Questions tagged [notation]
This tag is for questions on the meaning, history, and usage of various symbols and notation that are used to denote different quantities in physics. Don't forget to mention the reference, where you encountered those notations.
1,519
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Transformation of Yang Mills Field Strength
I am confused about the expression $$F_{\mu \nu} \to F_{\mu \nu}' = U F_{\mu \nu}U^{\dagger}.$$ I found related Phys.SE posts How would one show that a nonabelian field strength tensor transforms in a ...
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3
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Clarifying Bra-Ket Notation: Orthonormal Bases
I was asked to find the trace of $(A \in M_{n \times n})$, the matrix that can be written in the form:$$A=\frac{1}{n} \sum_{r, \, q \, = \, 1}^n (-1)^{r+q}|r \rangle \langle q| \quad ,$$ where {$|r \...
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Can someone explain this Feynman Diagram in the picture?
I don’t understand this diagram at all, and what is the meaning of the $g$?
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Question on the indexes of the lagrangians describing gauge theories
For a gauge group $SU(3)_{C}$ we can construct its principal and associated bundles; we can introduce spinor fields via spin structures and spinor bundles and so on, arriving in a lagrangian theory ...
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How to express symmetry of a mixed (1,1) tensor with upper and lower index?
In the context of general relativity, I am working with the energy-momentum tensor $T$, which is a rank-2 tensor whose components are usually denoted by $T^\mu_{\ \ \ \ \nu}$. However, I am unsure of ...
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Evaluating the commutator of derivative and position [duplicate]
In Zettili's book on quantum, the fully worked problem 2.6 asks to show
$$
\hat{A} = i(\hat{X}^2+1)\frac{d}{dx} + i\hat{X}.
$$
Is Hermitian. Where $\hat{X}$ is the position operator. I took the ...
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1
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33
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Notation to give units in legend/axis label/etc
When writing e.g. an axis label for a plot or a header for a table column that contains data that is associated with a unit (e.g. a length in meters), I always used to write it down like this:
...
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Why is time harmonic follow the form of $e^{-i\omega t}$, not $e^{i\omega t}$? [closed]
In physics, when we solve an PDE or ODE, the solution usually has the form of
\begin{equation}
f=C_+e^{i\lambda x}+C_-e^{-i\lambda x}
\end{equation}
and the "causility" will eliminate one ...
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2
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Unclear passage, autoket and eigenvalues
I am not understanding a passage that our professor wrote: those are the lines.
$e_0 \cdot \hat\sigma$ is an operator, whose eigenvalues are $\pm 1$. He applied this to a ket $|e_0, \pm 1 \rangle$:
$$...
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Meaning of Left-Right Arrow in a Fitting Formula [duplicate]
I initially posted this question on Astronomy Stack Exchange but the site seemed rather inactive so I will try to ask it again on Physics, hopefully it doesn't go against any rules.
I was reading this ...
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Minkowski inner product
I'm elementary in physics and I have a question about a notation. In the book, the author says that the rotation group is the set of linear transformations on $\mathbb{R}^n$ preserving the inner ...
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How do I understand the Hodge $⋆$ operator in Yang-Mills Lagrangian?
The gauge-invariant part in Yang-Mills Lagrangian is
$$
\mathcal{L}_{\text{gauge}} = -\frac{1}{2}TrF_{\mu\nu}F^{\mu\nu} = -\frac{1}{4}F_{\mu\nu}^aF^{a, \mu\nu}.
$$
Sometimes I see the lagrangian ...
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A question about a comment from Byron and Fuller, pg 533
Seeing the equation,
\begin{equation*} (\hat{A} -\lambda)G_\lambda
(\mathbf{x},\mathbf{y})=\delta^{(3)}(\mathbf{x}-\mathbf{y}) \tag{1}
\end{equation*}
in the answer
What is different between ...
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Planck constant imaginary instead of imaginary PDE coefficients in the Schrödinger equation
Trying to get a first understanding of QM. The Schrödinger equation in standard form for $\Psi$
$$ i \hbar\frac{\partial }{\partial t} \Psi(x,t)
=\left[-\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial t^...
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Notational meaning of $\nabla_{\lambda}V^{\rho}$ and $\nabla_{\mu}\nabla_{\nu}V^{\rho}$
This question is related to Reconciling different expressions for Riemann curvature tensor, but it's different since it asks for some notational clarification arising out of calculations I did. To not ...
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$\nabla$, $\cdot \nabla$, $\nabla \cdot$, $\nabla^2$ - What do they do? [closed]
I'm trying to teach myself Smoothed Particle Hydrodynamics. Unfortunately, my background is in electronics, so the Navier Stokes equations are somewhat alien to me, as is vector calculus. The video I'...
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Bianchi identity contradiction in Abelian case
In non-abelian gauge theory, such as P & S's chapter 15, eq. (15.89), we also have Bianchi identity.
Start with
$$\epsilon^{\mu\nu\lambda\sigma}[D_\nu,[D_\lambda,D_\sigma]]=0$$
and use $[D_\mu,D_\...
- 1,133
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Taking a function out from between a bra- and ket-vectors in the general case
I had a guestion on what kind of functions can one pull out of braket-term. For example I know that
$$
\langle{\psi_1}|c|\psi_2\rangle = c\langle{\psi_1}|\psi_2\rangle, \hspace{0.5cm} c\in \mathbb{C}.
...
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How to interpret $\int\mathrm{d}^2z$? [duplicate]
In chapter 6 of Tong's lecture notes on string theory when calculating the Virasoro-Shapiro/4-point Tachyon amplitude he arrives at the integral
\begin{align*}
C(a, b) = \int\mathrm{d}^2z\ |z|^{2a-2}|...
- 1,758
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Harmonic Oscillator Eigenket Notation
I'm reading the $3^{\mathrm{rd}}$ edition of Sakurai and Napolitano's Modern Quantum Mechanics, and I have a brief question about the notation used to describe the eigenstates of the harmonic ...
- 185
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What is $\vec{q}$ in this expression?
So I am having trouble following and understanding what $\vec{q}$ is in this evaluation. Here is my attempt at a solution:
Since the solution is for 2P to 1s transition it must be in the form of ...
2
votes
1
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Four-vector and Notation significance [closed]
As the title suggest, this has to do, on the most part, with four vector notation. I have a series of questions, the majority, related to this topic:
1- If we assume a lorentz boost in the x direction ...
- 1,136
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votes
2
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Trace and index manipulation
Imagine that I have a quantity $F_{ab}$ multiplying the stress tensor $T^{ab}$:
\begin{equation}
F_{ab} T^{ab}.
\end{equation}
There is also a metric, say $h_{ab}$. If I want to write the above ...
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Position of an index when raising and lowering indices
I'm reading Carroll's book on GR, page 25, and have a question about raising and lowering indices in 1.72:
For the first equation, why do we have (sorry I don't know how to leave spaces for the lower ...
- 1,305
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2
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How does one write Adjoint, Self-adjoint and Hermitian operators in Dirac notation?
The following portion is paraphrased from Mathematical Methods for Physics and Engineering by Riley, Hobson, and Bence.
The adjoint of a linear operator $\hat{A}$, denoted by $A^\dagger$, is an ...
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Why are $K_{\alpha}$ and $K_{\beta}$ emissions denoted by $\alpha$ and $\beta$?
Perhaps this is a silly question, but is there any reason for the labelling of $K$ emissions as alpha and beta? From what I know, all $K$ emissions relate to an electron transition down to the $n=1$ ...
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What does this notation mean in a many-body quantum system? [closed]
I'm studying the Many-body quantum system with the textbook Many-Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and Karsten Flensberg, and right now I'm feeling hard to ...
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1
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What is the symbol to differentiate between 3D and 4D tensors?
I am writing a computer program and in there I need to differentiate 3D tensors (metric tensor, Riemann tensor, Ricci scalar, Christoffel Symbols, etc.) from 4D ones.
I wanted to write something like $...
- 2,970
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Notation in the Liouville-von Neumann equation $ i\hbar\frac{dI}{dt} = i\hbar\frac{\partial I}{\partial t} + [I, H] $ [duplicate]
The Liouville-von Neumannn equation is defined by
$$
i\hbar\frac{dI}{dt} = i\hbar\frac{\partial I}{\partial t} + [I, H]
$$
where $I$ is any operator and $H$ is the Hamiltonian. I assume that the left-...
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Dirac Formalism/Notation Question
I'm reading the 3rd edition of Sakurai and Napolitano's Modern Quantum Mechanics, which (probably rightly) relegates wave mechanics to an appendix. Instead, it carefully develops Dirac's formalism, ...
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Notation of ghost fields $b$, $\tilde{b}$, $c$, and $\tilde{c}$ in Polchinski
I am terrifically confused by the notation in Polchinski's string theory book from chapter 3 to chapter 4. The ghost action of the bosonic string in conformal gauge is (3.3.24)
$$S = \frac{1}{2 \pi} \...
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Spectroscopic Notation - Does $n^{2S+1} L_J$ describe a Single Electron, or the state of multiple Electrons?
I was introduced to spectroscopic notation as $n^{2S+1} L_J$ (with L = "S, P, D..").
And the meaning that n stands for the principal quantum number (energy level, as known from the hydrogen ...
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Clarification of Notation in MTW's Gravitation, Section 6.4
Three difficulties concerning notation in MTW's Gravitation Section 6.4, which introduces a coordinate system for an accelerated frame:
the time axis e0' is the observer's 4-velocity, so he is always ...
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1
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What does $\partial_ν/\partial^2$ mean?
I found such notation in this article link, equations 24-25. I know that $\partial_μ$ is four-gradient, but it does not contain second-order derivatives. Only d'Alembert operator does, $\partial^μ\...
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votes
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Understanding this Lagrangian calculation
I was trying to understand this section of a Wikipedia article:
$$0 = \delta \int \sqrt{2T} d\tau =
\int \frac{\delta T}{\sqrt{2T}} d\tau =
\frac{1}{c} \delta \int T d\tau$$
For the life of me, ...
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What does the $\Delta x $ in Heisenberg uncertainty principle actually mean?
In the textbook ''Concepts of Modern Physics -Arthur Beiser'' in chapter 3 section 3.7 where the book talks about the uncertainty princple
While illustrating the physics behind the uncertainty ...
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Shankar's definition of adjoint [duplicate]
I think Shankar's definition of adjoint operator (in his QM book) differs from many other sources.
On page 26, he made the definition
$$\langle \Omega V|=\langle V|\Omega^\dagger \quad .$$
Now $\...
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Is there a way to rewrite all of circular motions in exterior algebra?
The torque is defined as the cross product between the position vector and the applied force:
$$\tau = \vec{r} \times \vec{F}. $$
The cross product only works in 2 and 3 dimensions and the ...
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Which finite-dimensional representations of the Lorentz group do $p$-forms correspond to?
On the Wikipedia article about the representation theory of the Lorentz group, the finite-dimensional representations $(1,0)$ and $(0,1)$ are referred to as "$2$-form" representations. On ...
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What does a dot over a spinor index signify?
My questions should be rather simple. I was trying to get through one of my professor’s papers, and I saw the following notation, first with regards to Dirac and Weyl spinors, but the notation ...
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Why can the time evolution operator be left or right multiplied on bra or ket? [duplicate]
In the book Modern Quantum Mechanics by Sakurai, it said that:
We see that the expansion coefficients of a state ket in terms of base kets are the same in both pictures: $$ \begin{aligned} &
c_{...
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Why is Lorentz Transformation defined with one super and one sub index?
I came across the Lorentz transformation in tensor form, usually written as
$$\Lambda ^\mu _{\nu}$$
I understand that the first index usually corresponds to rows and the second to columns, and while I ...
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Question on index notation
I am working my way through Carroll's text on GR and am having trouble understanding what it means when an index is inside/outside parentheses. For example, in his discussion of geodesic deviation, ...
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1
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Inner Product of two 4-vectors
I have a question on the inner product of two 4-vectors. As per the definition the inner product of two 4-vectors is defined as,
$$\vec A.\vec B = -A^0B^0+A^1B^1+A^2B^2+A^3B^3$$
From linear algebra, ...
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1
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Elementary question about Einstein notation
I have encountered, in a physics textbook, the following Lagrangian:
$$L=\dfrac{m}{2}g_{ij}(x^k)\dot{x}^i\dot{x}^j.$$
I understand that Einstein notation is being used, and therefore there is an ...
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Determinant of an operator in ket/bra/bracket form?
As is well known, two examples of basis invariant functions are the trace and
determinant functions. These functions can therefore be thought of as
a property of a linear operator, and not just a ...
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Time ordering of integral [closed]
Is $$T\int\mathrm{d}^4x\phi^4(x)$$ just notation for $$\int\mathrm{d}^4x~T\phi^4(x)$$ since after integrating we have no time dependence anymore?
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2
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478
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Navier-Stokes equation (notation for convection term)
Incompressible Navier-Stokes in vector notation is written as
$${\partial U \over \partial t}+(U\cdot\nabla)U =-\frac{1}{\rho} \nabla P + \nu \nabla^2(U),$$
where $U$ is velocity vector field $U=(u,v)...
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1
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21
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Generalized forces for virtual work - Why did they drop the summation?
I am going through a PDF by Subhankar Ray & J. Shamanna on virtual work here and according to the PDF, equation 29, they write gerneralized force as:
$$Q_j = -\nabla_k\tilde{V}\cdot\left(\frac{\...
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votes
1
answer
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Notation in Zee's quantum field theory
I am reading Anthony Zee's Quantum Field Theory in a Nutshell(1st edition). On page 123, he does an integration by integrating by parts:
$$\begin{align}\int&\frac{d\omega}{2\pi}\log\left[\frac{\...
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