Questions tagged [definition]

The definition tag is used in situations where the question is either about how some term or concept is defined or where the validity of an answer depends on a subtle definition of some term or concept used in the question.

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What is a "massive phase" in the string theory or CFT?

When reading through some articles, one encountered a vocabulary termed as a "massive phase" in the string theory or the CFT, in the case where a theory followed an RG flow between UV and IR....
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Arbitrarity of $i$ in the propagator

My question is simple: how arbitrary can the factor in front of the propagator be? What I mean by that is, if we call the wave operator $K$ and the propagator $G$, I've seen different books use ...
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Parity and intrinsic parity definitions

The action of parity operator on wavefunctions is defined as a reflection in the origin $$\hat{P}\Psi(\boldsymbol{r},t)=\Psi(\boldsymbol{-r},t)$$ In particle physics, though some books define its ...
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What is the difference between photoelectric effect and photo-ionization?

Photoionization, ionization by a photon, and the photoelectric effect aren't they identical? If not then what is the phenomenological difference between them?
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What is the difference between "cluster states" and "graph states"?

I wonder about the difference between the cluster state and the graph state. I guess the only difference is the graph of the cluster state is limited to a two-dimensional square lattice The concept of ...
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What is $B(N)$ crystal structure? What does this nomenclature stand for

Is it basic cubic with 20 atoms? I can't find the explanation for this nomenclature online. Maybe I could find it in a textbook, but if someone answers it here, other people can just google it.
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Can you explain me the definition of wave number as defined in theoretical physics?

Wavenumber, as used in spectroscopy and most chemistry fields, is defined as the number of wavelengths per unit distance. The corresponding formula is $$k=\frac{1}{\lambda}.$$ However, in theoretical ...
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What is an eigensystem? Could you provide a simple example? [closed]

Also, what is the difference between an eigensystem and the eigenspace?
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What exactly is order of magnitude?

I am little bit confused with what order of magnitude is. In my book it says, when we write approximate values of quantities in powers of ten i.e $10^b$, then $10^b$ is the order of magnitude. But ...
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3 answers
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Are Newton's laws just definitions?

I have read a bunch of articles online regarding my question but none have helped. Newton's Laws: In an inertial reference frame, an object's momentum doesn't change unless the object is acted upon ...
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Does Gas constant depend on molecular weight?

I came across the following question recently Calculate the difference between two specific heat of 1 g of helium gas at NTP. Molecular weight of helium = 4 and J = $4.186×10^7$ erg $cal^{-1}$ The ...
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Why can't we use integral of $x$, $y$ and $z$ in calculating moment of inertia

I've got no problems with calculating the moment of inertia/tensor of inertia of a cube using an integral over the lamina of a cube. However, I must be missing something obvious or making some sort of ...
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5 votes
2 answers
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Why does the Strange Quark have Strangeness -1?

I have been trying to find an explanation for the strange quarks negative strangeness value, I understand the term strangeness predates the quark model, but I'm unsure if terminology carry over is the ...
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What is the meaning of a conductor in equilibrium?

Electric field lines are always perpendicular to the surface of a conductor in equilibrium. what is the meaning of a conductor in equilibrium?
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Radial position operator

While trying to find the expectation value of the radial distance $r$ of an electron in hydrogen atom in ground state the expression is: $$\begin{aligned}\langle r\rangle &=\langle n \ell m|r| n \...
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Definition of a wave packet

In Shankar's QM book page 168, the author stated a wave packet is any wave function with reasonably well-defined position and momentum. What does he mean by resonably well-defined position and ...
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Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

I don't understand how the two could really be one and the same. E.g. we can exert forces $\vec{F}$ and $-\vec{F}$ on a body and it's acceleration will not change. I don't think it makes sense to say ...
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Can a primary constraint contain spatial derivative of the field?

I am currently studying the Hamiltonian formulation of GR and I have problems understanding this definition of primary constraint. In the textbooks, primary constraint occurs when a momentum conjugate ...
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What's the definition of temperature ? What's the meaning of reaching a zero temperature and infinity temperature? [duplicate]

I'm taking a course about statistical mechanics and it is completely new to me . We've learned about entropy and how when 2 different sub-systems comes to contact the entropy of the whole system keeps ...
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What is a state function?

What is a state function? I've been briefly introduced to the idea in an introductory module, and I'm confused by the whole idea, I understand the 'path dependence' from line integrals, but is it ...
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3 votes
1 answer
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What does "conformally coupled scalar" mean?

"Conformally coupled scalar $\phi$" - I encounter it a lot, but I can't find what it means.
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-1 votes
1 answer
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On what ground do you multiply $m$ with $v$ in the momentum equation $p=mv$? [duplicate]

I've read several other posts that says the momentum equation is the definition of momentum, and it has no proof. However, I would like to know what is the experimental observation where the ...
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2 votes
1 answer
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Prove that the fusion/crossing matrix was a function of $c,h$ only and was invariant between different theories

The fusion matrix or crossing matrix $$ F_{nm}\begin{bmatrix}i&j\\k&l\end{bmatrix} $$ relates the 4 point correlation function in the different channels. How to show that it was was a function ...
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NLO and NLL difference [duplicate]

The next-to-leading order (NLO) Feynman diagram is the next leading process having more vertices than the tree-level diagram, but what is next-to-leading-logarithm (NLL)?
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Covariant vs. contravariant definition of the Energy-Momentum tensor

I have a question regarding the definition of the energy-momentum tensor. I've seen it defined as a (2,0) tensor, so it has 2 upper indices $T^{ab}$, but many times it is written as a (0,2) tensor ...
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1 answer
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Why was the A-D-E type minimal model distinguished?

One was reading the paper where one encountered a word called "A Type minimal model", which seemed to indicate some historical identification. Latter one found it in the Wikipedia that in ...
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4 votes
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What is the physical motivation behind the mathematical definition of an inertial system?

In this German Classical Mechanics lecture by Frederic Schuller, it is given that a Newtonian spacetime with an absolute inertial frame is one in which $$ \nabla_{v} G=0$$ Where $\nabla_v$ is the ...
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4 votes
1 answer
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What is a propagating degree of freedom?

Given a gauge field theory, the various fields involved have (pointwise) degrees of freedom. For instance, if I consider the gauge theory of gravity in four dimensions, I have a set of tetrads $\{ e_\...
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Why is torque defined as $\vec{r} \times F$?

Here I cannot convince myself myself that it is units because the torque is defined to be in units of Newton meter is a reiteration of the law stated above. Why was it not $r^2 \times F$ or $r^3 \...
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1 vote
2 answers
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Radial Schrödinger equation: from $R_l(r)$ to $u_l(r)$

I am in the 3-dimensional radial Schrödinger equation, in the spherical coordinates, where we try to find the separable solutions $$\psi(r) = R_l(r) Y_l^m(\theta, \varphi) \equiv \frac{u_l(r)}{r}Y_l^m(...
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1 vote
1 answer
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How to differentiate the electric field on the surface of a conductor?

Given a conductor, let $n$ be the unit normal field of the surface and $E$ the magnitude of the electric field. How to understand the expression $$\frac{\partial E}{\partial n}$$ on the surface of the ...
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What does equivalent capacitance in general mean?

If you have some capacitors in series then their EC (= equivalent capacitance) means the capacitance of the capacitor which will store the same charge as any individual capacitor in the series when ...
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The confusion over the invariance of the correlation function and the mutually local field in the CFT

Consider the correlation function $$\langle \Pi_{i=1}^n V_i(z_i,\bar z_i) \rangle$$ such as $$\langle V_1(z_1) V_2(z_2) \rangle,(z_1>z_2)$$ by position the $z_i$ correctly, the exchange of the ...
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3 votes
3 answers
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When or why to use the $\equiv$ symbol in place of the $=$ symbol?

In literature, I read the following: A typical relationship*, often appearing in the literature, is: $$|-\nabla(\bar p+\rho g z)|\equiv \rho g J=q(\mu w+\rho Bq^m)$$ The nomenclature does not define ...
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How to show that in 2D CFT the marginal operator must have $(h,\bar h)=(1,1)$?

A related post might be What are marginal fields in CFT? where Qmechanic♦ pointed to Ginsparg secion 8.6. However, I heard about two argument. Claim 1:In a $D$ dimension CFT, the marginal operator ...
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2 votes
1 answer
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What does the Verma module in the reducible Virasoro algebra represent?

In the conformal field theory book by Francesco, Mathieu, Senechal, the Verma module is built from a primary field $|\phi\rangle$, and if one of the descendants is a singular vector $|\chi\rangle$, ...
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Inner product evaluation in QM

On wikipedia on the page for inner product it states that for any two $x,y$ in a vector space $V$ the inner product $(\cdot , \cdot)$ satisfies $(ax, y) = a(x,y)$ where $a\in\mathbb{C}$. The inner ...
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Mathematical Definition of Point Source

Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating". The usual definition in Physics describes it just as a source whose ...
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-1 votes
1 answer
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About dipole moment

The picture is taken from wikipedia page https://en.wikipedia.org/wiki/Electric_dipole_moment I don't understand the formula when it comes to continuous charge distribution. But I understand this one: ...
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What is the difference between Bohr-Sommerfeld and Wilson-Sommerfeld quantisation rule?

Is Bohr-Sommerfeld and Wilson-Sommerfeld quantisation rule the same thing? If not, what is the difference?
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How to find covariant derivative of a contravariant tensor?

Let I have a contravariant tensor $A^\alpha$, I want to find covariant derivative of the contravariant tensor, From the transformation of the contravariant tensor ($A^\alpha=\partial_\gamma x^\alpha A^...
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What's exactly is moment of inertia?

I know that angular momentum can be expressed in terms of moment of inertia tensor as follows, $$\vec{L}= I_{\text{tensor}}\vec{w}$$ Where $I_{\text{tensor}}$ is tensor for moment of inertia. It can ...
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de Sitter space vs de Sitter universe

I have heard of the term de Sitter space. From this post user G. Smith writes, De Sitter spacetime is curved; specifically, it has the same positive scalar curvature at every point. Likewise, when I ...
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1 answer
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How is the parity transformation defined? Especially for vector or tensor fields?

If I have a scalar field \begin{align} f: \mathbb{R}^3 &\rightarrow \mathbb{C}\\ (x, y, z) &\mapsto f(x, y, z) \end{align} We can define an operator $P$ that takes a function like $f$ and ...
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Formula for work done for both conservative and non-conservative force are different?

We know that the formula for Work Done by an constant force is W.D = Force x displacement x (cosine of angle between force and displacement). Situation: A mass m travels 10 meters towards  +ve axis ...
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What does Leggett mean by quantum states like $|\psi\rangle=(a|\psi_1\rangle+b|\psi_2\rangle)^N$?

In his article (p. 1986) Legett uses the notation $|\psi\rangle=(a|\psi_1\rangle+b|\psi_2\rangle)^N$ to classify "macroscopic quantum phenomena". Does the "$^N$" mean "$\...
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Complex valued Grassmann variables $(\theta \eta)^* $, $(\theta \eta)^T$ and $(\theta \eta)^\dagger$

Since hermitian conjugation and complex conjugation are serious issues in a QFT lagrangian with Grassmann variables, see here and here. Let us try to go to the bottom. We start by accepting the ...
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2 answers
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Are there two competing definitions of "inertia"?

The term inertia is often introduced by stating Newton's first law: An object stays at rest or moves with $\vec{v}=const.$, if the resultant force is zero. This feature of masses is called "...
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Is linear momentum of an open system conserved?

My understanding is that a system is a collection of particles. And according to Wikipedia, a closed system is one that does not allow transfer of matter in and out the system. However, my textbook ...
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What is the difference between isospin, weak isospin, hypercharge, weak hypercharge and the isospin third component $I_{3}$?

These terms crop up all the time in particle physics but I am confused as to what the difference is. I have read that hypercharge is the third component of isospin. This wikipedia page differentiates ...
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