Due to QFT books, we measure pole mass(physical mass) in experiments. From the Lagrangian point of view, renormalized mass is a parameter(in MS bar or some similar renormalization scheme that has an explicit renormalization scale)  We fix renormalized parameters ( renormalized mass, renormalized couplings and ...) at specific energy scale by experiments.  But the problem is that how do we measure renormalized mass? beacuase in any expriment we measure pole mass which is scale independent  For other renormalized parameters, I have no problem.
I am reading Schwarz QFT and I reached the mass renormalization part. So he introduces, after renormalization, a physical mass, defined as the pole of the renormalized propagator, and a renormalized mass which can be the physical mass, but can also take other values, depending on the subtraction schemes used. Are these masses, other than the physical one, observable in any way experimentally, or are they just ways to do the math easier (using minimal subtraction instead of on-shell scheme, for example)?   Also, in the case of charge renormalization, the explanation was that due to the vacuum polarization, the closer you are to the charge, the more you see of it, so the charge of the particle increases with the momentum you are testing the particle with. However, I am not sure I understand, from a physical point of view, why do you need to renormalize the mass. Is this physical mass (defined as the pole of the renormalized propagator) the same no matter how close you get, or it also changes with energy? And if it changes, what is shielding it at big distances?
Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ is reducible over $\mathbb{Q}$? We know that $f(x)=x^4+1$ is a .  My question is:     Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ has a linear factor over $\mathbb{Q}$?   Edit: Thanks for @Jyrki Lahtonen's answer, I want to do some modifications:     Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ is reducible over $\mathbb{Q}$?   Thanks in advance! There is a book I read in the 1980s or 1990s from a Ca.  library. It was a hard copy not a paperback. It is not "To Outlive Eternity/Tau Zero" by Poul Anderson (I have that one). It may have been written by a woman or someone whose last name starts with an "L".  A large crew of men and women are in a new super fast space ship. They are being chased by someone and they outrun the collapse of the universe, but they have lost their home planet. They watch as the universe is reborn. They go into orbit around a planet that looks like it can support life like theirs. They are moving super fast. They look like a ring of radiation going around the planet. They put down 10 super metal markers with scientific info onto the surface of the planet. They watch the planet develop and form life like the dinosaurs and then evolve into human like life forms.  There are 2 warring countries on the planet. They block or turn off the sun to freeze the planet and force the countries to form one world government. The planet gets freezing cold and the people start to freeze. The countries agree to form one world government. The people on the ship are welcomed to the planet. Dates and times: "on", "in", "at"? I’m often confused when I speak about times and dates. What is the rule for using on, in, and at in the following sentences?   I will do it ___ Tuesday. We married ___ March. He returned ___ the same day. Every day ___ the same time, I walk the dog. Computing convex hull of points using shapely Bending of light - photon's inertia instead of mass Using classical mechanics, the formula for gravitational attraction is   $$F = G\frac{m_1m_2}{r^2}.$$   This formula does not work for photons, and we need to use Einstein's theory of gravity to account for that, as the photon is massless. What if, instead of using the mass of the photon, we rather used the inertia of it?  The momentum of a photon is     $$p=\frac{h}{\lambda}.$$  Thus, using that, we can calculate its supposed 'mass' (inertia) as momentum is also equal to mass times velocity. So 'mass' of a photon is     $$m=\frac{p}{v}=\frac{h}{\lambda  c}.$$   If we use this mass as the mass of a photon, can we use Newton's equation for gravitational attraction? Awk: if pattern not found add some text at the end of file What do we mean by hyperparameters? Use a LookUp field in a Calculated Column Today I found something strange on my newly installed Windows 7 OS - my "users" folder C:\Users was shared and "Everyone" had full access... I disabled that and now it seems fine, however I'm a bit scared actually, I'd like to know what caused that and if my system is compromised. Cannot mount NTFS partition in Ubuntu 13.04 After I installed Ubuntu 13.04, I can't mount my NTFS partition.  Error mounting /dev/sda5 at /media/mrxfly/xFLyDiskData: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda5" "/media/mrxfly/xFLyDiskData"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda5': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option. Can I use my familiar to cast Warding Bond on myself? Find Familiar lets you cast touch spells through your familiar. Warding Bond is a Touch spell, that creates a connection between "you and the target". I can't find anything against it, but would it be possible to have my Wizard make his familiar cast Warding Bond on the Wizard himself, so that the Wizard gets the +1 to AC and saving throws and resistance to damage?  I realized after I wrote this much that Wizards don't get Warding Bond, but I think the question is still valid for multiclassers. what is the difference between IBE and ABE schemes Can somebody explain in simple words. real life example light help and limitations of these schemes etc. Test model coefficient (regression slope) against some value In R, when I have a (generalized) linear model (lm, glm, gls, glmm, ...), how can I test the coefficient (regression slope) against any other value than 0? In the summary of the model, t-test results of the coefficient are automatically reported, but only for comparison with 0. I want to compare it with another value.  I know I can use a trick with reparametrizing y ~ x as y - T*x ~ x, where T is the tested value, and run this reparametrized model, but I seek simpler solution, that would possibly work on the original model. Academic papers using Stack Exchange data I'm new to the ICS os, coming from Gingerbread from another phone. The phone's quite nice and fast when I first used it, but just this morning it started exhibiting weird actions. Camera360 doesn't open up automatically when I click it, the Camera closes for no reason, Pocket restarts when an article has an image, and TTPod resets the song to the previous song on my widget in the middle of a new song I'm playing.  I checked out the ram, and and was surprised to see 500+ mb used, 0 mb available. I looked at the list of programs and I see the usual culprits like Facebook, but the ram they're using doesn't add up to 500+ mb. Yeah, I know that the whole ram indicated isn't usable by the apps, but I don't think I've done anything to warrant the 0 mb. I close my apps. There are times when there's free 4 to 5 mb, but I think that too shouldn't be the case. I tried installing Advance Task Killer, it listed less than 10 apps, killed it, still the ram is what it is above.   I did a reboot, and now it reads 300+ mb usage, 200 something free.   What can I do? How do I ensure an app's closed on ICS? I installed GoLaucher because it has a handy task killer and I can see the ram freed in an instant, but I would like to know if there's a better way to handle the RAM. I was trying to understand the internal structure of AES (Advanced Encryption Standard)  The Standard order of steps within a round:   Substitute Bytes Shift Rows Mix Columns Add Round Key   Substitute Bytes, Shift Rows &amp; Mix Columns satisfies the two most important properties required for a secure cipher i.e confusion and diffusion   Substitute Bytes provides Confusion i.e. that each binary digit (bit) of the ciphertext should depend on several parts of the key.  Shift Rows along with Mix Column provides Diffusion i.e. if we change a single bit of the plaintext, then (statistically) half of the bits in the ciphertext should change  Changing the order of Step 1 and Step 2 won't have any effect. But to what extent can we change the order of other steps? Does it weakens the security of AES, and if so, how? Strange behaviour of macros C/C++ Splitting file based on size, but make sure that it ends with newline Is the XP for an encounter split among the party members or not? At this point, I am unclear as to how to handle encounter XP. Does each surviving party member receive a proportional share, or the full amount? That is, assume a 4-character party had completed an encounter worth 400 XP. Would each party member receive 100 XP, or 400 XP? Been trying to find graphic novel for decades - at least I think it's a graphic novel When I was a kid I had a book that I loved, as I think about it I'm pretty sure it would be characterized as a graphic novel although I was unfamiliar with that term at the time. It was a large hardcover comic book but a full-length story, probably a few hundred pages long.  This would have been about 25-30 years ago.  I recall a little about the plot: It starts with a spaceship crashing somewhere, I remember one of the first panels had the phrase that the ship "yawed wildly". I always remembered that because I had to look up the word "yawed".   The rest of the story is told in flashback form, with the rise of an empire, and I'm pretty sure there's a guy who's a slave or otherwise in the lower strata of society who rises to be the ruler of the world or something like that.    I thought that the title had the word "titan" or "empire" in it (Empire of the Titans, or Rise of the Titans, or something similar), but Google searches have been unfruitful.