference between $dM/dt = 0$ and $\partial M/\partial t=0$ [duplicate]

$\frac{dM}{dt} = 0$ represents a constant of motion $M.$ Why not $\frac{\partial M}{\partial t}$ represent a constant of motion $M$?
1
vote
1answer
99 views

Does $g_{\mu\mu}$ in an expression follow the Einstein summation convention?

Assume that I have the expression for a Christoffel symbol: $$ \Gamma^\mu_{\alpha \beta}=\frac{1}{2}g^{\mu \lambda}(\partial_\alpha g_{\beta \lambda}+\partial_\beta g_{\alpha \lambda} - ...
0
votes
1answer
101 views

QM angular momentum commutator solution using index notation

there are a few answered questions regarding the commutator of any two 3D angular momentum operator components $[L_i, L_j]$ , however, I am trying to go through fully using index notation so that I ...
0
votes
1answer
42 views

What does dimensionless quantity 'number of $g$' mean?

I am doing data analysis in which I found a quantity named "no. of $g$". I don't know what it means or what is its usage. Look at the image below. I want to know the meaning and usage of "no. of ...
2
votes
1answer
47 views

What does the zero in the differential operator $\partial_0$ mean?

I have noticed the differential operator $\partial_0$ in a lot of equations whilst studying quantum field theory. I am used to the notation $\partial_x$ meaning $ \frac{d}{dx} \\\\ $ etc. but just a ...
1
vote
0answers
55 views

Is $d^3r$ the same as $dV$, the volume element?

I've seen the term $d^3r$ being used instead of $dV$. Are they exactly the same? Do they have a different connotation?
1
vote
4answers
198 views

Trying to understand inner product notation

I I'm taking a QM course and I'm trying to make sense of why observables are sometimes conjugated for no apparent reason in their inner products. Right now I'm watching Dr. Susskind's lecture on ...
2
votes
0answers
30 views

Nomenclature of nuclear excited states

I read in an online portal about $^{112}$Sn nucleus making a transition from $0_{g.s}^{+} \rightarrow 2_{1}^{+}$ state. Also, some higher excited states were named as $0_{2}^{+}$, $3_{1}^{-}$, etc. ...
0
votes
0answers
25 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 ...
23
votes
5answers
3k views

Is there a rigorous definition of 'much greater than'?

I have encountered $\gg$ in many physics text books where it's used as a relation between constants or functions but in none of the text books I have read is it properly defined anywhere. If $A \gg ...
0
votes
1answer
113 views

What is this equation?

A while ago I came across this funny little bit of graffiti: What is this equation? What does it mean? What are the symbols? The notation reminds me of quantum mechanics, so I am tagging ...
0
votes
1answer
42 views

Expressing operator in bra-ket notation, knowing just matrix elements

This is in context of unitary transformations between two othonormal bases $\{ | e_i \rangle\}$ and $\{ | \bar{e}_i \rangle\}$. I define $U$ by $$U| e_i \rangle = | \bar{e}_i \rangle $$ Now I can ...
1
vote
2answers
53 views

Confusion about proportionality in Kepler's 3rd law of planetary motion

I was reading about Kepler's third law on planetary motion and came across in two books $R^3\propto T^2$ and in the other $T^2\propto R^3$. So, I asked the following question on Math.SE. If both mean ...
0
votes
0answers
32 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 ...
0
votes
1answer
82 views

What is the difference between $\frac{DA^\mu}{D\lambda}$ and $\frac{DA^\mu}{d\lambda}$?

I earlier asked this question How can you have $\frac{DA^\mu}{d\tau}$? I am now wondering: What is the difference between $\frac{DA^\mu}{D\lambda}$ and $\frac{DA^\mu}{d\lambda}$? In the linked ...
0
votes
1answer
87 views

How can you have $\frac{DA^\mu}{d\tau}$?

If a covariant derivative is given by: $$D_\nu A^\mu=\partial_\nu A^\mu +\Gamma^\mu_{\nu \lambda} A^{\lambda}$$ Then how does $\frac{DA^\mu}{d\tau}$ make any sense? Since there are no 'differentials' ...
2
votes
0answers
93 views

Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$ [closed]

I'm learning Dirac notation, and I found the following exercise: Verify that if $$|\psi \rangle=\sum_i a_i |i\rangle, \tag{1}$$ (where $a_i=\langle i|\psi \rangle$), with $$\langle i|j ...
0
votes
1answer
245 views

What is the recommended symbol for Volumetric flow rate? [closed]

I'm currently working on a paper with a mathematician. He always writes $\dot Q$ as well as $\dot V$ for volumetric flow rate and claims both are standard notations. Till now I always used $Q$ ...
1
vote
0answers
103 views

Perturbation theory, eigenvalues and eigenvectors for degenerate case (1st order)

I was trying to understand the perturbation theory, but I was lost in the notation... I have understood that I have to identify the unperturbed kets that are degenerated and find the matrix $V$, ...
4
votes
2answers
216 views

Tensors, indices and matrix notation - is there a common convention?

For a tensor named T with two indices, there are four possibilities: $T_{ij}$ , $T_i^{\ j}$, $T^i{\ _j}$ and $T^{ij}$. Is there a common convention as to how these tensors would be represented as ...
3
votes
1answer
43 views

What does the g mean after the isotope given?

I'm familiar with notation such as Sc-44m standing for the meta stable state of Sc-44. What does Sc-44g mean? There are a few examples of this notation; here's one: ...
4
votes
2answers
534 views

Schroedinger equation for hydrogen atom

I have got a problem understanding the meaning of the Laplace operator in the Schrödinger equation for the hydrogen atom. $$\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} ...
0
votes
1answer
66 views

Basic Notation Help Needed : Classical Mechanics, Unit Vectors

Can someone help me with some basic notation? Here's a situation where I'm surely missing some trivial piece of the puzzle: Example 1: given $W = \frac{1}{2}cpAv^2$ (air resistance), adding a unit ...
0
votes
1answer
50 views

Time evolution of expectation value of an operator

I'm studying QM from Sakurai, and I have a doubt regarding the proof given that in the case of time independent Hamiltonian the expectation value of an observable doesn't change with time. The ...