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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Confused about definition of gravitational potential energy (GPE)
The gravitational potential energy of a mass at a point in a field is defined as the work done by an external agent in bringing that mass from infinity to that point, without a change in kinetic ...
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Is the charge-conjugation symmetry in cond-mat physics different from that in QFT?
In condensed matter physics, the terms "particle-hole symmetry" and "charge-conjugation symmetry" are often used interchangeably. As far as I understand, they refer to the ...
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How the parity violation was shown in Experimental Test of Parity Conservation in Beta Decay?
I read that in Experimental Test of Parity Conservation in Beta Decay by C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson, Phys. Rev. 105, 1413 – Published 15 February 1957 the ...
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What does an upside down delta mean - covariant vectors? [duplicate]
I was scrolling through a wiki article on terminal velocity when I spotted an upside down delta. What does this symbol mean? How is it applied in other contexts?
EDIT: If possible could someone expand ...
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Relation between $SL(2,R)$ and $U(1)$ symmetry
I have an action that I have proven to be invariant under an $SL(2,R)$ symmetry. But I actually want my action to be invariant under an $U(1)$ symmetry (because i know that for the system I am ...
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What is the difference between covariant and contravariant tensors? [duplicate]
What is the difference between covariant and contravariant tensors?
I have been seeing in a lot of problems but I´m not sure what is the difference or if is only a equivalent notation.
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Callen Postulate II
In his classic text, Callen gives the key postulate (Postulate II) as
There exists a function (called the entropy $S$) of the extensive parameters of any composite system, defined for all equilibrium ...
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Definition of stress (Mechanical Properties of Solids)
See, it's a simple question.What exactly is stress? Is it the restoring force applied by the body in reaction to deformation force or is it the deformation force itself? I had this doubt because in ...
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What does really mean to glue the endpoints of a closed string?
I'm almost all string theory standard textbooks such as Polchinski, Barton Zwiebach's book, etc. It is stated that the Worldsheet (or parameter space) flor the closed string is such that the points $(\...
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What does it mean for a material's elasticity to be non-linear?
Hooke's law only applies to materials with linear elasticity, usually for small displacements.
Now, if you imagine having a material that does not deform permanently when crossing a specific limit, ...
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Physical and mathematical relation between $(\tau, \sigma)$ parameters and coordinates $X^\mu$ in String Theory
When we define the parameter space for a string Worldsheet $\Sigma$ to be diffeomorphic to, say, $\mathbb{R} \times [0,1]$ or $\mathbb{R}\times S^1$, and use standard coordinates $(\tau, \sigma)$, $\...
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Thermal and non-thermal radiation
The definition of thermal radiation given by Zemansky ("Heat and thermodynamics", pag 95) is the following:
"The radiation emitted by a solid or a liquid by virtue of its own
...
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What is the opposite of "periodic boundary conditions"?
I am writing a paper on solid-state physics and use periodic boundary conditions (PBC) for a calculation. To motivate why I use PBC, I write a paragraph about what would happen if I did not use PBC. I ...
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Can $d/t =$ speed ever be wrong? Is there a more accurate way to determine speed?
Is there a more accurate way to determine speed? I am asking because this has to do with an accident reconstruction where my son was killed.
The investigators are trying to conclude his speed prior to ...
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Are the definitions of force and acceleration circular? [duplicate]
Force is defined by acceleration , and acceleration requires the determination of" inertial frames".
But an inertial frames also requires the knowledge of forces which requires measuring ...
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Is it possible to deduce the chemical potential from a molar fundamental equation?
In Callen, it's shown that for a simple system, the entropy can be written as $U(V,S,N) = Nu(v,s)$ where $s = S/N$ and $v = V/N$. One can then prove (as I asked here) that both the temperature and the ...
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What is meant by " a basis is diagonal"?
I am trying to understand Schmidt decomposition. I am stuck in one sentence here. See the example picture.
Here, I can understand everything except the line "For both
HA and HB the Schmidt basis ...
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Is an entropy maximum being unique a tacit assumption in thermodynamics?
In Chapter 1 of his famous textbook on thermodynamics, Callen gives (among various other posulates) the following postulate:
Postulate II There exists a function ( called the entropy S) of the ...
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On the additivity of entropy
In Chapter 1 of his famous textbook on thermodynamics, Callen gives (among various other posulates) the following postulate:
Postulate III The entropy of a composite system is additive over the ...
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AdS, nearly AdS, and asymptotically AdS
Recently, I took a seminar about JT gravity, and the speaker said about exact Ads, nearly Ads, and asymptotically Ads.
I want to know the difference(i.e., the form of metric? or the conditions on ...
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Sigma models as topological quantum field theories
I'm wondering how sigma models are supposed to define TQFTs. Suppose I want to consider a 2D TQFT with target $X$ (see page 15 of https://www.ams.org/bookstore/pspdf/ulect-72-intro.pdf)*. According ...
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What exactly is an infinitesimal symmetry?
I see this term used a lot, especially in the context of Lie algebras. I have seen it used (though not defined) in both math and physics books, and I could not find a good definition anywhere on the ...
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Per unit quantity meaning
What does per unit quantity mean? like distance covered per unit time? Or mass per unit volume?
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Wilsonian RG vs. continuum RG
As far as I understand one classifies the renormalization group (RG) into the Wilsonian RG and the continuum RG. The Wilsonian RG gives finite predictions by introducing a cutoff $\Lambda$ and absorbs ...
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Defining Tegmark's level IV multiverse [closed]
I am bit bothered by the "definition" of Tegmark's level IV multiverse. I have read that it is a "collection of all mathematical models" (whatever that means). I have also read ...
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Definition of vectors [closed]
I know that we call a quantity a vector if it has magnitude and direction and follows vector laws of addition(the triangle law and parallelogram law). But why only it should only follow addition laws ...
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If commutes with all generators, then Casimir operator?
Is the statement "if an operator commutes with every generator of the Lie group, it is a Casimir operator" true? (I'm interested in the case of quadratic Casimir invariants, but any answers ...
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Rigorous Theory of Path integrals [duplicate]
Does there exist a mathematical rigorous theory of the Feynman-Path-Integral in Quantum Mechanics or Quantum Field Theory?
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Difference between spontaneous and irreversible process?
I am confused about the difference between a spontaneous process and an irreversible process. Based on what I read so far, both processes increase universe's entropy. I never heard of any reversible ...
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What is actually the clear, precise and world-wide accepted definition of TENSION FORCE?
This is a long post, but only because I have explained the scenario very very clearly,90 percent of this post is explaining you a simple situation,my doubt is only 5-6 lines at the very end of this ...
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Radial quantization and time order
In CFT, one ususally begins quantization by defining radial ordering on the complex plane, with the notion of radial ordering being the equivalence of time ordering. This is often "motivated"...
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Terminology of different equilibria?
I've heard many equilibrium terms:
Translational equilibrium
Rotational equilibrium
Static equilibrium
Dynamic equilibrium
The different terminology is slightly confusing. My understanding is as ...
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Are rates a scalar, a vector or both?
Are all rates in physics a scalar, a vector or both?
It seem to me like all rates in science are vectors.
Examples of rate that are vectors are rate of charge flow, rate of heat transfer, rate of mass ...
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Meaning of shake-off in nuclear physics
What does shake-off mean in nuclear physics?
The word appears, for example, in the title of this article: "Shake-off in the ¹⁶⁴Er neutrinoless double-electron capture and the dark matter puzzle&...
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Geodesic eqn for non-affine parameterization
I am confused about a point regarding parallel transport and geodesics. The basic idea of a geodesic is the unaccelerated test particle moves in a straight line, or the tangent vector of a curve $x^b(\...
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Symmetry breaking, gauge invariance and superconductivity
I still have some confusions over symmetry breaking in superconductivity.
To begin with it’s clear gauge symmetry can’t be spontaneously broken, since it’s not a symmetry to begin with. I want to ...
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What's the notations $\mathbb{B}_I$ and $g_{\infty,l}(\Delta, u,v)$ in the Zamolodchikov recursion relations?
Weizmann Lectures on the Numerical Conformal Bootstrap 1907.05147 Eq. 3.19
\begin{equation}
g_{\Delta,l}(u,v)=
g_{\infty,l}(\Delta, u,v)+\sum_{I}\sum_{m\in\mathbb{B}_{I}} \frac{c_{I,m}}{\Delta-\Delta_{...
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Is there a serious ambiguity in the definition of the cross-product of unit vectors?
Consider a force F acting along the x-axis applied to a directed lever arm L parallel the y-axis, and with the conventional torque T parallel to the z-axis, with the three vectors a right-handed triad....
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On the definition of the Van Vleck-Morette determinant
Let $M$ be a Riemannian manifold and $\sigma$ the world function. The Van-Vleck-Morette determinant $D$ is defined by
$$D(x,x')=\det(-\sigma_{;\mu\nu{}'})$$
Regarding the semi-colon: In chapter $4.1$ ...
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Inner product of the material derivative [duplicate]
I have question about the inner product of the material derivative.
$$\frac{D\mathbf{v}}{Dt}=\frac{d\mathbf{v}}{dt}+\mathbf{v}\cdot\nabla\mathbf{v}.$$
How can you calculate the second term inner ...
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Is temperature held fixed in this derivative for pressure?
In Ashcroft and Mermin, they use the thermodynamic identity
$$P = -\left(\frac{\partial E}{\partial V}\right)_N$$
to compute the pressure of an electron gas. Is temperature $T$ also held fixed here?
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What is the Heisenberg-Weyl Algebra?
I did all the courses on Quantum Mechanics and QFT which my faculty offers and up to now no one defined to me what a Heisenberg-Weyl algebra actually is.
This appears in my studies when studying the ...
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Could someone give me an example of what gauge freedom is and how it relates to gauge transformations?
As title states. I am confused about this topic--what it actually means in practice.
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What exactly is field strength renormalization?
One thing I have not fully understood is what field strength renormalization is. In Peskin & Schroeder's book "An Introduction to Quantum Field Theory" (Section 7.1) they introduce it as ...
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How can work be a function of position when non-conservative forces don't act the same way at each point?
My textbook and wiki/online articles all claim that work is given by the integral
$$W=\int_\gamma\vec{F}\boldsymbol{\cdot}\text{d}\vec{s}$$
where the $\text{d}\vec{s}$ is some infinitesimal step along ...
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What is $R$ in torque? [closed]
I am confused of what is $R$ in torque is it the distance to the axis of rotation or to a specific point or origin of axis of rotation (pivot)? the forces should treated as lines?
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Why is Newton second law only valid in inertial observer [closed]
It is very confusing that 1st law be used in inertial frame. For 2nd law we have many different sayings.
On what condition is 2nd law be used in inertial observer?
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A covariant derivative construction with torsion
Is there a covariant derivative, $\nabla$, that takes into account torsion, $T^\mu_{\;\;\alpha\beta}$, and covariant derivative of the metric equals zero, $\nabla_\alpha g_{\mu\nu}=0$? If yes, is ...
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Is it correct to say that the term "phase space" is valid only when applied to canonically conjugate coordinates and momenta?
Is it correct to say that the term phase space is valid only in relation to canonically conjugate coordinates and momenta?
Is there a simple/short way to terminologically distinguish the phase space ...
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What exactly is the difference between temperature and heat? How is specific heat capacity related?
When I’ve searched online for the difference between temperature and heat, I’ve seen it defined as:
Heat is the total kinetic energy of an object’s particles, whereas temperature is the average ...
