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0answers
28 views

Indicating that indices are equal in Einstein notation

tl;dr: I have an expression like this: (dramatization) $$ R_{\mu\nu} = \begin{pmatrix} B^{00}C_{00} & 0 & 0 & 0 \\ 0 & B^{11}C_{10} & 0 & 0 \\ 0 & 0 & B^{22}C_{20} ...
3
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1answer
658 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 ...
0
votes
2answers
68 views

Unitary operators evolving the set of Pauli matrices

Consider the Heisenberg picture of Quantum Mechanics. For a two state system we have the Pauli matrices evolving according to the relation $$\sigma_i(t)=U^+\sigma_i(0)U$$ where $U=e^{-iHt/\hbar}$ and ...
2
votes
1answer
30 views

What are the units pm/K?

I can only think of picometres, but it doesn't seem to make sense. Here is the context, from the paper 'Towards Reproducible Ring Resonator Based Temperature Sensors', Klimov et al., Sensors & ...
0
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0answers
37 views

Different subscripts for $\nabla$ operators while deriving force on system of many particles

Consider a system of 4 particles in an external conservative field. So force acting on each particle is derived from potential energy $U(x,y,z)$of the particle+field system: Total (external) force on ...
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0answers
42 views

Conventions for propagators in Feynman diagrams [on hold]

So far, I picked up the following rules for the propagators: Scalars: Dashed Fermions: Solid Abelian gauge boson: Wavy Non-abelian boson: springy Ghost: Dotted This made much sense to me until I ...
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0answers
22 views

The possible atomic term symbols for electron configuration of $3p^1 3d^1$ [closed]

An atom has an excited electron configuration of $3p^1 3d^1$. What are the possible atomic term symbols for this electron configuration?
1
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1answer
39 views

What is $bfr$ in this expression?

I am reading 'Fundamentals of Quantum Mechanics' by Sakir Erokoc and came across this expression in relation to transition probabilities: $$\vec p=e \langle \psi_b |bfr|\psi_a \rangle$$ Which can be ...
0
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1answer
31 views

Can a sum of Pauli matrices be a real value?

In the page 2 of Quantum Annealing for Constrained Optimization, the authors introduced a constraint term under the Constrained quantum annealing (CQA) section. The ultimate goal is to work out a ...
0
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0answers
42 views

Extending projection operator to infinite-dimensional case

Hi I have a basic question regarding bra-ket notation. Given that $\{|e_n \rangle \}$ is a discrete orthonormal basis, $$\langle e_m | e_n \rangle = \delta_{mn}$$ then $$\sum_{n}|e_n \rangle \langle ...
0
votes
1answer
66 views

Dirac Notation With Comma

Does $\langle A,B\rvert$ mean $\langle A\rvert\langle B\rvert$? If so how is an operator applied to this in $\langle A,B\rvert \hat O $? For an example say the annihilation operator acting on ...
0
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1answer
51 views

When dealing with spinor indices, how exactly do we obtain the barred Pauli operator?

In the set of SUSY notes I'm following, the Pauli operator is given as: ${(\sigma^\mu)}_{\alpha\dot{\alpha}} = (I_2, \sigma^1, \sigma^2, \sigma^3)$. The antisymmetric tensor that lowers and raises ...
11
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2answers
504 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 ...
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votes
1answer
34 views

Symbol $p^{0}$ of particle [closed]

This is a very trivial question, but I cannot seem to find the answer anywhere in a textbook or the internet. My question is, what particle is represented by this symbol? $$p^{0}$$
-1
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1answer
67 views

Dot product in index notation [closed]

This is a question about a small exercise I am trying to do in order to check if I am correct. Such type of quantities can appear in propagators in QFT. Since I am not an index expert I need some ...
2
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0answers
40 views

What does the direct sum symbol (⊕) mean in the context of uncertainties

I've noticed the symbol ⊕ used in a context I'm unfamiliar with. In several papers about the the calculation of the uncertainty of quantities measured with hadron colliders. For example the ...
0
votes
1answer
55 views

What is uppercase ${\cal O}$ in electrodynamics?

I'm a bit puzzled as to what the symbol ${\cal O}$ means in electrodynamics, I'm reading this paper here http://arxiv.org/abs/astro-ph/0404512. See equation 43 which is in page 12, what is this ...
1
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0answers
39 views

Are there any symbols left? [closed]

I have looked through most of the symbols used in physics and math. It seems like there are none left in the alphabet and the greek alphabet. Are we screwed if we find a new constant? Edit: How do ...
5
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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 ...
1
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1answer
39 views

Solving systems of equations using Levi-Civita and index notation?

I'm doing some self-studying out of Hughston and Tod's Introduction to General Relativity and I stumbled upon a few problems asking me to solve systems of equations using Levi-Civita and index ...
3
votes
2answers
221 views

Tensor index notation with e.g. square brackets

I want to learn playing with indices and some notation in General relativity. But in every book just is used this notation. I know upper and lower but I don"t know the meaning of some combination of ...
2
votes
1answer
315 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? ...
2
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1answer
182 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
1
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1answer
41 views

Correct way to write Pauli matrices

This is purely a question of notation for the Pauli matrices. What is the correct way to write them for use as operators? Would I just write the vector of the matrices as a vector i.e ...
0
votes
1answer
94 views

The Lie derivative of the metric $g_{ab}$ and index notation

I don't quite know where to start this question. I'm essentially not understanding how to compute the Lie derivative of a given metric and vector. So I have the following definition: $$ ...
0
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0answers
44 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 = ...
0
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1answer
40 views

Ordering of Contravariant and Covariant spinors. Understanding the spinor space

I've been referring to Pg.36-Pg.38 in Introduction to Supersymmetry by Wiedamann. For understanding the precise origin of dotted, undotted indices on Spinors. He starts off my saying that $M$ acts on ...
0
votes
1answer
34 views

Calculating motion of equation in tensor form

for the Lagrangian density $$\mathscr{L}=\frac{1}{2}(\partial_{\mu}A^{\mu})^2$$ how can I get this $$\frac{\partial{\mathscr{L}}}{\partial(\partial_{\mu}A_\nu)}=(\partial_\rho A^\rho)\eta^{\mu\nu}$$ ...
1
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0answers
50 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 ...
0
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2answers
45 views

Can you set all dummy indices equal to each other? [closed]

According to the Einstein summation convention, can you set all dummy indices within a same expression equal to each other? Example, if both α and β are dummy indices in a same expression can you set ...
1
vote
3answers
66 views

What is the $ds^2$ notation in relativistic physics?

Could someone please explain me intuitively how $ds^2$ represents distance in relativistic physics?
0
votes
1answer
47 views

Using the Metric in Book Gravitation (MTW)

Here is the whole Box 2.2, at Page 55 The dot behind the second $-p^2$ seems to be a "planck mass" (sarcasm, flea egg) or just the book's style to use Dot behind the equations. So the Equation is ...
0
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2answers
31 views

Sig Figs, Combined Operations

Using the sig fig rule for addition / subtraction seems to break in certain circumstances. For example (I'm using underlines to show sig figs): $\underline{66}+\underline{66}-\underline{1.3}\times ...
0
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0answers
68 views

Need some help understanding Relativistic Notation

My question originates from what is done in the book on Quantum Field Theory book by Mark Srednicki on page 21 (if anyone has it). So say you have an inertial frame that is represented in the ...
0
votes
1answer
69 views

Is the unit symbol written twice when using the +\- symbol?

When notating error using the $\pm$ symbol, are the units only ever included at the end? For example: 10.2 $\pm$ 3.2 m rather than 10.2 m $\pm$ 3.2 m This seems to be correct though I ...
0
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2answers
106 views

Derivation of Schrodinger's wave equation

To derive $$i \hbar \frac{\partial}{\partial t} \psi = H \psi,$$ we start with $$i \hbar \frac{\partial}{\partial t} |\alpha \rangle = H| \alpha \rangle$$ and then multiply by $\langle x|$ on the ...
3
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1answer
91 views

Working with indices of tensors in special relativity

I'm trying to understand tensor notation and working with indices in special relativity. I use a book for this purpose in which $\eta_{\mu\nu}=\eta^{\mu\nu}$ is used for the metric tensor and a vector ...
2
votes
3answers
745 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?
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2answers
313 views

Any resources to learn how to interpret formulae/diagrams?

Are there any materials exploring intermediate levels (of any sub-subject) which give plain English descriptions along side formulas/equations/diagrams/notations?
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 ...
2
votes
1answer
31 views

Question about the expression of Witten Index

I am studying supersymmetry by myself. I do not understand the expression of Witten index, which is ${\rm Tr}(-1)^{F}$. What does it mean by writing $-1$ to the power of an operator $F$? Is this ...
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 ...
5
votes
5answers
358 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 ...
1
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1answer
116 views

What does $L^2(S^1,\mu_H)$ mean?

It's a Hilbert space, $\mu_H$ stands for the Haar measure on $U(1)$, but what does $S^1$ mean? I found it in one of my quantum mechanics books which approaches from a very 'mathematical' way.
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4answers
56 views

Same equation, different meanings

I went into a physics classroom today and saw this equation written on the board: $$ E = \frac \sigma \epsilon $$ At first I thought it referred to the electric field $ E $ between 2 parallel plates ...
5
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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 ...
1
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2answers
33 views

Notation of complex valued atomic orbitals

Atomic orbitals are usually labeled $1s$, $2p_x$, $2p_x$, $2p_z$ and so on. These wave functions are defined to be real valued. The original wave functions are complex valued. The $2p_x$ orbital is ...
3
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1answer
71 views

What do variables with a numerical subscript mean in astronomy?

I am wondering if anyone can help me understand what a variable with a subscript on it means. The paper: B.F. Schutz, Nature 323, 310 (1986). The variable in question is this distance $r_{100}$ and ...
2
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0answers
25 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} & ...
3
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2answers
66 views

Computational advantages of various notations for electromagnetism [closed]

Most undergraduate electromagnetism classes and textbooks use vector notation to describe Maxwell's equations. However, there are other notations like differential geometry and geometric calculus ...