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37
votes
1answer
5k views

Differentiating Propagator, Greens function, Correlation function, etc

For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
30
votes
3answers
5k views

Mathematically-oriented Treatment of General Relativity

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ...
26
votes
8answers
2k views

Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
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 ...
23
votes
2answers
1k 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 ...
22
votes
8answers
7k views

Is there a symbol for “unitless”?

I'm making a table where columns are labelled with the property and the units it's measured in: Length (m) |||| Force (N) |||| Safety Factor (unitless) ||| etc... I'd like not to write "unitless" ...
16
votes
4answers
3k views

What does Peter Parkers formula represent?

Okay, so the trailer for the new Spider Man movie is out and appearently our friendly physicist from the neightborhood came up with something. However I can't find out what this is. Transcription: ...
16
votes
2answers
8k views

Difference between $\Delta$, $d$ and $\delta$

I have read the thread regarding 'the difference between the operators between $\delta$ and $d$', but it does not answer my question. I am confused about the notation for change in Physics. In ...
14
votes
1answer
2k views

Meaning of an image on Feynman's shirt

Is there any physical meaning of the image on Feynman's T-shirt?
13
votes
2answers
344 views

Searching books and papers with equations

Sometimes I may come up with an equation in mind, so I want to search for the related material. It may be the case that I learn it before but forget the name, or, there is no name for the equation ...
11
votes
2answers
509 views

Tensor product in quantum mechanics?

I often see many-body systems in QM represented in terms of a tensor products of the individual wave functions. Like, given two wave functions with basis vectors $|A\rangle$ and $|B\rangle$, belonging ...
10
votes
5answers
2k views

What exactly is $\hat{\psi}^\dagger(x)$? An operator or a function?

I've recently read Cohen-Tannoudji on quantum mechanics to try to better understand Dirac notation. A homework problem is giving me some trouble though. I'm unsure if I've learned enough yet to ...
10
votes
4answers
929 views

How to indicate that a unit is dimensionless [duplicate]

For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below: ...
9
votes
3answers
274 views

Why is the $dx$ right next to the integral sign in QFT literature?

I've noticed that in QFT literature, integrals are usually written as $\int \!dx ~f(x)$ instead of $\int f(x) dx$. Why?
9
votes
2answers
3k views

Derivative with respect to a vector is a gradient?

I've encountered in some books (and even completed an exercise from the Goldstein by using it), a strange notation that seems to work exactly like a gradient, I have tried to look for an explanation ...
9
votes
1answer
184 views

Group notation $\otimes$ and $\oplus$ used for representations of quarks and mesons

I've been trying to figure out this statement from the PDG quark model summary (PDF). Following $\mathrm{SU}(3)$, the nine possible $q\bar{q}′$ combinations containing the light $u$, $d$, and $s$ ...
8
votes
3answers
2k views

Is there a physical or mathematical symbol for “happens when”?

How would you denote symbolically, "Equilibrium happens given that ..."?
8
votes
5answers
2k views

Is 'amp' a technically invalid term?

I've been told to use the term ampere in exams and class (I'm in high school), instead of amp as it's not a valid unit, although I've been using the amp for years along with all of my friends who do ...
7
votes
4answers
794 views

How are electric flux calculations not double integrals?

A disk of radius 0.10 m is oriented with its normal unit vector $\hat{n}$ at 30$^{\circ}$ to a uniform electric field $\vec{E}$ of magnitude 2000 N/C. What is the electric flux through the disk? ...
7
votes
4answers
988 views

Is there a recognised standard for typesetting quantum mechanical operators?

Firstly, I wasn't sure exactly where to put this. It's a typesetting query but the scope is greater than $\TeX$; however it's specific also to physics and even more specific to this site. I've ...
7
votes
1answer
822 views

Difference between $\partial$ and $\nabla$ in general relativity

I read a lot in Road to Reality, so I think I might use some general relativity terms where I should only special ones. In our lectures we just had $\partial_\mu$ which would have the plain partial ...
7
votes
1answer
282 views

ket vector with two “entries”

This is a very simple question. I am learning about angular momentum. In my lecture notes, the symbol $|\lambda,m_l \rangle$ was defined as a eigenfunction of a central potential. Two assumptions are ...
7
votes
1answer
342 views

How are the definitions of a coherent state equivalent?

I am trying to understand coherent states. As far as I could find there are three equivalent definitions and in general many sources start from a different one, still I fail to see their equivalence. ...
7
votes
1answer
244 views

Why is the Lane-Emden equation written the way it is as opposed to some other typical form?

The Lane-Emden equation is typically written as $$\frac{1}{\xi^2} \frac{d}{d\xi} \left( \xi^2 \frac{d\theta}{d\xi} \right) = -\theta^n,$$ which makes sense given the derivation on the Wikipedia page. ...
7
votes
2answers
4k views

Derivatives of operators

How do derivatives of operators work? Do they act on the terms in the derivative or do they just get "added to the tail"? Is there a conceptual way to understand this? For example: say you had the ...
7
votes
1answer
568 views

Ж (“zhe”) in string theory?

I was just recently watching a TED talk about string theory, by Thad Roberts, and at around 11:10 into the video he mentions a constant for maximum spacial curvature called "zhe" (the Cyrillic symbol ...
7
votes
4answers
1k views

Are covariant vectors representable as row vectors and contravariant as column vectors

I would like to know what are the range of validity of the following statement: Covariant vectors are representable as row vectors. Contravariant vectors are representable as column vectors. ...
7
votes
2answers
426 views

Historical reason behind using $ν$ instead of $f$ to stand for frequency in the equation $E=hν$?

Normally, we use the letter $f$ to stand for frequency in equations. $$T = 1/f$$ $$v = \lambda f$$ $$Φ +E_k = h f$$ So I'm curious as why the letter $ν$ (nu) is used to represent frequency in the ...
6
votes
2answers
391 views

When can I use $\wedge$ instead of curl?

It seems in some circles the wedge product is used in preference to curl. I have a basic understanding of Green and Stokes' formula, I wish to use the $\wedge$ notation from now on. Can someone tell ...
6
votes
5answers
1k views

What is the meaning of following expression $C=\frac{\delta Q}{dT}$ mathematically?

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even Wikipedia) writes wrong expressions (from ...
6
votes
3answers
3k views

What does an integral symbol with a circle mean?

I have frequently seen this symbol used in advanced books in physics: $$\oint$$ What does the circle over the integral symbol mean? What kind of integral does it denote?
6
votes
5answers
190 views

Is $ds^2$ just a number or is it actually a quantity squared?

I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime ...
6
votes
2answers
558 views

Why isn't invariant notation common?

In principle, one can write quantities in a manifestly invariant - rather than covariant - fashion in e.g. special relativity. For example, rather than writing just $x^\mu$, we could write the basis ...
6
votes
3answers
360 views

Tensor product notation convention?

For two particle state, the Dirac ket is writren as $$\lvert\textbf{r}_1\rangle \otimes \lvert\textbf{r}_2 \rangle. $$ Then how do we write its bra vector, $$\langle\textbf{r}_1\rvert \otimes ...
6
votes
2answers
353 views

Why distinguish between row and column vectors?

Mathematically, a vector is an element of a vector space. Sometimes, it's just an n-tuple $(a,b,c)$. In physics, one often demands that the tuple has certain transformation properties to be called a ...
6
votes
1answer
132 views

$\pm$ (light-cone?) notation in supersymmetry

I would like to know what is exactly meant when one writes $\theta^{\pm}, \bar{\theta}^\pm, Q_{\pm},\bar{Q}_{\pm},D_{\pm},\bar{D}_{\pm}$. {..I typically encounter this notation in literature on ...
5
votes
4answers
814 views

Does bra-ket always assume all space?

One thing I never understood about the bracket notation is the limits of the inner product. Given $ \langle \psi∣\psi \rangle$, what can I say about the limits of integration of the inner product? ...
5
votes
3answers
108 views

which letter to use for a CFT?

In math, one says "let $G$ be a group", "let $A$ be an algebra", ... For groups, the typical letters are $G$, $H$, $K$, ... For algebras, the typical letters are $A$, $B$, ... I want to say ...
5
votes
2answers
431 views

A confusion about notation in Goldstein

On treating systems of particles, Goldstein starts with the consideration that whenever there are $k$ particles on a system, the $i$-th one obeys the relation $$\dfrac{d}{dt}{\bf p}_i = {\bf ...
5
votes
1answer
265 views

Why the speed of light is represented by $c$? [closed]

In almost every textbook, I've found that the speed of light is $c \approx 3 \times 10^8\: \mathrm{m/s}$. I wonder why it's just $c$ ?
5
votes
3answers
358 views

Error in books of conformal field theory?

If you look at the book Conformal Field Theory (by Philippe Francesco, Pierre Mathieu and David Senechal) or the lecture notes Applied Conformal Field Theory (by Paul Ginsparg), and many other places: ...
5
votes
2answers
732 views

Bra-ket notation and linear operators

Let $H$ be a hilbert space and let $\hat{A}$ be a linear operator on $H$. My textbook states that $|\hat{A} \psi\rangle = \hat{A} |\psi\rangle$. My understanding of bra-kets is that $|\psi\rangle$ is ...
5
votes
2answers
314 views

Beta decay: is it OK that the products are not electrically neutral?

I'm just learning about radioactivity, and there's one thing I'm unclear about. Take $\beta -$ decay, for example. Since a neutron splits into a proton and an electron (and an anti neutrino), but ...
5
votes
2answers
229 views

Unknown letter ℑ used in an equation

I need to write by hand the equation from the attached snapshot but I really don't know what letter is that seen in the front of square brackets [ . Can anyone help ...
5
votes
2answers
342 views

In what order should unit symbols appear?

I am trying to represent the result of a dimensional analysis calculation and I can't find an official document that lists the order that unit symbols should appear. For example, when I google ...
5
votes
1answer
84 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 ...
5
votes
2answers
662 views

What is the gamma five matrix $\gamma_5$?

This Wikipedia page explains that for each of the four main gamma matrices $\gamma^{\mu}$, you can find the covariant matrices $\gamma_{\mu}$ with the equation $\gamma_{\mu} = ...
5
votes
5answers
361 views

Why is the candela a base unit of the SI?

The candela is defined as The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540\cdot10^{12}$ hertz and that has a radiant ...
5
votes
1answer
554 views

Why is $L^2$ norm of the gradient called kinetic energy?

I'm reading Lieb-Loss's book 'Analysis', chapter 7. The authors refer to the following integral: $$\tag{1} \lVert \nabla f\rVert_2^2=\int_{\Omega}\lvert \nabla f(x)\rvert^2\, d^nx $$ as the kinetic ...
5
votes
1answer
80 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 ...