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
188 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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380 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 ...
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1answer
1k views

Dirac action and conventions

I have a (possibly) fundamental question, which is driving me crazy. Notation When considering the Dirac action (say reading Peskin's book), one have $\int dV\;\bar{\psi}\left(\imath\not\partial-m\...
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1answer
226 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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57 views

Error of $-i$ factor in light cone indices in conformal field theory in Becker's book

In Becker's book of String theory Ch-$3$ I'm getting an error of factor $-i$ in the definition of lightcone indicies after Wick rotation. The convention of the book is following $\sigma_{\pm}=\tau\pm\...
4
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1answer
237 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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450 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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158 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 ...
4
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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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201 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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161 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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71 views

Lorentz transformation in QFT

A Lorentz transformation can be seen as a change in reference frame. So, after apply a Lorentz transformation to a system (or change the reference frame), how should the state and field operator ...
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54 views

Spinor covariant derivative conventions

The covariant derivative of a spinor $\psi$ is given by $$ \nabla_\mu \psi = \partial_\mu \psi + \Omega_\mu \psi $$ where $\Omega_\mu$ is the spin connection. In equation (7.227) of Geometry, Topology ...
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83 views

Time reverse transformation of 4-potential and its relation to Lorentz transformation

Until now, I thought electromagnetic potential $A^{\mu}(x)$ transform like $x^{\mu}$ under the Lorentz transformation: $$A^{\mu}(x)=\Lambda^{\mu}_{\ \nu}A^{\nu}(x).$$ But according to time reversal ...
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75 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
287 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}...
3
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1answer
93 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 ...
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1answer
246 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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86 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
684 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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214 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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637 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 ...
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1answer
160 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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1answer
527 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 ...
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94 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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27 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 ...
2
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224 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
327 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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1k views

Stress Tensor Sign Convention

I'm hoping someone can clear up this confusion I have with the stress tensor. So here is what a stress tensor looks like as described by many authors: I understand that the shear stresses acting on ...
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332 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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64 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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455 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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432 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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210 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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170 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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155 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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72 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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323 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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100 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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378 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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163 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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216 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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43 views

How do we Wick rotate the Maxwell $U(1)$ gauge theory's field strength $F$?

How do we Wick rotate the Maxwell $U(1)$ gauge theory's field strength, say in 3 space and 1 time dimensions? Suppose we start with a Lorentz signature with coordinates $(x_0, x_1, x_2, x_3)$, then we ...
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41 views

Problem with derivation of Dirac equation

In my book on QFT (Lancaster & Blundell) while deriving the Dirac equation, they arrive at the following result: $$(\partial ^2 +m^{2})=(\not\!\partial -im)(\not\!\partial+im)$$ They then state: &...
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43 views

How to show ${\epsilon^{ij}}_k {\epsilon_{ij}}^l = -2\delta^l_k$ for the Levi-Civita symbol?

I am trying to prove the following identity for the levi civita symbol $${\epsilon^{ij}}_k {\epsilon_{ij}}^l = -2\delta^l_k,$$ taken from the Ashok Das QFT book pg 153, equation 4.102. I made use of ...
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57 views

Wick rotation on Ward identities

I'm having trouble performing a Wick rotation back to Minkowski spacetime ($\eta_{\mu\nu}=(-1,1,1,\dots)$), following page 19 in the lecture notes here by C.P. Herzog. I have this expression (equation ...
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62 views

Feynman rules for derivative couplings with identical particles

Consider the interaction Lagrangians given by \begin{align*} \mathcal{L}_1 = A_\mu \ \pi^{0} \ \partial^{\mu} \pi^{0}\\ \mathcal{L}_2 = B^{\mu\nu} \ \partial_\mu \pi^{0} \partial_{\nu} \pi^{0}\\ \...
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54 views

Algebra of Noether's charges and algebra of symmetry transformations

I'm trying to understand the connection of algebra of transformations under a commutator and algebra of Noether's charges under Poisson bracket. I have a problem that results I infer from theoretical ...