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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Why are generators defined oppositely in Weinberg's vs. Maggiore's QFT books?

I've been confused about the sign conventions used in Weinberg's QFT book for a long time. Here's my question: The generators $J^{\mu\nu}$ are defined in this book as $$U(1+\omega)=1+\frac{i}{2}\...
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1answer
216 views

Proportionality Constant in Einstein Field Equations

The Einstein Field Equations: $$G_{ab}~=~8\pi T_{ab}.$$ I am familiar with how to obtain the $8\pi$ proportionality factor through correspondence with Newtonian gravity, but am wondering if this ...
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1answer
132 views

Convert propagators from Euclidean to Minkowski spacetime

I'm looking for a rule to "convert" the propagators of a quantum field theory formulated in Euclidean spacetime into those of the same theory but in Minkowski spacetime (with the $\operatorname{diag}(-...
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224 views

Fermion four-point vertex Feynman rules

So I have a theory which has a four-point fermion interaction $$\mathcal L_{int}=-g(\bar\psi\partial\!\!\!/\psi)(\bar\psi\partial\!\!\!/\psi).$$ I'd like to derive the Feynman rule for the ...
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188 views

Confusion about gamma matrices in Euclidean spacetime

I have encountered a number of sources with differing definitions of the transition from Minkowski spacetime to Euclidean spacetime. I'd like some clarification as to how to go from Minkowski to ...
4
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144 views

Where do the intrinsic parities of particles come from?

It is known that some particles have negative intrinsic parity - for example pion $\pi$. I was wondering if this parity can be understood. I read somewhere that parity of quarks is defined to be ...
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127 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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190 views

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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155 views

What decides the signs and coefficients of terms in superfield?

I'm working on a problem in 3d field theory and I'm confused about how to write the superfields. Specifically, I'm not sure if the signs and coefficients of terms are purely a matter of convention or ...
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67 views

Difference between sign conventions in the action of $\mathcal{N}=4$ SYM

In the paper called Wilson Loops in N=4 Supersymmetric Yang-Mills Theory, the authors define the action for the $\mathcal{N}=4$ Supersymmetric Yang-Mills (SYM) theory including the following term: $$...
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2answers
257 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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1answer
82 views

Dot convention inductors in series: what is going on

So I'm really confused with mutual inductors and dot convention. If your answer is going to be a link to any website I can assure I read them all and that only left me more confused. So here are my ...
3
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1answer
185 views

Sign of counterterm vertex factor (Srednicki)?

My question is about a mere minus sign which, although irrelevant in my specific problem (as will be shown), I fear may bite me later on. In Srednicki chapter 14, the author is computing the 1-loop ...
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82 views

Why are neutrino flavour eigenstates expressed in terms of the elements of the complex conjugate of the PMNS matrix?

If we have $$ \begin{pmatrix} \nu_e\\ \nu_{\mu} \\ \nu_{\tau} \end{pmatrix} =\begin{pmatrix} U_{e1} & U_{e2} &...
3
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1answer
600 views

What is the Planck scale magnetic field strength?

Using the constants $\mu_0$ (or $\varepsilon_0$), $c$, $\hbar$, $e$ and $G$, it is possible to define two quantities with units of magnetic field : \begin{align} B_1 &= \sqrt{\frac{\mu_0 c^7}{\...
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195 views

Conventions in defining spherical harmonics and associated Legendre polynomials

Relevant Background Spherical harmonics are defined with several different conventions: the definition used in quantum mechanics according to Wikipedia is $Y_l^{\,m}(\theta,\phi) = (-1)^m\sqrt{\frac{...
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620 views

General proof of formulas of geometric optics?

In most lf textbooks formulas of geometric optics like lens maker formula and base formula for that are proven (or rather verified from my point of view) by taking specific case (ray diagram) and ...
3
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1answer
450 views

Plane waves in QFT

Suppose we work in the metric $(-1,+1)$. How do we describe an incoming particle with a plane wave; $\exp(-\mathrm ikx)$ or $\exp(+\mathrm ikx)$? What's the difference? Does it change if we work in ...
3
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1answer
150 views

Is there something wrong in my book's derivation of work done on charge?

For finding potential at a point due to a +ve charge $(q)$, we find work done to move a unit +ve charge $(q_o)$ from infinity to that point in the presence of +ve charge $(q)$ Since both charges ...
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88 views

Can an affine first-order polynomial system be chaotic?

While studying chaos theory, one of the basic principles presented to me was that chaos only occurs in deterministic nonlinear systems. This pointed me to learn more about the differences between ...
2
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1answer
146 views

Gauss' Law in 2D?

At first I thought it was $$∮E.dl=Q/ϵ.$$ So i've read through some sources here and on the internet and most of them said that $$∮E.dl=2πq.$$ But I'm confused. Can anyone explain where does the $...
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24 views

Origin of the factor of $i$ in the photon propagator

I'm following Peskin and Schroeder and am having trouble tracking down a particular factor of i that is persistently used in the definition of Green's functions. For example, equation 9.52 states that ...
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2answers
80 views

Is the voltage between the two points $A$ and $B$ denoted as $U_{AB}$ or $U_{BA}$? And why?

Consider the following circuit Is the voltage between the two points $A$ and $B$ denoted as $U_{AB}$ or $U_{BA}$? And why?
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210 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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56 views

Right-Hand Rule and Reactance

In this paper by Guo et al., it is claimed on p. 4 that for a coil in a magnetic field, the induced current in the coil can follow either a right-hand or a left-hand rule, depending on the reactance. ...
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1answer
266 views

Possible Error in Marion and Thornton's Classical Dynamics of Particles and Systems

so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3 The rotation matrix associated with 1.2a and ...
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319 views

Levi-Civita in 4 dimensions to 3 dimensions

i was calculating Pauli ljubanski vector in the case of massive particles . considering the rest frame(m,0,0,0) $W_i =-(m/2)\epsilon_{0ijk} M^{jk}$. I got $\epsilon_{0ijk}=\epsilon_{ijk}$. so, $W_i=-...
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61 views

How does GR reconcile its model of a smooth manifold against the limitations of the planck length?

To paraphrase the classic text, Gravitation by Misner, Thorne, and Wheeler, it is said that we are to accept the model of a continuous spacetime manifold, despite the calculated "violent fluctuations ...
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411 views

Notation for vectors and covectors

This is probably a very simple question, and I think I know the answer, but I cannot find a place to solidly confirm this. So if I want to write a vector $\mathbf{V}$ in terms of its contravariant (...
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402 views

How should we use time reversal operator?

In Peskin & Schroeder's QFT textbook, section 3.6. Time reversal operation on a operator, for example, Dirac field $\psi(t,x)$, is $$ T\psi(t,x)T $$ Some other textbooks, mostly, like QFT written ...
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194 views

Anticommutator BRST charge and $c$-ghost mode

My goal is to compute the anticommutator $\{Q_B, c_m\}$ where $Q_B$ is the BRST charge in string theory and $c_m$ is the $m$th mode of the $c$ ghost field $$ c(z) = \sum_m \frac{c_m}{z^{m-1}} $$ (...
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164 views

Continuation to Euclidean BTZ Black hole

BTZ black hole in Lorentzian signature is given by $$ ds^2= -fdt^2+f^{-1}dr^2+r^2(d\phi + N^{\phi} dt)^2 $$ $$ f=-M+r^2+\frac{J^2}{4r^2},~~~~~ N^{\phi}=-\frac{J}{2r^2} $$ $f$ can be wriitten as $$ f=\...
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137 views

Configuration space of a classical gauge theory: Physics vs. Mathematics

Let's have a look on a gauge theory on a trivial fiber bundle, as it is seen by mathematicians: We have a trivial vector bundle $(E, \pi, M; V)$ with group structure. We denote the sections of $E$ by ...
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70 views

Doubts about Chern-Simons state as a solution of the Hamiltonian constraint in quantum gravity

I've been doing some work with both Baez's Knots, gauge fields and gravity (1) and Gambini, Pullin's Loops, knots, gauge Theories and quantum gravity (2), lately. I have basically two problems: I ...
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0answers
302 views

The sign of a focal length

We know that for converging lens, $f>0$ , for diverging lens, $f<0$. But for many materials I have read so far, it says that: "the focal length of a concave lens is 8 cm." I thought that the ...
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3answers
576 views

Limits of Integration Trig, Mag Field Infinite Length Wire

I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it. Here's the set up: ...
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2answers
4k views

Can we define tension in a string as the reactive force produced in a string being pulled at both ends?

In my textbook, the definition of tension was given that Tension is the reactive force which exists when string is being stretched at its both end. After it there was a case given that to calculate ...
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0answers
99 views

What is “above” and what is “below” the surface of a sphere?

When studying Electromagnetism using D.J. Griffith's Introduction to Electrodynamics, the boundary conditions for the electric potential across a surface charge density are expressed using the normal ...
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294 views

Question about Origins in Galilean transformation

I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, $y'=...
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0answers
157 views

Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) $\hat{H}_{e-...
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208 views

Sign convention with the $AdS$ metric

One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$. But do the signs ...
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2answers
95 views

How does the transformation of 4-derivative into a 4-momentum actually happen in a derivative coupling?

Consider a derivative coupling with $$\mathcal{L}_{int} = \lambda \phi_1 (\partial_\mu \phi_2) (\partial_\mu \phi_3),\tag{7.101}$$ and a scalar field $$ \phi(x) = \int \frac{d^4p}{(2\pi)^3} \frac{1}{\...
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75 views

“$10^{\mathrm{th}}$” Index skipped in M-theory

Why is it that in M-theory, the 11-dimensional vectors are labelled with indices $0 \dots 9,11$. For example, the spatial momentum components are $p_{1}, \dots, p_{9}, p_{11}$. Why is the $10^{th}$ ...
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1answer
50 views

How to decide which way are the limits of an integral?

So, I'm trying to calculate the electric field at a point $r$ distance away on the perpendicular bisector of a finite line charge having uniform charge density $\lambda$ I arrive at the following ...
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0answers
62 views

Conceptual Question on Maxwell's 3rd Equation in Integral Form

$$ \oint_C \vec{E} \cdot d \vec{l} = -\frac{d}{dt} \oint_S \vec{B} \cdot d \vec{A} $$ where $S$ is a surface and $C$ is its boundary. Why is there no negative sign in front of the left-hand side? I ...
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1answer
53 views

Lorentz transformation of Weyl fields

In the Srednicki's textbook, Chapter 35, the author states (Equation 35.28): $$ U(\Lambda)^{-1}[\psi^\dagger \bar\sigma^\mu \chi ] U(\Lambda) = \Lambda^\mu_{\,\,\nu} [\psi^\dagger \bar\sigma^\nu \chi ]...
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0answers
63 views

Regarding number of degrees of freedom of a dynamical system (as well as it's relation to number of equations of motion)

I would like to know why in the context of vibrating systems, we define degrees of freedom in terms of number of independent coordinates (by coordinates I mean the numbers which specify the components ...
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1answer
105 views

Quantization of the Klein-Gordon equation, sign problem

In Peskin and Schroeder, they quantize the Klein-Gordon field in the following way. They write the Fourier transform of $\phi(x,t)$ $$ \phi(x,t)=\int \frac{d^3 p}{(2\pi)^3}e^{ipx}\phi(p,t) $$ after ...
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41 views

Complex notation convention for time variation

In describing plane wave EM variation, some textbooks use the complex notation $\exp(i\omega t)$, while others use $\exp(-i\omega t)$. Is there a motivation for chosing one or the other convention, ...
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27 views

Question on notation convention regarding partial derivatives

H.Risken's book "The Fokker-Planck Equation" contains the following formula for the general 1D Fokker-Planck equation: $\frac{\partial W}{\partial t}=\left[-\frac{\partial}{\partial x}D^{(1)}(x)+\...