Questions tagged [notation]

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Formatting of quark fields

I try to follow the ISO 80000-2 norm when typesetting physics. This is more a typesetting question but I did not want to ask this at the TeX SE site since this only applies to physics and I am not ...
6
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1answer
235 views

Is it correct to sum over either index of the metric the same way?

I don't know if the following is correct, i want to compute the following derivative $$\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta} \...
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86 views

When was the phrase “beta function” of renormalization first used?

My question is a historical one: when was the phrase "beta function", as it pertains to the renormalization-group equations, used in physics? I am talking about this beta function: $$\beta_g\equiv \...
4
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151 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 ...
3
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1answer
73 views

Dot convention inductors in series: what is going on

So I'm really confused with mutual inductors and dot convention. If your answer is going to be a link to any website I can assure I read them all and that only left me more confused. So here are my ...
3
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109 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 ...
3
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225 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 ...
3
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212 views

Group theory notation used in physics (AdS/CFT)

This in the context of the AdS/CFT correspondence. I am reading this review on AdS/CFT Aharony et. al. (The MAGOO review) The abstract can be found here Equation (2.50) of the above paper lists the $...
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41 views

Notation for the vector space of (real) classical solutions

I am aware that this might not be the best place to ask, but I can't say I know of any other better alternative so I apologize in advance. I'm following Wald's book on QFT in curved space-time and I ...
2
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1answer
80 views

Understanding Einstein Summation in the Geodesic Equation

I am trying to teach myself general relativity. I believe I do not fully understand Einstein summation. I have two versions of the same question Non-relativistically: If $V^μ= ů$ (the velocity) ...
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391 views

Notation for vectors and covectors

This is probably a very simple question, and I think I know the answer, but I cannot find a place to solidly confirm this. So if I want to write a vector $\mathbf{V}$ in terms of its contravariant (...
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53 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} & \...
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52 views

Vibrational quantum notation

Reading articles on spectroscopy I often see this notation: 30001 <- 01101, 00011 <- 00001 in context of molecular ...
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157 views

Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) $\hat{H}_{e-...
2
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1answer
2k views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
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2answers
36 views

Finding the new force of vectors

It's been a while since the last time used vectors. I came across with the following question. Find the Net force (size and orientation) of the vectors $$ \vec{A}=15,37^{\circ},\,\vec{B}=5,162^{\...
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23 views

Notation of basis functions for irreducible representations

In character tables for symmetry groups, there are typically basis functions for each irreducible representation given. There are basis functions given like $xy$, $S_x$ or $R$. Could someone explain ...
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0answers
27 views

Question on notation convention regarding partial derivatives

H.Risken's book "The Fokker-Planck Equation" contains the following formula for the general 1D Fokker-Planck equation: $\frac{\partial W}{\partial t}=\left[-\frac{\partial}{\partial x}D^{(1)}(x)+\...
1
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1answer
70 views

Confusion about expressing an inner product using the Einstein summation convention

I think this likely comes down to the following expression, $$g’^{ab}e’_a e’_b = \delta ^a_b $$ Is this in agreement with the Einstein summation convention? Because even though the two indices are ...
1
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1answer
42 views

Is this a projection of a tensor state?

Take the state $|\Psi\rangle $ living in a product space of space 1 and space 2 with orthonormal bases $\varphi,\phi $ $$|\Psi\rangle=\sum_{i,j}a_ib_j|\varphi_i\rangle\otimes|\phi_j\rangle $$ Is the ...
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67 views

Where does this alternative form of Faraday's law come from?

In the Sears-Zemansky physics book on page 1007, there is an alternative way to express Faraday's law for a moving conductor in a magnetic field: $$d\mathcal E =\left(\vec v \times \vec B\right)\cdot ...
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23 views

Different between index locations on tensors

My question is in regard to the position of upper and lower indices on tensors, specifically in this case I am considering position 4-vectors and the Minkowski matrix. On the Wikipedia page I see ...
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35 views

Notation in a question on probabilities and particle counting

I'm working through Stephen Barnett's book on quantum information and have come across the following question (1.5, for anyone keeping track at home) A particle counter records counts with an ...
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2answers
126 views

Proving the raising and lowering of the raising and lowering operator

I am given a written proof of $\hat A^{\dagger}[u_n] = \sqrt{n+1} \ u_{n+1}$, and from it, and told to similarly prove $\hat A[u_n] = \sqrt{n} \ u_{n-1}$. However, in the written proof for $\hat A^{\...
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2answers
133 views

Covariant and contravariant coordinates - index notation

I am learning about electrodynamics and have recently been introduced to the four vector. I also come fresh to the idea of covariant four vectors and contravariant four vectors. My question concerns ...
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0answers
100 views

Most used convention about Christoffel symbols

Just a simple question: what is the most used form for Christoffel symbols, (1) or (2), see below: (1) $$\Gamma_{ij}^{k} = g^{kl}\Gamma_{lij}$$ and then, we have: $$\Gamma_{lij}=\Gamma_{lji}$$ (2) $...
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0answers
94 views

Indexes in the Gaussian functional integral

This is a question spawning from a comment made to my previous question. There I was asking about taking some functional derivative in the effective action of the non-linear sigma model. The comment ...
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0answers
54 views

Notation for string modes in open string Hamiltonian

I'm learning string theory from Becker, Becker & Schwarzs textbook. I'm having some trouble with some notation that isn't clearly explained: In chapter 2, The Bosonic String in the section titled ...
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55 views

What does this notation mean $\mathcal{H}=\Gamma(\mathbb{C} , \mathcal{L})$ (holomorphic function space)?

What does the $\Gamma$ notation mean in $\mathcal{H}=\Gamma(\mathbb{C} , \mathcal{L})$? $\mathcal{H}$ is the space of holomorphic functions on $\mathbb{C}$ and $\mathcal{L}$ is the trivial complex ...
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77 views

Linear operators and the inner product

I pick the inner product involving the linear operator $\Omega$, $\langle i|\Omega|j\rangle$, from the $n\times n$ matrix $\Omega_{ij}$ as structured in page 21 of Principles of Quantum Mechanics by R....
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68 views

The Action for Electric-Magnetic Duality

In the paper A Duality Web in 2+1 Dimensions and Condensed Matter Physics on page 34, the action for electromagnetic field in Lorentzian signature is given by $$S=\int d^{4}x\sqrt{-g}\left(\frac{-1}{...
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59 views

A confusing 2-component spinor notation

In Michael Dine's Supersymmetry and String Theory, the Lagrangian for QCD of one single quark is written as (in equation (5.1)) $$ \mathcal{L} = -\frac{1}{4g^2} F^2 + i\bar{q} D^\mu \sigma_\mu \bar{q}...
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1answer
94 views

What are plane waves in Bethe ansatz

I study Bethe ansatz, although my background is mathematics not physics. Can somebody explain to me what is plane waves? I have seen in many papers this expression that "The idea of the Bethe ansatz ...
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1answer
99 views

For the ground state of tin, why is it not possible to have a triplet D state?

I have been looking at electron configuration and understand the use of hund's rules, the Aufbau principle and the Pauli exclusion principle but am having difficulty with a question that has come up ...
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0answers
144 views

Does a tensor product of Fock spaces specify the order of operators?

Suppose I have 2 fermionic Fock spaces $A$ and $B$ with states denoted as $|n\rangle_A$ and $|m\rangle_B$, where $n$ and $m$ are quantum numbers specifying the occupation numbers in the single ...
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162 views

Index notation with four-gradient

Reading Schwarz's textbook on quantum field theory, early on he gives the Lagrangian $$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-A_{\mu}J_{\mu}.$$ With $F^{\mu\nu}=(\partial_{\mu}A^{\nu}-\partial_{\...
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0answers
196 views

Understanding Dirac equation notation

I'm trying to recover the Einstein energy-momentum relation from the Dirac equation. I'm given a solution wavefunction, $$\psi = u(E,\vec p) e^{i(\vec p\cdot\vec x - Et)}$$ with $$\vec u = N\begin{...
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340 views

Partial derivative vs Total derivative

This is essentially a follow up to my question here since I seem to have some difficulties regarding the differences between partial and total derivatives. Consider a Lagrangian density $$\mathcal{...
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0answers
355 views

Perturbation theory, eigenvalues and eigenvectors for degenerate case (1st order)

I was trying to understand the perturbation theory, but I was lost in the notation... I have understood that I have to identify the unperturbed kets that are degenerated and find the matrix $V$, ...
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0answers
372 views

Index notation for a Lagrangian with second derivatives

I'm finding the field equations for a hypothetical Lagrangian with dependence on the second derivative of a scalar field, $L\left(\phi,\phi_{,\mu},\phi_{,\mu\nu}\right)$, and in the analogue to the ...
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0answers
248 views

Notation - d.o.f.'s for Grassmann delta functions in a SUSY field theory amplitude

I was reading the following paper http://arxiv.org/pdf/1306.2962v1.pdf as I stumbled upon an issue concerning counting and assigning the Grassmann degrees of freedom that appear in grassmann delta ...
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73 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} = \sum_{j}A_{...
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654 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 | \...
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18 views

Notation for submatrices / subspaces and their partial traces

I‘m dealing with an observable on a N-dim Hilbert space and in some sense fix the Nth coordinate and regard the system thus as composite with a 1-dim and a (N-1)-dim subspace. Now I require to perform ...
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41 views

This tensor equation in Gerard t' Hooft's notes on General Relativity

This question probably has a simple answer that I'm just missing, but in Gerard 't Hooft's lectures on GR he has the following: $$X^{\mu}=Y_{\mu\alpha}Z^{\alpha\beta\beta}.$$ Why is the result of ...
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1answer
21 views

Clarification on the notation of a paper about hybrid

Here is a screenshot from this paper by J. P. Foster and F. Weinhold. This paper focuses on a model of hybridization. It therefore considers movement of electrons in three dimensions. The author does ...
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36 views

Terminology for the symmetric vector product on the Bloch sphere

I was reading the paper "The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem" by Diederik Aerts, Massimiliano Sassoli de Bianchi. ...
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1answer
61 views

Question about Einstein summation convention

I'm dealing with the following: $$\eta^{\alpha \mu} \eta_{\alpha \nu} \phi,_{\beta \mu}$$ $$\eta^{\alpha \beta} \phi,_{\alpha \beta}$$ where $\eta$ is the Minkowski metric and $\phi$ is a function ...
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51 views

The mathematical structure of $\widehat{su(2)}_k$

Some of my colleagues work on CFT's and quantum groups and I hear them talk a lot about $\widehat{su(2)}_k$ algebras. According to them (and the general physics literature) these are what ...
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77 views

Is there a notation alternative to Hertz?

Hertz, as we all know, is a unit of frequency where 1 Hz equals one cycle per second. Conversely ...