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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Variational principle with $\delta I \neq 0$
In Covariant Phase Space with Boundaries D. Harlow allows boundary terms in the variation of the action. If we have some action $I[\Phi]$ on some spacetime $M$ with boundary $\partial M = \Gamma \cup \...
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What is the general definition of symmetry in quantum mechanics
Consider a quantum system with Hilbert space $\mathcal{H}$ and Hamiltonian $H$. Let $G$ be a Lie group and $U$ a unitary representation of $G$ on $H$. What are the most general conditions that $H$, $G$...
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What does it mean by "condensation" of anyons?
My question is motivated from the paper Boundary degeneracy of topological order by Juven Wang and Xiao Gang Wen.
Consider a (2+1)D system with boundary, described by abelian Chern-Simons theory. Due ...
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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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What is the Haldane phase?
I'm trying to look up what is the Haldane phase, but the only thing I find is examples of physical systems that "realize" the Haldane phase, such as the AKLT model, but no clear definition of what ...
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Physicist path integral and cylinder set measures
Path integral via discretization
So let me start with what seems to be the point of view of physicists (corrections are highly appreciated since this is just what I understood!). Let a quantum system ...
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Quantum (spin/thermal) Hall v.s. (Spin/Thermal) Quantum Hall effects
Are the following concepts defined correctly, as I understand:
Quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low ...
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What is the general definition of a quench?
I've seen the term "quench" used in many different contexts.
It's easy to understand the meaning when the context has a simple physical analogue, such as lowering the temperature of a system to cause ...
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Is potential energy always defined by a position in a field?
Most potential energies appear to have their basis in a field, but do all? I know gravitational energy has the form $mgh$, which has a position term $h$ but no velocity. More "internal" ...
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What is capacitance, in general?
In circuit analysis software capacitance can be measured between any two nodes of a circuit or of a multiterminal device.
In practical terms we take $C_{ij}$, the capacitance between $i$ and $j$ as ...
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How is Infinitesimal coordinate transformation related to Lie derivatives?
I am reading the book "Gravitaion and Cosmology" by S. Weinberg. In section 10.9, while discussing Lie derivatives of tensors of different ranks, he makes a general comment:
The effect of an ...
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Why is mass nonnegative/is the nonnegativity of mass a convention?
In An Introduction to Tensor Calculus and Relativity, Lawden provides the definition of mass by considering a collision between two massive particles $p$ and $q$ with masses $m_p$ and $m_q$, ...
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What exactly are resonances in particle physics?
I am very confused about this, are they an excited state of a particle where an electron is excited to an upper energy level, which seems less likely to be the case since the resonant states of ...
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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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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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336
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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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Where did the $q^{1/8}$ factor in the Ramond sector come from?
D-Branes Clifford Johnson page 116
For the Ramond sector, the zero point energy of
a single fermion is $1/24$. After multiplying by two, we see that this is again
correctly obtained in our partition ...
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Dualities in Physics and Fourier Transforms
In many articles, authors compare physical dualities to Fourier transforms.
For example:
Joseph Polchinski, in his article "String Duality" (hep-th/9607050v2), writes: "Weak/strong ...
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What are virtual and apparent forces?
Acceleration in a rotating frame can be written as: $$\underline{a}=\frac{\partial^2\underline{r}}{\partial t^2}+\frac{\partial\underline{\omega}}{\partial t}\times\underline{r}+2\underline{\omega}\...
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What is a Hikami box?
Can anyone tell me what is the physical meaning of the image below (Hikami boxes)? (Especially the dashed line.)
Furthermore (and this is less important), why are these boxes needed for weak anti-...
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Are monochromaticity and coherence in the context of lasers two sides of the same coin?
We know that monochromatic lasers produce monochromatic light, i.e., all photons have the same wavelength $\lambda$ (ideally). Coherence, on the other hand, states that the phases of photons are in ...
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What is the definition of canonical momentum in curved spacetime?
For a classical field theory of a field $\phi$ defined on a flat Minkowski background with an action
$$ S_\text{flat}[\phi] = \int \mathrm{d}^n x \mathcal{L}(\phi, \partial_\mu \phi),$$
we take the ...
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Weird Black Hole definition
I'm quite new to the topic of Black Holes, and I can't understand the definition (given in Wald, R.M. (2005). The Thermodynamics of Black Holes. In: Gomberoff, A., Marolf, D. (eds) Lectures on Quantum ...
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Difference between different approximations in QM and other definition of the integral
I am currently studying the path integral formalism by myself and I am a bit lost within all the different way to solve the integrals we have. I have one big question:
It sounds maybe a bit strange ...
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279
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What picture is the $S$-matrix defined in?
I am looking into the definition of the $S$-matrix, and have found two different cases. Firstly I have seen it derived that (see here, link to Google books p110):
$$ S=U_S(\infty,-\infty)$$
But more ...
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Holonomy twisting
There is Witten's topological twist of standard SUSY QFTs with enough SUSY into Witten-type TQFTs. What is a holonomy twist?
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Is renormalization associated with a volume scale or with an energy-momentum and length scale?
Given that real-space renormalization blocks together small volume elements to construct larger volume elements, is it more appropriate/helpful to consider the renormalization scale to be a volume ...
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Is there any difference between Wick time order and Dyson time order?
Reading A Guide to Feynman Diagrams in the Many-Body Problem by R. Mattuck, I am getting the feeling that I missed something subtle related to time order. When deriving the Dyson series for the ...
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What is the definition of bound state in quantum field theory?
I asked a question a while a go what is a bound state and the question was closed because there is a similar question.
Now since best description we have to describe nature in quantum field theory
How ...
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57
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What are the extra terms in the generalized momentum regarding the Lagrangian formalism?
In the lectures, we have defined the generalized momentum in the Lagrangian to be:
$$p_i=\frac{\partial L}{\partial\dot q_i}.$$
But with this definition, if we do not make any assumptions about the ...
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Why $C^{\infty}(\Sigma, \mathbb{R}^D)$ instead of $\text{Emb}(\Sigma, \mathbb{R}^D)$ in string theory $\sigma$-model?
In most String Theory textbooks, e.g. Polchinski, Blumenhagen et. al., GSW, Becker & Schwarz, Zwiebach, the dynamics of the string is firstly motivated geometrically by the Nambu-Goto action $S_{...
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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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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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1
answer
78
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Gauge symmetry and Gauge Transforms
In QFT or CFT, say the action is invariant under some local transformation. Can we call that transformation a Gauge transform?
There is a specific notion of gauge transform in math which is defined as ...
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Are Bell's inequality and CHSH inequality the same?
Are Bell's inequality and CHSH inequality different? I tried to read about them and I understood that both disprove local hidden variable theory but I do not understand how they are different(if they ...
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Two definitions of vectors and general spinor transformations
The usual definition of a vector is that its components transform contravariantly under the change of coordinate chart on the underlying manifold -- it is an element of the tangent bundle of the (let'...
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Difference between symmetries of a theory and symmetry of a system
I am trying to motivate the role of symmetries in physics. In doing so, I would like to distinguish between a theory's symmetries and the symmetry of a system. The ideas are similar but I am not able ...
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What's the difference between the spin $s=h-\bar h$ and the world sheet momentum $P=L_0-\bar L_0$?
The eigenvalue under rotation is usually called the spin, $s$, and is given in terms of the weights as $s = h − \bar h$
(Tong's string lecture notes page 75)
where
$L_0 − \bar L_0$ generates ...
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What is the vector space associated with the $U(1)$ character in the $c=1$ free boson?
The U(1) character of the zero mode were
$$
\chi^{ U(1)}_{h(n=0,m=0)=0}=\frac{1}{\eta(\tau)}
$$
this was different from the so called Virasoro character
$$
\chi^{Vir}_0= \frac{1}{\eta(\tau)} ( 1-q)
$$
...
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answer
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Coordinates on a compactified dimension in bosonic string theory
In the simple case of compactification on the circle of radius $R$, $S^1_R$, most sources on string theory, e.g. here (Kevin Wray, An Introduction to String Theory, page 197), it is stated that the ...
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Is there a formal definition for apparent weight?
Is there a formal definition for the apparent weight that does not depend on the situation?
For example, when a body stands on a solid floor the apparent weight is defined via force that floor exerts ...
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What do $<111>$, $[010]$, $(111)$, and $\{100\}$ represents for a cubic crystal lattice?
I want to know the difference between different notations in crystal lattice. I know what Miller indices are but what does these four different notations really mean.
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Conformal Field Theory and Vertex Operator Algebra
I am trying to understand CFT from the viewpoint of both math(in particular using VOA) and physics. Now, in Math, we use the VOA to make sense of fields corresponding to certain states. We define for ...
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What is the definition of a tetrad/vielbein?
This is hopefully a simple question about definitions.
In mathematics, we have the tangent frame bundle, which is often just called the frame bundle. Local smooth sections are then called smooth ...
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Difference between Fixed Nuclei approximation, Born-Oppenheimer approximation, adiabatic nuclei approximation
I was reading some papers and depending on the author some would use the terms Fixed Nuclei approximation, Born Oppenheimer approximation, adiabatic nuclei approximation almost interchangeably whilst ...
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What are the differences between FFN, VFN, GMVFN and ZMVFN PDF schemes in QCD?
What are the differences between the fixed flavour number (FFN), variable flavour number (VFN), general-mass variable flavour number (GMVFN) and zero-mass variable flavour number (ZMVFN) schemes for ...
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Brownian Motion (Geometric, Fractional, Drift)
I have been researching Brownian motion for a while and have come across terms/types of Brownian motion such as fractional, geometric, and Brownian motion with drift. I understand the physical meaning ...
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3
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Weight in Newtonian mechanics
What do we mean by the term weight? Is it an upward force exerted by an object to counteract the downward force of gravity (or) is it the downward force itself? Is the magnitude of the weight always ...
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About the definition of world-line in Arnold's book
I am reading Arnold's Mathematical Methods of Classical Mechanics. I have some questions about the definition of world-line. The book says:
A curve in Galilean space which appears in some (and ...
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What is a neutrino state if not a particle?
When reading about the 2015 Nobel prize and how this led to the possibility of the existence of sterile neutrinos I am told that:
"(...) three active neutrinos $\nu_e$, $\nu_\mu$, $\nu_\tau$, are ...
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