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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Can the composition law of a group be defined only when considering a representation or realisation of the Group?
When we talk about, lets say, the Lorentz group, we define the action of the Lorentz transformation $\varLambda$ on
\begin{alignat}{1}
x^{\mu} & \in\mathbb{R}^{1,3},\\
x^{\mu} & \rightarrow x'^...
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In what sense is $\int (u \cdot \nabla) u \cdot u dx$ an energy flux?
Due to the nature of this question I have have cross-listed it on mathSE.
Let $u$ be either a solution to either the Euler equations or Navier-Stokes equations over a domain $\Omega$. In fluid ...
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What is the name of the transformation from one harmonic oscillator basis to another centered elsewhere?
If I have a harmonic oscillator basis centered at $x=2$, how do I rewrite it in terms of the harmonic oscillator basis centered at $x=0$? To be more specific:
If $|\Psi_n\rangle$ is the $n$th ...
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The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT
I'm reading Vol. 2 of Weinberg's QFT. As what I learnt from both P&S and Weinberg, the generating function is defined as
$$
Z[J] = \int \mathcal{D}\phi \exp(iS_{\text{F}}[\phi] + i\int d^4x\phi(x) ...
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Why isn't work a state function?
I've heard the example, that work is path dependent. But whether I climb a mountain directly or in serpentines, in the end it's the same amount of work, with the one difference that it takes me longer ...
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Equivalent definitions of Wick ordering
Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
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Why is Wigner-Seitz cell considered primitive?
During the lecture I listened, as well as in the internet, in Wikipedia for example, unit cell was defined as the parallelepiped spanned by the translation vectors. Primitive cell was defined as the ...
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Kinetic Energy equation: Is $K=\frac12mv^2$ a Definition, or a derived Theorem?
I am trying to understand classical physics as a mathematical model. I will first specify the trail of thoughts that led up to this question. (Please correct me if anything is wrong with the reasoning ...
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Is there any difference between Wick time order and Dyson time order?
Reading A Guide to Feynman Diagrams in the Many-Body Problem by R. Mattuck, I am getting the feeling that I missed something subtle related to time order. When deriving the Dyson series for the ...
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Mathematical meaning of a position eigenbra $\langle x_0 |$
Let $|x_0\rangle$ be an position eigenket. The physical picture I have for $|x_0\rangle$ is a particle located at $x_0$. Thus it should be represented by a delta function $\delta(x-x_0)$.
For $f\in L^...
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Renormalization group equation, the Callan-Symanzik equation, and renormalization group flow
I am learning about the renormalization group and I am getting confused on some terminology.
For the massless $\phi^4$ theory the Callan-Symanzik equation is:
$$\big[ M \frac{\partial}{\partial M} + \...
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Clarification regarding the meaning of Universal Time UT1
I've been reading the book "From Sundials to Atomic Clocks: Understanding Time and Frequency" by James Jespersen and Jane Fitz-Randolph which is available at https://www.nist.gov/system/...
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Why is angular momentum defined so?
We know angular momentum is defined as $mvr$. In the context of Lagrangians and Noether's theorem, this definition pops up as the conserved quantity due to rotational symmetry of the system. Is there ...
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What exactly is kinetic energy? [duplicate]
What exactly is kinetic energy? I know that kinetic energy is the energy that an object obtains by the virtue of its motion, but I need an exact answer. So, potential energy, like there are three main ...
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Definition of angular velocity in rotational motion of a non-rigid body? [closed]
Consider a particle in rotational motion with radius r and angular velocity w both varying with time, what is the relationship between the displacement u and w of the particle? $w=\frac{\partial u}{\...
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Inconsistent definitions of Entropy [duplicate]
On the wikipedia page "Entropy", entropy is defined as $S=k_B \ln\Omega$, where $\Omega$ is "the number of microstates whose energy equals the system's energy". This is what I had ...
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In physics, what is the difference between a fact and a definition?
For example, I came across this statement:
"It is a fact that the components of force are derivatives of potential energy, but it is not a definition."
What does this statement mean?
I ...
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Contracting the metric tensor with its inverse yields Kronecker delta
It's probably straightforward, but I would like to see the proof of the identity:
$$g_{\mu\nu}g^{\nu\alpha}=\delta^\alpha_\mu.$$
In the book 'Spacetime and Geometry' by Carroll, this identity is the ...
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What actually is Boyer-Lindquist coordinates?
I want to know the difference between spherical and Boyer-Lindquist coordinates. Don't they both use $r, \theta, \phi$ parameters? I've searched books and sources on the internet and there's none that ...
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Definition of quenched data set/disoprder in the context of spin glass
I cannot come across a good definition of what "quenched" means in the context of spin glass problems. I see such use as "quenched connectivity", "quenched data set", &...
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Fierz idendity (supersymmetry)
So basically I have two Fierz identities involving spinors:
$$\psi^a \psi^b = -\frac{1}{2} \epsilon^{ab} \psi \psi$$
And
$$\overline{\psi}^{\dot{a}} \overline{\psi}^{\dot{b}} = \frac{1}{2} \epsilon^{\...
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Difference between stationary states, collision states, scattering states, and bound states
A few weeks ago, I was presented one-dimensional systems in my QM class, and of course one-dimensional potentials too. Nonetheless, I'm still a bit unclear about the terminology my professor uses. ...
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Cosmology - Anthropic Principle [closed]
What do cosmologists actually mean by Anthropic Principle? What are the differences between weak and strong Anthropic Principle?
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Matter vs antimatter asymmetry per particle [duplicate]
What is called matter and what is called antimatter is just a convention, isn't it? For example, suppose we call the bottom, the charm and the down quark antimatter and we call the strange, top, and ...
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Definition of generalized force in Lagrangian formalism
In some texts (e.g. Taylor's Classical Mechanics), the generalized force is defined to be (I'll simplify to one particle in one dimension for ease of notation): $Q \equiv \frac{\partial{L}}{\partial{q}...
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Are Hermitian operators Hermitian in any basis? [closed]
Given a Hilbert space and a Hermitian operator defined on it, will the operator exhibit Hermiticity in any basis used to span the space? My thought on this is that this must be the case, after all, if ...
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Has there been a big change in 1983 when the definition of the metre changed?
The metre was defined at the end of the $18^{th}$ century as the ten-millionth part of the quarter of the meridian (from the north pole to equator). Then, from $1983$ the definition changed for the ...
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Equation of Torque
The magnitude of torque is defined as the product of the perpendicular (to the object) component of the force I apply and the distance between the axis of rotation and the point of application of the ...
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Conflicting definitions of vector conjugate in QM
Let $e$ be a finitely matrix representable operator.
In physics, specially in quantum mechanics (QM), it is customary to define the conjugate operator $e^{\dagger}$, as the adjoint or the Hermitian ...
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What is the difference between $(\mathcal{H}\setminus \{ 0\})/\mathbb{C}^*$ and $\mathcal{H}_1/U(1)$?
Let $\mathcal{H}$ be a Hilbert space. We define the projective Hilbert space $\mathbb{P}\mathcal{H}$ as $\mathcal{H}\setminus \{ 0\}/\mathbb{C}^*$. Then $[\Psi]=\{ z\Psi :z\in \mathbb{C}^*\}$.
On the ...
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Definition of heat
Heat is defined as any spontaneous flow of energy from one object to another,
caused by a difference in temperature between the objects. We say that “heat”
flows from a warm radiator into a cold room, ...
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What exactly is force - apart from "the ability to do work"? [duplicate]
Does force - any kind - have an identity of its own apart from the set of effects it brings about? Or is it just "that which" ... "causes"; does this and that, makes certain ...
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Motivation behind Definition of Moment of Inertia [duplicate]
I was studying rotational mechanics a while ago, and came across the idea of moment of inertia. The moment of inertia of an object describes its resistance to angular acceleration. The definition of ...
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The meaning of the stress-energy-momentum tensor
I just learned some General Relativity and have a couple of questions about the stress-energy-momentum tensor $T$.
In what follows, please let’s suppose that General Relativity and the Standard Model ...
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Definition of generalized momenta in analytical mechanics
I've seen mainly two definitions of generalized momenta, $p_k$, and I wasn't sure which one is always true/ the correct one:
$$p_k\equiv\dfrac{\partial\mathcal T}{\partial \dot q_k}\text{ and }p_k\...
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What is preselection?
Looking for a definition of preselection I find either statistical or electoral definitions. I was trying to find something similar to What is postselection? or What is postselection in quantum ...
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Is 2d CFT partition function invariant under $SL(2,\mathbb{Z})$ or $SL(2,\mathbb{C})$?
In Applied Conformal Field Theory by Paul Ginsparg page 8,
the globally defined infinitesimal generators $\{l_{-1},l_0,l_1\}
\cup
\{\bar l_{-1},\bar l_0,\bar l_1\}$ resulted the finite form of the ...
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How the partition be invariant if the correlator not invariant under global conformal transformation?
Under the global conformal transformation
$$\tau \rightarrow \frac{a\cdot \tau +b }{c\cdot \tau + d}, ad-bc=1, a,b,c,d\in\mathbb{Z} $$
the partition function is invariant
$$Z(\tau,\bar \tau)= Z( \frac{...
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How was holomorphic function (local) restricted to special conformal group (global) in 2d conformal transformation? [closed]
An example could be found on this pdf file and the discussion was the 2d conformal transformation. Usually, the conformal transformation was derived locally such that the local conformal ...
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Is Jones calculus a "calculus" in the proper mathematical sense? [closed]
I've come to understand "calculus" as the mathematical study of continuous changes in a mathematical function or physical system. Differential and integral calculus are broad examples of ...
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How is matter defined in physics? [duplicate]
I have heard matter defined as energy within a closed system and that any such closed system will have mass.
Is this correct?
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Simple Harmonic Motion definition with proof
I'm currently Grade 11 and learning physics with the topic of oscillations, sadly my teacher didn't really give me a good understanding, besides a formula we have to memorize and just use mindlessly. ...
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What is intrinsic parity? Why is negative intrinsic parity possible?
What is intrinsic parity? It seems that it is a concept only for relativistic quantum physics. Why is it not relevant for non-relativistic quantum mechanics?
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Is there a rigorous definition of state of matter? [duplicate]
Solid, liquid, and gas are all states of matter. However, I have never seen a rigorous definition of what a state of matter is. Is there such a definition somewhere? I would like to see such a ...
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Tangent vectors as equivalence classes of curves
Given a smooth (differentiable) manifold $M$ and intervals $I_1,I_2\subset\mathbb{R}$, two curves
\begin{equation}
\gamma_1:I_1\to M\quad\text{and}\quad\gamma_2:I_2\to M~~,
\end{equation}
are ...
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Why is this called a `Harmonic Oscillator Chain'?
Consider the following general setup:
Assume have a chain of atoms (of mass $m=1$) in one dimension interacting with their nearest neighbor through a interaction potential $U$, and which are in an ...
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What is resistivity? [closed]
What is actually resistivity?
I read that when the temperature increases the the resistance of the conductor increase. Length and area of a material doesn't change so it means that the resistivity of ...
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Equivalence of gauge-invariance and physical observable
This is somewhat philosophical than physics.
In gauge theories, it is true (more like the first principle) that
\begin{equation}
\text{ physical observable } \Rightarrow \text{gauge invariant}
\end{...
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Simple definition for the generator of an infinitesimal transformation
Studying quantum mechanics, or QFT, the concept of generator $G$ of an infinitesimal transformation $T$ keeps showing up. My problem is that I don't have in mind a solid (dare I say "rigorous&...
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What does "non-dispersive" mean in terms of waves and group velocity?
I'm confused about the term wave group velocity: It is usually explained in terms of a superposition of harmonic waves with very closely spaced wave vectors and frequencies. It is then easily shown, ...
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