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
$$U(1+\omega)=1+\frac{i}{2}\...
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Why does the dielectric current density operator is twice its value?
In second quantization, the time-independent Hamiltonian for free fermions is written as
$$\mathcal{H}_0=\sum_\sigma\int\mathrm d^3 \mathbf r\; \Psi^\dagger_\sigma(\mathbf r) \frac{\hat{P}^2}{2m } \...
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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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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\...
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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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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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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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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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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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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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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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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 ...
user56199
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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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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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Sign ambiguity of two diagrams in Mahan's book
In Mahan's book 'Many-particle Physics' 3rd Ed., Eq. (3.213) on page 135 gives a sign rule for Matsubara Green's functions $$(-1)^{m+F}$$ where $F$ is the number of fermion loops and $m$ is the order, ...
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