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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Mathematical definition of the fine structure constant [closed]

Many physicists would like to know the mathematical definition of the fine structure constant. Unfortunately, Wikipedia only gives about a dozen physical definitions. Does anyone know something new ...
Aleksandr Rybnikov's user avatar
-1 votes
3 answers
73 views

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 ...
V T Naveen Mugundh's user avatar
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2 answers
90 views

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 ...
physicsrev's user avatar
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1 answer
76 views

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 ...
Mahtab's user avatar
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1 answer
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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, ...
GedankenExperimentalist's user avatar
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0 answers
47 views

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 ...
Sumwun Yumaynotno's user avatar
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0 answers
19 views

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 ...
V T Naveen Mugundh's user avatar
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0 answers
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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 ...
parabolatomorrow's user avatar
1 vote
1 answer
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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\...
Joan S. Guillamet F.'s user avatar
0 votes
1 answer
114 views

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 ...
Mauricio's user avatar
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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 ...
ShoutOutAndCalculate's user avatar
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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{...
ShoutOutAndCalculate's user avatar
1 vote
0 answers
38 views

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 ...
ShoutOutAndCalculate's user avatar
0 votes
3 answers
128 views

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 ...
BenjaminDSmith's user avatar
-1 votes
1 answer
69 views

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?
Gerry's user avatar
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1 answer
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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. ...
Kenneth Albert's user avatar
1 vote
0 answers
64 views

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?
S. Kohn's user avatar
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2 answers
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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 ...
user107952's user avatar
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1 vote
2 answers
198 views

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 ...
hodop smith's user avatar
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2 answers
55 views

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 ...
Monty's user avatar
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2 answers
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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 ...
Alex's user avatar
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1 answer
51 views

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{...
Keith's user avatar
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1 answer
65 views

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&...
Noumeno's user avatar
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1 answer
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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, ...
MichaelW's user avatar
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1 vote
0 answers
112 views

Difference between Bogoliubov-Shirkov renormalization group and Wilson's Renormalization group

I just learned the Wilsonian renormalization group from a QFT lecture, I heard that there is another renormalization group called Bogoliubov-Shirkov renormalization group which is a true group instead ...
Inuyasha's user avatar
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1 vote
1 answer
48 views

Definition of the left-right derivative symbol in the Klein-Gordon scalar product [duplicate]

At the start of QFT, studying the Klein-Gordon scalar field, it is often mentioned that the following is the definition of the scalar product in the space of the solutions: $$\langle f _{\vec{k}}|f_{\...
Noumeno's user avatar
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0 answers
35 views

What is momentum exactly? [duplicate]

What is momentum exactly? I am confused that, is momentum a property of particle or something different. Whenever i look for it's definition it is product of mass and velocity of a particle. At ...
Vidushi Aggarwal's user avatar
4 votes
3 answers
203 views

Is there a unified conceptual definition of mass?

Last night I posted this question: Since light has inertia and experiences gravity, what does it mean for photons to be massless?, which I now think was overly wordy and didn't properly express what I ...
Mikayla Eckel Cifrese's user avatar
1 vote
1 answer
110 views

On the $\ast$ map in the Osterwalder-Schrader axioms

I'm studying "A Mathematical Introduction to Conformal Field Theory" by Schottenloher and there is one point on the Osterwalder-Schrader axioms that I am a bit confused about. They are ...
Gold's user avatar
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8 votes
2 answers
504 views

Is there a sharp definition of an unstable nuclide?

This may be a somewhat philosophical question, but here goes. Wikipedia claims that several nuclides (e.g. hydrogen-5) have half-lives shorter than $10^{-22}$ seconds. This is on the same order of ...
tparker's user avatar
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6 votes
2 answers
170 views

Why is the angular momentum of photon $\hbar$ if the spin is 1?

I saw in many places that the spin of photon which is a boson is 1. Which we can write as $s=1$. I also saw that the angular momentum of a particle with spin $s$ is $\sqrt{s(s+1)}\hbar$. If both is ...
Zjjorsia's user avatar
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1 vote
1 answer
185 views

$SO(3,1)$ is locally $SU(2)\times SU(2)$, what does *locally* mean here?

I am learning Lie group and Lie algebra. I saw in a YouTube video "Supersymmetry lecture 02" from OpenCourseWare (OCW) at University of Cambridge at 11:17 that $SO(3,1)$ is locally $SU(2) \...
Fermion's user avatar
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0 votes
2 answers
59 views

Formal mathematical definition of radiance and irradiance

Radiance is defined as $$L = \frac{\partial^2 \Phi}{\cos{\theta} \partial A \partial\Omega}$$ and irradiance as $$ E = \frac{\partial \Phi}{\partial A},$$ where $\Phi$ is the radiant flux, $\Omega$ is ...
mathslover's user avatar
0 votes
4 answers
122 views

Mass of an object [duplicate]

The mass is said to be matter content of an object. Is there any detailed definition of mass because the phrase , "matter content of an object" uses the word matter whose definition is ...
12jjsioe383's user avatar
6 votes
2 answers
183 views

Are all events along a Cauchy surface always space-like separated?

I'm new to relativity. Are all events along a Cauchy surface always space-like separated? I know that a necessary condition of a Cauchy surface is that every inextendible causal curve intersects the ...
John Smith's user avatar
1 vote
6 answers
173 views

Why is current defined as $dQ/dt$ even though it is not defined as the rate of 'change' of flow of charges?

I do not understand this definition. $dQ/dt$ represents the rate of CHANGE of charge flow at an instant even though current is defined as only the charge flow per unit time.
Dhyaneshwar's user avatar
0 votes
0 answers
59 views

What is the difference between wavefunction renormalization and field strength renormalization?

A while ago I asked a question asking what is field strength renormalization (What exactly is field strength renormalization?). I now have a better way of thinking about this, which is that it relates ...
CBBAM's user avatar
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0 votes
0 answers
78 views

Is the vector representation the fundamental representation of the Lorentz Group?

The vector representation of the Lorentz Group has dimension 4, while the group has dimension 6. If it's not the fundamental representation, which one is?
TrentKent6's user avatar
1 vote
3 answers
120 views

Are Lissajous figures SHM(s)?

Are Lissajous figures SHM(s)? I have been studying perpendicular superposition of SHM(s). And i understand that 2 shm having same angular frequency and differed by phase pi/2 when superimposed ...
Amit Rai's user avatar
  • 143
-2 votes
2 answers
96 views

On the physical meaning of functionals and the interpretation of their output numbers

I am studying about functionals, and while looking for some examples of functionals in physics, I have run into this handout . Here are two questions of mine. 1- This handout starts as follows (the ...
user avatar
1 vote
2 answers
62 views

Confusion in definition of Potential Energy

Potential energy is defined like this. $ΔP.E=-W_{AB}$. This means that the potential energy at point A minus potential energy at point B should equal the negative of the work done by a conservative ...
Hammock's user avatar
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9 votes
4 answers
4k views

Understanding Wikipedia's definition of a spinor

I originally asked this question on math SE but I'm asking it again here due to the lack of responses. I should note that I come from a mathematical background and not a physics one so I am not ...
CBBAM's user avatar
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0 votes
0 answers
64 views

What is the difference between interaction energy and self-energy?

From my understanding self-energy is the energy required to put charges in a certain charge distribution and interaction energy is the potential energy caused by the interactions between particles, ...
randomdude's user avatar
4 votes
1 answer
231 views

Physical motivation for the definition of Spin structure

I'm pretty confused about the motivations behind defining a spin structure on a manifold. Let me explain. In quantum mechanics, particles are represented by irreducible unitary projective ...
eomp's user avatar
  • 121
0 votes
1 answer
109 views

Are electrons and positrons part of a family of 4 (8? 16?) similar particles?

EDIT: Completely rewritten because of the 'needs clarity' tag and some useful related questions appearing in the side-bar. I hope this is clear now This answer gives a long list of properties of ...
Vincent's user avatar
  • 289
3 votes
5 answers
1k views

Relationship between bel and decibel

Bel is a unit of $log_{10}$ of ratio of two quantities. 1 Bel = $\log_{10}\frac{P_1}{P_2}$ On Wikipedia it says: 1 decibel = $\frac{1}{10}$ bel According to this definition then, 1dB = $\frac{1}{10}$ $...
Dinesh Katoch's user avatar
0 votes
0 answers
79 views

The frequency is off by a factor of $2 \pi$?

I was reading Morin's Introduction to Mechanics, and the following material came up: At equilibrium point $x_0$ expanding the Taylor series, we see $V(x)=\frac12 V''(x_0)(x-x_0)^2$ so comparing this ...
Aditya_math's user avatar
1 vote
0 answers
84 views

What is a hypersurface?

What is the concept of hypersurface in general relativity? I know it could be characterized into three categories but how do we define hypersurface (in general) in physics? I didn't get what thing it ...
Talha Ahmed's user avatar
3 votes
1 answer
180 views

The equipartion theorem and degree of freedom in case of vibration

I have been taught in chemistry that, the energy of a vibrational freedom is $RT$ (ie, twice that of rotational/translational) The degree of freedom which I found in chemistry, for the vibrational ...
Ninjametry's user avatar
1 vote
3 answers
94 views

Exact Definition of electrostatic field

Some documents define an electrostatic field as the electric field of a stationary charge or steady current. However, in other documents, they are defined them as electric fields satisfying $\nabla \...
KHJ's user avatar
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