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0
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1answer
41 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
51 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
175 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 ...
5
votes
4answers
513 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
25 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 ...
2
votes
1answer
101 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 ...
-3
votes
0answers
51 views

Why does $d$ mean? [migrated]

What do the $d$'s mean? I've seen them in other formulas as well.
4
votes
0answers
89 views

Tensor fields and vector bundles [migrated]

Let $M$ be a differentiable manifold, $TM$ and $T^*M$ a tangent and cotangent bundle of $M$ and let $\Gamma (TM),\ \Gamma (T^*M)$ be spaces of smooth sections of $TM$ and $T^*M$. Let $T_s^r (M)$ ...
1
vote
1answer
30 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 ...
13
votes
7answers
702 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 ...
3
votes
0answers
39 views

Group Theory - quotient group notation? [migrated]

What is the difference between the following terms: $\mathbb{Z}_{4}$ , $\mathbb{Z}/4$ and $\mathbb{Z}/{4}\mathbb{Z}$ ? I am pretty sure the first one is the cyclic group with addition modulo 4... ...
0
votes
2answers
29 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
73 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
84 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
38 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
105 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
57 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} ...
5
votes
1answer
156 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
37 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
64 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
69 views

What is this form of notation called?

$$^{14}_6C \rightarrow ^{14}_7N + E^{-} + \bar{\nu}_e$$ Just curious!
2
votes
2answers
111 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
124 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
72 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
174 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
90 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
97 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
161 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. ...
3
votes
2answers
169 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
71 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
188 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
64 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
104 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
52 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
103 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 ...
2
votes
1answer
72 views

What do physicists mean by ${g^{i}}_j$?

Maybe this is an idiot question, but in relativity I see a lot of ${g^{i}}_j$ for a metric tensor $g$. Is this just $$\delta^i_j ~=~ g(dx^i \sharp, \partial_{ x^j})~?$$
5
votes
2answers
116 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 ...
1
vote
1answer
79 views

Notation: What is $\delta_{mn}$?

In a textbook, I found this relation for eigenvalues of total angular momentum: $$(L^2)_{mn} = \langle l,m \rvert L^2 \lvert l,n\rangle = \hbar^2l(l+1)\delta_{mn}$$ What is the $\delta_{mn}$ refer ...
10
votes
5answers
739 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 ...
0
votes
0answers
39 views

Russell-Saunders Term

The Russell-Saunders term states that: $$^{2S+1}L_{J}$$ Now, if I'm not mistaken, $L$ is the total orbital angular momentum, $J = L + S$, but what is $S$ exactly? I know it's the total spin angular ...
3
votes
1answer
88 views

Notations for statistical / systematic / numeric errors?

I constantly see the notation $$ 5.143(13) $$ for specifying that a value was measures / calculated to be 5.143 with an estimated error of 0.013. I have come to wonder though, just how commonly ...
2
votes
2answers
196 views

Notation for anti-symmetric part of a tensor

I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$ But how can write $E_{[a} F_{bc]}$ like the above? Can you provide a reference where this notational matter is discussed?
3
votes
2answers
91 views

How to deal with the notation of a function $f$ vs its value $f(x)$ in Physics?

This doubt is very silly, but anyway, I think it's worth asking. The problem is: when we work with mathematics, in many situations we want to consider sets $A$ and $B$ and functions $f : A \to B$. ...
0
votes
2answers
53 views

Feynman's subscript notation

Consider this vector calculus identity: $$ \mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) ...
2
votes
3answers
98 views

Question about the Dirac notation for partial trace

I saw the following definition for the partial trace operator: $\rho_A=\sum_k \langle e_k|\rho_{AB}|e_k\rangle$, where $e_k$ is basis for the state space of system $B$. From what I know, in the ...
2
votes
1answer
135 views

Term symbol - how do we know the number of electrons $e^-$?

Lets say I have a term symbol $^4D_{5/2}$. From this I can simply read the total quantum numbers numbers $L=2$ and $J=5/2$. Now the superscripted number $4$ is called multiplicity if I am not ...
1
vote
2answers
204 views

How do you show from the index notation that the change of frame formula for a metric must involve the transpose?

Let $x^\mu$ and $x^{'\mu}$ be two coordinate systems related by $$dx^{'\mu}~=~S^\mu{}_\nu~ dx^\mu.$$ In index notation the metric in both systems are related by: ...
2
votes
0answers
84 views

Topological quantum computation : Anyon model

Could someone tell me about Frobenius-Schur indicator and the associated cups and caps notation in context of anyon model. One possible reference could be Parsa Bonderson thesis which is freely ...
1
vote
2answers
189 views

Should we necessarily express the dimensions of a physical quantity within square brackets? [duplicate]

For example, should we write the dimension of mass, e.g. $\mathrm{kg}$ as $[M]$ or is it enough to write it as $M$?
1
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0answers
136 views

Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...