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.
2,256 questions
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Why is Kinetic energy not an explicit function of acceleration?
A few days ago a high schooler asked me this question to which I couldn't give an answer.
His main question was that acceleration is also a property of a moving body so why is Kinetic energy which ...
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What is resistance precisely?
Is there a mathematical definition for resistance because I cannot find any. On the internet I find definitions such as:
The electrical resistance of an object is a measure of its opposition to the ...
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Does every object in space have a weight (disregarding negligible external forces)?
Defining weight as the "gravitational force acting on an object", and disregarding the minimal impact that gravity has on objects considered to be 'gravitationally unbound', do all objects ...
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Is pressure only define at the surface in contact?
Is pressure only defined at the surface of an object or a container in contact with the fluid as per the definition of pressure,
Pressure is the force applied perpendicular to the surface of an ...
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Definition of conjugation of complex Grassmannian numbers
In Peskin and Schroeder QFT page 300 it is said that the complex conjugation of a Grassmannian number is defined to reverse the order of products:
$$ (\theta \eta)^* = \eta^* \theta^* \tag{9.65}$$
...
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Locality in statistical field theory
In a lot of introductions to Landau-Ginzburg theory, which gives the partition function in the form of a functional integral $$\mathcal{Z}[F]=\int \mathcal{D}\phi e^{-\beta F(\phi)}$$
it is said that ...
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Work force displacement vector doubt
I have known, work is defined as the scalar product of applied force component in the line of the displacement and the displacement, or the product of force component applied in the direction of ...
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How are $t$ and $u$ channel processses different? [duplicate]
I do not understand how the diagrams for t and u channel processes given on wikipedia are different, and why it is meaningful to list them. Below are the two processes I reference:
It seems to me ...
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Entropy in a thermally isolated system
In page 141 of the book "Concepts in thermal physics" it is said that for a thermally isolated, the change in entropy is bigger or equal to 0 since $dQ=0$.
But since the system is thermally ...
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Derivative for the Maxwell field [closed]
I'm struggling with the following expression, which occurs in the derivation of the Maxwell Lagrangian in field theory.
$$\frac{\partial(\partial_{\mu}A^{\sigma})}{\partial(\partial^{\nu}A_{\lambda})}...
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answer
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What is symmetry in the context of physics? [duplicate]
What is symmetry in the context of physics?
Yes I have seen the description of the tag:
"Symmetries play a big role in modern physics and have been a source of powerful tools and techniques for ...
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The definition of the Lie Derivative
I am aware that an answer to an almost identical question already exist, however, I found the already existing answer not helpful (at least to my current question).
Carroll defines, in his book, the ...
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How are Fermionic and vector valued quantum field theories rigorously defined?
A scalar (spin 0) quantum field is rigorously defined as an operator valued distribution. By Wick rotating to Euclidean space we can view a quantum field theory as a measure over distributions. How ...
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What exactly is Fresnel distance?
I've been trying to understand fresnel distance with fraunhoffer diffraction in mind. As far as I understand it's the distance from the slit at which the effects of diffraction is next to zero . For ...
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Parity of a function [duplicate]
I am given the following definition:
If I have an operator $M_1$ such that $M_1(x_1,x_2,x_3)=(-x_1,x_2,x_3)$ and similarly for $M_2$ and $M_3$. If for a function $f(\vec x)$ we have $f(M_\alpha\vec x)=...
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What exactly in QFT makes a field/particle on- or off-shell?
If we are to write down a quantum field definition, could we tell if the definition is on- or off-shell?
If we are to write down a quantum field interaction, could we tell from the expression and not ...
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What is the spectroscopic factor in nuclear physics?
In the book by Ring and Schuck, the so-called spectroscopic factor is defined as
$$ S_k = |\langle \Psi_{A+1} |a_k^\dagger | \Psi_A \rangle |^2 .$$
By this definition, the spectroscopic factor is ...
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Leibniz rule and Nakahara's definition for functional derivatives with respect to Grassmann variables
In Nakahara's book "Geometry, Topology and Physics" in section 1.5.7 (I'm reading the second edition) he defines the functional derivative with respect to Grassmann variables. He does so in ...
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Some questions on extraction of quantum probabilities from vectors and Hilbert space?
I am reading book called "A Unified Grand Tour of Theoretical Physics" by Ian D Lawrie.
I have started bra ket notation and state vectors. Could somebody explain to me how
$$P(a,b,c..| \Psi)
...
user441992
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Sign of canonical commutator
In quantum mechanics, the canonical commutator relations are:
\begin{equation}
\left[\hat{x}_{i},\hat{p}_{j}\right] = i\hbar\delta_{ij}
\end{equation}
Is there a physical reason why they have a plus ...
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What is the definition of Force?
I've come across so many abstract definitions of force—like "an interaction between two bodies" or "something that changes the state of motion or shape of a body." But what exactly ...
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Calculate scalar QED vertex using LSZ formula
I am self-studying QFT using the Schwartz book "Quantum field theory and the standard model", and I am reading chapter 9 about Scalar QED.
I am trying to calculate the following vertex using ...
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Time-like separated and Space-like separated events
I am trying to get an intuition about Time-like separated and Space-like separated events. I understand the definition of these terms, but I lack intuitive understanding of what these concepts ...
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Precise form of two-mode squeezed state
Starting with the two-mode squeezing operator
$
S_2(\xi) = \exp \left( \xi^* a_1 a_2 - \xi a_1^\dagger a_2^\dagger \right)$, we can factor it into [1]
$$
S_2(\xi) = \frac{1}{\cosh r} \exp\left( -a_1^\...
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Is my understanding of the "existence statement" interpretation of the 1st Law of Newton correct?
It is often questioned by people who have begun learning physics why the 1st Law of Newton is necessary, since the 2nd Law seems to imply it anyways. A modern interpretation of the first law that ...
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How does a steel ball's weight vary at different water depths?
A steel ball becomes lighter when immersed in water - its mass is the same but its measured weight is less. So, does the steel ball weigh less, at a water depth of one kilometre, than the same ball a ...
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What is "free" and what is "interacting" in the interaction picture?
How do we rigorously and systematically discern between the "free" and the "interacting" part of a Hamiltonian? That is, how can we find $\hat{H}_{\text{free}}$ and $\hat{H}_{\text{...
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Directional Notation for Forces and Gravity
It is said that $F_{12}$ is the force on object 1 by object 2. In Newton's law of gravity, $$\vec{F_{12}} = -\frac{Gm_1m_2}{r_{12}^{2}}\hat{r}_{12}.$$ $\hat{r}_{12}$ points from object 1 to 2, $\...
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Sign convention on thermodynamics - Problem 6.6 Heat and thermodynamics [closed]
I made the problem 6.6 of Heat and thermodynamics by Zemansky. But I have a question with the sign of the final result from section c). If I use $W= P \Delta V$ instead $W= - P \Delta V$, my answer is ...
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Why does $W = \int F\cdot \mathrm{d}s$ rather than $\int s\cdot\mathrm{d}F$ [duplicate]
Conventionally, infinitesimal work is defined as $\delta w = F\cdot ds$ and its integral as the work $$w(P_1 \to P_2) = \int_{P_1}^{P_2} F\cdot ds \tag{1}.$$
The word work, of course, can be assigned ...
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Is the weight of a floating body zero?
My physics book says that the apparent weight of a floating body is zero which is understandable since the buoyant force cancels out the gravitational force on the body.
However, further in the book ...
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What does the term "components of operator" in JJ. Sakurai's book Modern Quantum Mechanics mean?
We now demonstrate that if we take the infinitesimal translation operator to be
$$
J(dx^{\prime})=1−i\mathbf{K}·dx^{\prime} , \tag{1.202}
$$
where the components of $\mathbf{K}$, $~ K_x$, $ K_y $, and ...
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What exactly is voltage? What does it have to do with work? [duplicate]
I am a student and recently learned about electricity. I was reading about voltage. I see that the definition is the work done/charge. I think the work refers to the work done by the electrons as they ...
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How is Newton's First Law equivalent to the postulate that inertial systems exist?
Some of the modern mechanics textbooks provide further comments on Newton's laws and aim to refine them. To understand these modern interpretations, I'm referring to "Introduction to Mechanics&...
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Would a time-dependent gravitational force be conservative?
Under normal circumstances, the gravitational force near Earth's surface, $F_g = mg$ is clearly conservative. You can see this either by noting conceptually that the force is constant and work done by ...
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Is a frame of free falling observer inertial in Newtonian mechanics?
It seems to me that a frame of an observer undergoing free fall on Earth (before entering its exosphere) is not inertial in Newtonian mechanics, even though it is inertial in special and general ...
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A confusing thing about the Hermitian adjoint
There's something I don't understand here:
$$\forall |\psi\rangle\ \ \text{et}\ \ |\varphi\rangle\in\mathcal{E}, \qquad \langle \psi |\hat{A}^\dagger|\varphi\rangle=\langle\psi|\hat{A}|\varphi\rangle^...
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Choosing between proper velocity and ordinary velocity [closed]
A question of mine on proper velocity was recently shut down so I have deleted it and decided to rephrase with focusing on more specific points. I have also checked formerly posted questions but seen ...
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Lagrangian density in General Relativity
Just a silly question, but shall we include $\sqrt{-g}$ inside the Lagrangian density in GR? In other words, is it
$$S = \int{\mathcal{L}d^4x} \Longrightarrow \mathcal{L} = \sqrt{-g}\left(\frac{1}{2\...
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Exact definition of linear resistance
We are studying electric circuits in class and are now coming across resistance. Our professor classified types of resistance into four groups based on two factors:
linear and non-linear
time-varying ...
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What is an inertial frame in terms of acceleration?
After learning about the difference between coordinate and proper acceleration, I am now confused on the precise definition of an inertial reference frame in terms of proper and coordinate ...
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Why are there so many different definitions of Work in classical physics by different books and physicists , and which is correct?
Alot of different books , authors and physicists define work differently in classical physics and mechanics.
For example , Halliday & Resnick FUNDAMENTALS OF PHYSICS defines Work as
Work is ...
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Why care that 1-particle states $a^{\dagger}_{\mathbf{p}}|0\rangle$ have $\langle\mathbf{p}|\mathbf{q}\rangle$ which are lorentz invariant?
When defining momentum eigenstates, Peskin+Schroeder (in Chapter 2) define
$$
|\mathbf{p}\rangle = \sqrt{2E_\mathbf{p}} a^{\dagger}_{\mathbf{p}}|0\rangle.
$$
The prefactor of these states $\sqrt{2E_\...
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What is the difference between $u$ and $t$ channels in Feynman diagrams?
My question is very simple: can someone explain to me the difference between the $u$-channel and the $t$-channel in Feynman diagrams? I can't understand what is the "role change" in $u$-...
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Alternating Current versus Direct Current
I was given an $I$ v/s $t$ graph that looks like this:
Will it be classified as AC or DC? The current switches directions once, so not DC (current flow should be in one direction only). I don't ...
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Definition of coordinate acceleration
In 4-acceleration,
$$A^\lambda=\frac{dU^\lambda }{d\tau } + \Gamma^\lambda {}_{\mu \nu}U^\mu U^\nu$$
I wonder whether the term $\frac{dU^\lambda}{d\tau}$ (for indexes $\lambda=0,1,2,3$) should be ...
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What is the criterion for oscillatory motion?
A ball bouncing (consider ideal elastic collisions) moves to and from about some point, but there is no equilibrium position. This motion sure is periodic... but is it oscillatory?
What is the ...
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How to completely stop a particle with a given generalized momentum?
I have the following question. In order to stop a particle with a given generalized momentum, do I need to counter only the mechanical momentum, or the whole generalized momentum?
Could someone please ...
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What are conformal Killing spinors?
There are various definitions of Killing spinors and Conformal killing spinors that I see in literature which is a bit confusing to me. So, I want to clarify the nomenclature.
My question is for a ...
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Analogue of (anti)commutation relation for anyons
In textbook quantum field theory, bosons obey something like
$$[b_\sigma(\vec{x}, t),b_{\sigma'}(\vec{y}, t)^\dagger]\propto \delta_{\sigma \sigma'}\delta(\vec{x} - \vec{y})$$
and fermions obey ...
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