Questions tagged [conventions]

A convention is a set of agreed, stipulated, or generally accepted norms. It typically helps common efficiency or understanding but is not required, as opposed to a strict standard or protocol.

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134 views

Correct way to define parity of two parafermions

I am checking the literature on parafermions and it seems that people define the parity of two parafermions to be $\gamma_{a}^{-1}\gamma_{b}$. Is this definition always valid? How does one come up ...
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About the definition of super Hilbert Spaces

I have found in the literature at least two different definitions of $\bf{super}$ Hilbert spaces: Definition 1: A super Hilbert space is a complex super-vector space $\mathcal{H}=\mathcal{H}_0\oplus \...
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Has the relative sign in the Dirac equation any meaning?

I know there are many questions about this topic and also various answers, but it's never stated explicitly, why there is a certain sign before the mass term in the Dirac Lagrangian. I'm also confused,...
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289 views

Quantizing Klein-Gordon Field: Sign Problem

I'm trying to re-derive the Quantization of the Klein Gordon Field but I'm running into sign problems. My starting point is: $$ \phi(x,t) = \frac{1}{(\sqrt{2 \pi})^3} \int \tilde{\phi}(k,t) e^{i kx}...
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When work done is taken negative in electrostatics?

Let us say a point charge Q was moved across a potential difference V, then work done would be : QV. This work is taken negative when done external agent, Please explain when It is negative and ...
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1answer
509 views

Identities of Pauli matrices in two-component spinor formalism

I'm reading the review by H. K. Dreiner, H. E. Haber and S. P. Martin (arXiv:0812.1594) about the two-component spinor formalism. There are some identities and notational conventions which lead to ...
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1answer
13k views

How to determine direction of current mentally in complex electrical networks?

I wanted to ask, as stated above, how would one work out, by considering such thing as potential differences provided by the battery, the path of the current in a complex network such as given below: ...
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109 views

Sign Convention in Field Theory

I am working with some field theory and I am at a point where I would like to change my sign convention from $(-+++)$ to $(+---)$. I am worried at some point I will just equations with the wrong sign ...
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3answers
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Long range forces?

A force/field which depends inversely on the square of the distance of the source from the point of interest (like electric field depends on $1/r²$, where $r$ is the distance between the the source ...
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1answer
340 views

Direction of integration and boundary limits in electromagnetism?

I have encountered several problems regarding the choice of direction of integration and the boundary limits, this semester in electromagnetism. Is there some rule, so I don't do it wrong again. In ...
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234 views

Why $\kappa = 8 \pi G$ in $D$ dimensional spacetimes?

Probably another question without an answer! ;-) In most books/papers I saw on General Relativity, everybody writes $\kappa = 8 \pi G_D$ in the right part of Einstein's equation, even for spacetimes ...
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1answer
2k views

Index of representation of $SU(N)$ fundamental and adjoint

Im getting crazy trying to derive this simple expression. Say $f^{abc}$ are structure constants of a Lie algebra of $SU(N)$ with $[T^a, T^b]=i f^{abc}T^c$. Then chosing normalization such that $$\...
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1answer
79 views

$\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki

The theta angle due to the chiral gamma^5 rotation of chiral fermion results in the phase alpha(x) that has different + or - sign for (1) Peskin&Schroeder, (2) Weinberg or (3) Srednicki. Here ...
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2k views

“Natural units” of mass

Gravitational attraction is given by $\frac{GMm}{r^2}$ while attraction due to electric charge is given by $\frac{q_1 q_2}{r^2}$. Why does gravity need a constant while electric charge doesn't? ...
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1answer
268 views

Two conjugations of supernumbers

Let $\theta$ and $\eta$ denote odd complex supernumbers (also known as Grassmann numbers), $a$ and $b$ arbitrary complex supernumbers. Say that $a$ is $\circ$-real (resp. $\circ$-imaginary) if $a^\...
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199 views

Quantization of Klein-Gordon field (what is creation operator there and what annihilation)

Recently in my class we studied quantization of fields and I'm brooding over an argument/ motivation on the construction of the quantization of the Klein-Gordon field. Recall the "classical" ...
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Newton's Law of Cooling: $\delta Q$ or $\mathrm{d}Q$?

In this popular answer, I invoked Newton's Law of Cooling/Heating: $$\dot{q}=hA\Delta T\tag{1}$$ $$\dot{q}=\frac{\mathrm{d} Q}{\mathrm{d}t}\tag{2}$$ $$\dot{q}=\frac{\delta Q}{\mathrm{d}t}\tag{3}$$ $$\...
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416 views

Ambiguity in assigning intrinsic parity

We know that, fermions can have intrinsic parity either $\eta_P=+1$ or $=-1$. How does one then fix the intrinsic parities ofthe elementary particles, uniquely? Again, the intrinsic parity of a baryon ...
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2answers
4k views

Usage of singular or plural SI base units when written in both symbol as well as name [closed]

I have multiple doubts related to the usage of singular or plural SI base units when written in both symbol as well as name. I have framed this question under two parts, namely, Part (a) and Part (b)....
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1answer
6k views

What is the origin of the naming convention for position functions?

In physics, position as a function of time is generally called $d(t)$ or $s(t)$. Using $d$ is pretty intuitive, however I haven't been able to figure out why "s" is used as well. Is it possibly based ...
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7answers
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Why does positive work done by internal conservative forces $\implies$ decrease of potential energy?

Potential energy can be thought as the amount of work that the force can potentially do on the point because of its position. $$W=-\Delta U=U_{initial}-U_{final}$$ A positive work done by a force ...
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1answer
336 views

Confusion about square bracket notation in the the Kronecker delta symbol

I am not sure I understand what the short-hand anti-symmetrization means. I.e. I know that $$\delta_{cd}^{[ab]} ~=~ \frac{1}{2}(\delta_{c}^{a}\delta_{d}^{b} - \delta_{c}^{b}\delta_{d}^{a})$$ but how ...
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1answer
315 views

Definition of vector cross product

I hope I'm right in saying that the cross-product, $\vec{A}\times \vec{B}$ of two vectors is defined by a right hand rule (e.g. if $\vec{A}$ points along the forefinger and $\vec{B}$ along the second ...
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635 views

Matrix multiplication and tensorial summation convention

I'm reading this introduction to tensors: https://arxiv.org/abs/math/0403252, specifically rules concerning summation convention (ref. page 13): Rule 1. In correctly written tensorial formulas free ...
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3k views

The Zero Electric Potential of the “Earth”

I know its the potential differences that matter and generally we define the zero of the electric potential according to our convenience. I would like you to look at this standard problem: Charge $-Q$...
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3answers
11k views

What is the direction of area vector while calculating magnetic flux?

In my textbook, as a preliminary to Faraday's law of induction, magnetic flux is defined over a closed loop as $$\Phi_B = \oint \vec{B}\cdot d\vec{A}$$ Then it draws a parallel with electric flux ...
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1answer
210 views

Sign ambiguity when going from position to momentum space evaluating Feynman diagrams

When calculating a simple diagram I came across an ambiguity in the conservation of momentum, i.e. it seems to me that the particle could come out of the process with opposite momentum with respect to ...
3
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1answer
16k views

Direction of Potential Gradient & Electric field

Potential gradient is the negative of the electric field: $dV=-\vec{E}\cdot \operatorname{d}\!\vec{r}$ Does the negative sign mean that the direction of potential gradient $\operatorname{d}\!V\!/\!...
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2answers
908 views

Signs in proof of gravitation potential energy (GPE)

Proof of gravitational potential energy. Work done by gravity in bringing mass from infinity to a distance of $r$ between masses. When we use the integration formula and arrive at the answer we ...
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4answers
642 views

Do air conditioner power ratings violate the 2nd law of thermodynamics?

I just got a new AC rated at 6000 BTU and wanted to determine its power consumption. Some research on AC conventions quickly reveals that 6000 BTU really means 6000 BTU/h, where BTU is a measure of ...
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1answer
795 views

Is reflection just a particular case of scattering?

I was talking to a colleague about optical scattering from a metallic nanoparticle, and we had a very simple doubt. If you have a particle that's small compared to the illuminated area, you can use ...
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2answers
80 views

The value of the volume form on an orthonormal frame

In a Riemannian space, what is the value of the canonical volume form on a frame? In particular, say, an orthonormal frame. One does not usually need to know anything about the value of a ...
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2answers
144 views

About integration measure in the completeness formula of coherent state

In Negele's book "quantum many-particle systems", the completeness formula for coherent state is $$\int {\frac{{d{\phi ^*}d\phi }}{{2\pi i}}{e^{ - {\phi ^*}\phi }}} \left| \phi \right\rangle \left\...
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2answers
2k views

Different signatures

I was working out the christoffel symbols, once where the metric that I am using has (+---) signature and another time where it has (-+++) signature because two books had different signatures and I ...
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2answers
3k views

Approximating Taylor series for a harmonic oscillator

The elastic potential energy is defined as $$V\left ( x \right )=\frac{1}{2}kx^{2}.$$ Then suppose the point $x=x_{0}$ is the point of a local minimum. We know that any potential about a local minimum ...
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3answers
9k views

Density of states of 3D harmonic oscillator

Consider the following passage, via this image: 5.3.1 Density of states Almost all of the spin-polarized fermionic atoms that have been cooled to ultralow temperatures have been trapped by magnetic ...
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1answer
7k views

Work Done by Gravitational Force

[Bit a long question] Here in this question, I need to know clear my doubts on Gravity, more precisely Work done by a Conservative Force(here, gravitational force). Ok, suppose there is an object ...
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1answer
59 views

Is there a basis for naming these empirical fluid model coefficients in terms of flow regime?

Given any flow restrictive device (e.g. pipe, orifice, screen, etc.) one can measure data as the pressure drop across the device relative to the flow rate through the device. And from this data one ...
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2answers
611 views

Einstein GR and metric signature

Let us take the einstein Equation $R_{\mu\nu} -\frac{1}{2}g_{\mu\nu}R = T_{\mu\nu}$. I'm just ignoring all the constants. For a perfect fluid, $$T_{\mu\nu} = (\rho + P)u_{\mu}u_{\nu} - Pg_{\mu\nu}.$$ ...
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2answers
748 views

Potenial difference from electric field and line integral

I am really confused about the relation of potential difference and the electric field. The relation between potential and electric field is $$V_{ab} \equiv V_a - V_b = -\int_{b}^a{\vec{E}\cdot\vec{...
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2answers
32k views

Potential inside a uniformly charged spherical shell [closed]

If the magnitude of the electric field inside a uniformly charged spherical shell is zero then is how potential a non-zero constant equal to the potential of shell itself? How does a non-zero ...
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1answer
851 views

Fleming's left hand rule

in Fleming's left hand rule is the direction of current showing the direction of the flow of electrons or the direction of positive charge?
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1answer
2k views

Levi-Civita symbol in Euclidean space

Suppose a component of tensor field is described by $B^k=\varepsilon^{kij} \phi_{ij}$. If we define $B^k$ in an Euclidean space then does the rising or lowering of the indices of the Levi-Civita ...
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2answers
2k views

Why can we assume a current direction when using kirchhoff's circuit law?

Reference direction: When analyzing electrical circuits, the actual direction of current through a specific circuit element is usually unknown. Consequently, each circuit element is assigned a ...
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3answers
712 views

Are contravariant basis vectors and basis 1-forms identical?

The reason I'm asking this is because I am trying to develop a set of notes from my reading of MTW (and Wrede, Menzel, Bergman, etc.). I represent covariant basis vectors with $\mathfrak{e}_{i}$, ...
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1answer
65 views

Operator $A$ only act on the neighboured state or operator but not the entire expression?

In state vector formalism $A|\psi(x)><u(x)|=(A|\psi(x)>)<u(x)|$, where $A$ only act on $|\psi(x)>$ However, in terms of wave formalism, suppose $A$ is the well known $\frac{d}{dx}$. ...
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4answers
719 views

The definition of the Lorenz gauge condition

The inner product of two vectors in space-time is: $$(x_1, y_1, z_1, t_1) \cdot (x_2, y_2, z_2, t_2) = x_1 x_2 + y_1 y_2 + z_1 z_2 - t_1 t_2$$ So $$(\frac{\partial }{\partial x}, \frac{\partial }{\...
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1answer
624 views

Trouble in deriving the Rayleigh-Jeans formula from the steps shown on HyperPhysics site

Hi I am very new to this aspect of physics and I am having trouble with the derivation of the Rayleigh-Jeans from the steps shown at the hyperphysics web site. I have emailed Dr. Rod Nave who is ...
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1answer
101 views

Unit definition concerning light and metre [closed]

A stupid question. I see metre is officially defined based on the speed of light: The meter is the length of the path travelled by light in vacuum during a time interval of 1 / 299 792 458 of a ...
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2answers
2k views

Cross product and the right hand rule - what is the intuition behind it? [duplicate]

I understand that by convention, the cross product is defined to be the vertical projection of vector $A$ on $B$ in the case of $A \times B$. But the vertical projection of $A$ on $B$ would still be ...