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3
votes
2answers
241 views

Tensor index notation with e.g. square brackets

I want to learn playing with indices and some notation in General relativity. But in every book just is used this notation. I know upper and lower but I don"t know the meaning of some combination of ...
0
votes
2answers
58 views

Can you set all dummy indices equal to each other? [closed]

According to the Einstein summation convention, can you set all dummy indices within a same expression equal to each other? Example, if both α and β are dummy indices in a same expression can you set ...
1
vote
3answers
72 views

What is the $ds^2$ notation in relativistic physics?

Could someone please explain me intuitively how $ds^2$ represents distance in relativistic physics?
0
votes
1answer
55 views

Using the Metric in Book Gravitation (MTW)

Here is the whole Box 2.2, at Page 55 The dot behind the second $-p^2$ seems to be a "planck mass" (sarcasm, flea egg) or just the book's style to use Dot behind the equations. So the Equation is ...
0
votes
2answers
33 views

Sig Figs, Combined Operations

Using the sig fig rule for addition / subtraction seems to break in certain circumstances. For example (I'm using underlines to show sig figs): $\underline{66}+\underline{66}-\underline{1.3}\times ...
0
votes
0answers
72 views

Need some help understanding Relativistic Notation

My question originates from what is done in the book on Quantum Field Theory book by Mark Srednicki on page 21 (if anyone has it). So say you have an inertial frame that is represented in the ...
0
votes
2answers
112 views

Derivation of Schrodinger's wave equation

To derive $$i \hbar \frac{\partial}{\partial t} \psi = H \psi,$$ we start with $$i \hbar \frac{\partial}{\partial t} |\alpha \rangle = H| \alpha \rangle$$ and then multiply by $\langle x|$ on the ...
3
votes
1answer
100 views

Working with indices of tensors in special relativity

I'm trying to understand tensor notation and working with indices in special relativity. I use a book for this purpose in which $\eta_{\mu\nu}=\eta^{\mu\nu}$ is used for the metric tensor and a vector ...
5
votes
1answer
82 views

Meaning of integral signs in classical physics

When I began studying physics, by myself, on a universitary textbook, F.J. Keller, W.E. Gettys , M.J. Skove, Physics, about one year ago, I believed that all the integrals that I was going to find in ...
2
votes
1answer
35 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
119 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
58 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
39 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
68 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
35 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
139 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
92 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 ...
3
votes
1answer
344 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 ...
3
votes
0answers
47 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
68 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
167 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 $\{\partial_\rho\}_{\...
-2
votes
1answer
125 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
24 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 \nabla^2\phi^*-\...
1
vote
3answers
166 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
57 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
28 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
67 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
88 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
1answer
63 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
41 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
83 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
311 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
70 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
136 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 anti-...
1
vote
1answer
131 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
119 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} - \partial_\...
0
votes
1answer
167 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
59 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
56 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
87 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
518 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
38 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
27 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
115 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
49 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
67 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
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 $\...
0
votes
1answer
86 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
91 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' ...