The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
1answer
40 views

How you call the constant $\alpha$ within the heat equation in general and in terms of electromagnetism?

The heat equation or diffusion equation does contain a constant $\alpha$. $$\frac{\partial u}{\partial t} - \alpha \nabla^2 u=0$$ How is it called? I'm interested in a general name which can be ...
3
votes
5answers
1k views

Why aren't units with powers, like cm³, surrounded by parentheses?

Since $\renewcommand{\unit}[1]{\,\mathrm{#1}} 1\unit{dm} = 10^{-1}\unit{m}$, it follows that $1\unit{dm^3} = 10^{-1} \times 10^{-1} \times 10^{-1} \unit{m^3} = 10^{-3} \unit{m^3}$. However, in ...
1
vote
1answer
87 views

Ricci curvature tensor, definition of symbols

So I know that $$R_{μν}:=R^λ_{μλν}$$ is the Ricci curvature tensor (where $R^λ_{μλν}$ is the Riemann Tensor). This is in Einstein's field equations: $$R_{μν}-\frac{1}{2}g_{μν}R=\frac{8πG}{c^4}Τ_{μν}$$ ...
1
vote
2answers
110 views

Tricks at manipulating creation/annihilation operators

Manipulation of terms in algebras different from the standard one (e.g. boolean algebra) can be a bit unnatural but there are always shortcuts that can help you. I was wondering if there is a list ...
4
votes
0answers
97 views

What decides the signs and coefficients of terms in superfield?

I'm working on a problem in 3d field theory and I'm confused about how to write the superfields. Specifically, I'm not sure if the signs and coefficients of terms are purely a matter of convention or ...
1
vote
1answer
67 views

Problem regarding quantum mechanical notation of photons

I have recently been reading about spontaneous parametric down conversion(SPDC). I do clearly understand the process. What has been intriguing lately is the notation. For those of you who are ...
6
votes
2answers
513 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 ...
0
votes
2answers
84 views

Minkowski metric and definition of coordinate differentials?

This is probably a really silly confusion I have about the definition of “coordinate differentials”, which I thought were things like $dx,dy,dz$ etc. The Minkowski line element ...
4
votes
2answers
140 views

Conventions regarding partial derivatives

Look at this expression: $$\frac{\partial}{\partial t} (V-\mathbf{v}\cdot\mathbf{A}).$$ This expression occurs in Griffiths EM book (4th ed, p.444). $V=V(\mathbf{r},t)$is the scalar potential, ...
7
votes
1answer
261 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 ...
1
vote
2answers
235 views

Tensor algebra doubt

Is it possible to take a tensor to the other side of the equation, and the tensor becomes its inverse(i.e contravariant becomes covariant and vice versa)? It is a stupid question, but It confuses me. ...
1
vote
1answer
139 views

Naming vectors in free body diagrams

Is there a convention for naming the vectors? Suppose there is a box on a table. I'm going to draw the forces acting on the box. So I focus on the box and ignore forces acting on the table, the ...
4
votes
2answers
1k views

What is the symbol Å?

I saw this symbol like: $$\lambda=3000\overset{\circ}{\text{A}}$$ and I don't know what this means. Is it a frequency? (since $\lambda$ is usually used for frequency)
0
votes
1answer
67 views

What does this sort of notation mean?

I'm revising for my exams at the moment and am seeing this notation everywhere Can anyone tell me what these mean?
1
vote
0answers
105 views

Index Notation Double Curl

My question is about Einstein notation. It does not matter the specifics of this example (the del operator could be another random vector), I just want to know if my assumption about notation is ...
3
votes
1answer
85 views

What does $\int_C V \,d\mathbf{l}$ mean?

What does $$\int_C V \,d\mathbf{l}$$ mean? I initially thought it was simply a line integral around $C$, that is, if $\mathbf{r}: [0,1] \longrightarrow \mathbb{R}^3$ is a paremetrization of $C$, then ...
3
votes
1answer
125 views

What is the difference between $\nabla _{\sigma} $ and $ \nabla^{\sigma}$?

What is the difference between: $\nabla _{\sigma} $ and $ \nabla^{\sigma}$? I've been told that the first is the covariant derivative, however I'm just starting a course on spacetime geometry and ...
0
votes
1answer
795 views

Index Notation with Del Operators

I'm having trouble with some concepts of Index Notation. (Einstein notation) If I take the divergence of curl of a vector, $\nabla \cdot (\nabla \times \vec V)$ first I do the parenthesis: ...
0
votes
1answer
107 views

Kronecker delta in inertial tensor

I feel confused in (11.9) how does the book prove the following identity: $$\sum\limits_{i} w_{i}x_{\alpha,i} \sum\limits_{j} w_{j}x_{\alpha,j} = ...
2
votes
3answers
190 views

Ordering of differential operators

If we write something like: $\partial_a X_{\mu} \partial^a X^{\mu}$ Does that mean the first derivative is only applied to the first X? ($\partial_a X_{\mu})( \partial^a X^{\mu}$) Or is the ...
7
votes
4answers
689 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? ...
0
votes
3answers
221 views

Lowering and Raising Kronecker Delta

When an index of the Kronecker-delta tensor $\delta_a^b$ is lowered or raised with the metric tensor $g_{ab}$, i.e. $g_{ab}\delta^b_c$ or $g^{ab}\delta_b^c$, is the result another Kronecker-delta ...
3
votes
1answer
310 views

Question on index notation and metric tensor

I found this expression in my SR notes: $$ (\Lambda^{-1})^{\lambda}_{\ \ \ \sigma} = g^{\lambda\mu}~\Lambda^{\rho}_{\ \ \ \mu} ~g_{\rho\sigma} = \Lambda_\sigma^{\ \ \ \lambda}$$ I know where it ...
1
vote
1answer
36 views

Uncertainty Definition QM

On my introductory course in Quantum Mechanics, the uncertainty of an operator $A$ in the state $\psi$ is defined by $$(\Delta A)^2_{\psi}=\langle(A-\langle A \rangle_{\psi})^2\rangle _{\psi}$$ I'm ...
21
votes
8answers
1k 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 ...
0
votes
1answer
77 views

Theoretical Physics Notation (Hamilton-Jacobi in the Relativistic Domain)

I am having trouble understanding how to solve some theoretical physics problems I have come across. Specifically how to convert the Hamilton-Jacobi equation: $$(\partial_\mu S+e A_\mu)^2=m^2$$ From ...
0
votes
1answer
306 views

Writing an arbitrary operator in bra-ket notation

An annoying fact about my physics textbook (Griffiths' Introduction to Quantum Mechanics) is that it introduces bra-ket notation without telling us how to use it. So I have a two-part question for SE: ...
1
vote
2answers
91 views

Why in the relativistic quantum mechanics $ \gamma_4$ name is not used instead of $ \gamma_5$?

I have seen in the in the Dirac equation $$\gamma_0,\gamma_1,\gamma_2,\gamma_3.$$ Then I have seen the definition of a new matrix $$\gamma_5=i\gamma_0\gamma_1\gamma_2\gamma_3.$$ Now my question is why ...
1
vote
1answer
86 views

The exact definition of conjugate momentum density

After checking various websites, I've seen the conjugate momentum density defined as either: \begin{align*} P_r ~=~ \frac{\partial \mathcal{L}}{\partial \dot{A}_r} \end{align*} or \begin{align*} P_r ...
0
votes
1answer
206 views

What does the $\Delta$ notation mean? E.g. for potential energy: $\Delta U$ vs just $U$? What is the difference?

I've seen in this article that potential energy is defined like this: $U=-\int _{\text{ref}}^r\overset{\rightharpoonup }{F}\cdot d\overset{\rightharpoonup }{r}$. However I've seen in other text books ...
2
votes
1answer
110 views

A simple question about matrix product with spinor indices

I have a big problem with dotted and undotted spinor indices. For example, suppose we have two convolutions: $$ \sigma^{\dot {a} a}F_{ab}, \quad \sigma^{\dot {a} a}F_{\dot {a} \dot {b}}, \quad F_{ab} ...
1
vote
1answer
193 views

Atomic nearest neighbor notation

I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says: Do you mean NN, NNN, etc., or NN, 2NN, 3NN? ...
5
votes
1answer
207 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 $c$ ?
1
vote
0answers
47 views

Are derivative indices summed in indicial notation?

A paper I'm reading uses indicial notation and the convention that $u_{j,k}$ means the derivative with respect to $x_k$. Which one of these interpretations are correct? $$A_{ijk}u_{j,k} = ...
0
votes
0answers
72 views

How should the implicit sum $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted?

$C$ is a 3x3x3x3 tensor. How should the expression $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted? This is my guess: $$ \sum_{i=1}^3\sum_{j=1}^3 \sum_{k=1}^3\sum_{l=1}^3 C_{ijkl}u_{i,j}u_{k,l} $$
0
votes
2answers
78 views

What is this form of notation called?

$$^{14}_6C \rightarrow ^{14}_7N + E^{-} + \bar{\nu}_e$$ Just curious!
2
votes
2answers
135 views

Affine connection notation

Can ${g}^{\mu\sigma}{\Gamma}^{\rho}_{\sigma\nu}$ be written as ${\Gamma}^{\mu\rho}_{\nu}$? If so how come this symbol never appears in any GR book?
2
votes
2answers
356 views

Bracket Notation on Tensor Indices

I know about the () symmetrisation and [] anti-symmetrisation brackets on tensor indices so long as they appear on their own, such as : $$V_{[\alpha \beta ]}=\frac{1}{2}\left ( V_{\alpha \beta ...
1
vote
2answers
167 views

Dealing with dirac notation with regards to different basis'

So this should be a pretty simple question. So we say that $\langle x | \psi \rangle = \psi(x)$. In other words $\psi(x)$ is the ket $|\psi\rangle$ expressed in terms of the $x$ basis. Now suppose ...
7
votes
1answer
365 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 ...
2
votes
0answers
212 views

Why the letter $B$ for magnetic fields? [closed]

Is there a reason behind the usage of this letter to represent magnetic fields, or is it a randomly made choice?
1
vote
1answer
119 views

What does $\nu$ mean in relativity?

I decided to teach myself relativity over the Christmas holiday, and I've gotten a bit stuck. Coordinates in space time can be defined by a collection of coordinates, $$ x^0 = ct \\ x^1 = x \\ x^2 = ...
6
votes
1answer
244 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. ...
6
votes
2answers
925 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 ...
4
votes
1answer
98 views

Higgs mechanism in QED

I'm trying to understand the Higgs mechanics. For that matter, I'm exploring the possibility of giving mass to the photon in a gauge-invariant way. So, if we introduce a complex scalar field: $$ ...
5
votes
3answers
284 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: ...
1
vote
1answer
72 views

Gradient of a two-component field

I have a two-component field: $$\phi(\vec{x}) = \left( \begin{array}{c} \phi_1(\vec{x}) \\ \phi_2(\vec{x}) \end{array} \right)$$ with $\phi^T = (\phi_1, \phi_2)$. And I am trying to evaluate: ...
0
votes
1answer
204 views

Notation in Quantum Mechanics

When we write equations in QM, in certain places, the wave function is represented as $\psi(x,t)$, which is the wave function in position space, and in some other places, it is written as $\Psi(t)$. ...
2
votes
1answer
60 views

What is the chemical symbol for Mu-mesic atoms?

Is there a convention for chemical symbols of mu-mesic atoms, at least for ones bound to light atomic nuclei?
1
vote
1answer
173 views

Understanding vectors in physics: notation

We have the formula for the Lorentz force $$\textbf{F} = q \space(\textbf{E} + \textbf{v} \times \textbf {B})$$ This is a simple formula you learn in high school, but I'm interested to self-study ...