Gamma matrices Puns

Hi, for the vacuum polarisation problem (photon self energy): https://i.imgur.com/FV5YqTf.png, we can reduce the (relevant) bit of the feynman amplitude down to this: https://i.imgur.com/aZ4gTm7.png

Any help with figuring out how to manipulate these gamma matrices to get from the first to the second line in that picture? (And if you have a bit more time, how i can figure out that it's logarithmically and not quadratically divergent?) EDIT: I guess these facts help? https://i.imgur.com/kAUTNjp.png

I figured out how to manipulate them to get the second line, just need to figure out how that's logarithmically rather than quadratically divergent now

Howdy ya'll.

I'm trying to really understand the following equation:

[; \left[ \gamma^ {\mu} , S^ {\rho \sigma} \right] = \left( \mathcal{J}^ {\rho \sigma} \right)^ {\mu} _{\ \nu} \gamma^ {\nu} ;]

where gamma represents the four gamma matrices, S are the six generators of the spin 1/2 representation of the lorentz group, and [; \mathcal{J} ;] are the six generators of the "ordinary" lorentz transforms. You can also write this as:

[; \Lambda_ {1/2} ^ {-1} \gamma ^ {\mu} \Lambda_{1/2} = \Lambda ^ {\mu} _ {\ \nu} \gamma ^ {\nu} ;]

by exponentiating each of the operators.

Here's how I think I'm supposed to interpret this: when we perform a similarity transform on the gamma matrices using the spin representation of the lorentz group (which puts the gamma matrices in a different but algebraically equivalent basis), we get the same answer as if we had treated the all gamma matrices as a single four-vector and operated on them with an ordinary lorentz transformation. Thus, we have found that our gamma matrices are invariant when we change both the vector and spinor indices simultaneously.

I have one more question, if what I have understood so far is correct: does this mean that when you specify a particular spin representation of the lorentz group, you are then forced to choose a matching ordinary representation? E.g., are the chiral representation and dirac spin representations of the lorentz group each associated with a different representation of the ordinary lorentz group?

If you wanted to as-seamlessly-as-possible integrate gunfighting, motor vehicles, etc., from the 20th-into-21st Centuries into your TSR-era D&D game, where would you source rules and statistics? The Boot Hill stuff in the 1e DMG didn't help me.

To be clear, I want adventurers swinging longswords and casting spells, alongside people shooting guns (all sorts) and throwing grenades, in combats that involve cars and helicopters, using the same attack-matrices-or-THAC0-versus-an-Armor-Class rules we all know and love. I want a set of statistics and simple mechanics I can plug-and-play into my existing OD&D-into-AD&D rules framework without giving myself a week of math homework.

Do these rules exist? Has anybody done a backwards-conversion of D20 Modern? I'm totally ignorant about Gamma World and don't have recourse to a reference copy; is that what I need? HELP. Please? Thanks!

Good evening captains!

I've always been a huge fan of energy weapons builds, they're pretty much everything I've ever played, and I've gotten pretty good at it I'd say. But it's time to try something new, so I decided to work on an EPG build on the Legendary Glenn. I've tried to incorporate elements from several guides I've found but they weren't always as helpful as I wanted. I've cobbled together most of a build with everything I've had on my character, but there are still some unanswered questions below the build.

For the stuff I have access to (and that could be relevant): 10th Anniversary bundle, Gamma Vanguard Pack, New Genesis Bundle, ETM, SIA, and some other stuff that's more relevant for energy builds. I won't mind spending a bit more but I don't want to get Lockbox ships and Lobi gear.

I will try to update the build posted here as I get suggestions.

#Captain Details

#Space Skill Tree

Admiral&

I've been slowly grinding Zen since before the Dilex capped, and since we've got a Zen store sale going (and probably a short break between events), I'm thinking it's time to cash in. Now I'm calling on the Reddit Hive Mind to help determine what's going to give me

Factors for consideration.

• Got a little over 12,000 zen, so that's my limit,
• Like any other purchases, my main concern is buffing my main (Fed, Engineer), with any benefits to trickle down to other characters (Basically, one of each type, plus an extra Fed), which are mostly used for grinding Dil, plus the occasional "I'm bored, let's switch things up a bit" round of play.
• My main's primary ship is Antiproton-based, and has centered around FAW3/TS3/Entwined Tactical Matrices. Combined with the Ba'ul beams, it definitely spanks the "weenie swarms" that have been popular lately (like at the end of 9th Rule or a good portion of the KCW). The only downside is that I seem to pull quite a bit of aggro with it. However....
• I've been toying with swapping out the Ba'ul beams for crafted-with-[Pen] ones and FAW3 for BO3, and using ETM to swap between the two modes. However, I often find BO3 is getting locked out by ETM's FAW1, so swapping that trait out for something else and going full BO may be warranted.
• BOFFs are mostly-okay; been waiting for my fleet colony to reach T5 so I can get a Kentari Sci, since I accidentally deleted Mr. Potato Head. 'Til then, I've been filling in with the Holo Bashir we got from the Health Care giveaway.

So here's what I'm considering.

• Cardassian Intel Bundle (4500 Zen sale price) - I like Intel ships; has Calm Before the Storm trait; unlocks Spiral Wave Disruptors (useful on other builds/toons), some of the consoles look fun
• Gamma Vanguard Pack (11250 Zen sale price) - All the stuff from the Cardassian bundle; plus a bunch of ships with the Wingman function the; BOFFs to fill in holes in a number of toons.
• Tucker Tactical Miracle Worker Cruiser (2250 Zen Sale Price) - If I decide to go back to straight-up FAW, the trait will help keep it up longer.

Any insight for any of these, or even something else I may have missed?

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

The doctor says it terminal.

Alot of great jokes get posted here! However just because you have a joke, doesn't mean it's a dad joke.

THIS IS NOT ABOUT NSFW, THIS IS ABOUT LONG JOKES, BLONDE JOKES, SEXUAL JOKES, KNOCK KNOCK JOKES, POLITICAL JOKES, ETC BEING POSTED IN A DAD JOKE SUB

Try telling these sexual jokes that get posted here, to your kid and see how your spouse likes it.. if that goes well, Try telling one of your friends kid about your sex life being like Coca cola, first it was normal, than light and now zero , and see if the parents are OK with you telling their kid the "dad joke"

I'm not even referencing the NSFW, I'm saying Dad jokes are corny, and sometimes painful, not sexual

So check out r/jokes for all types of jokes

r/unclejokes for dirty jokes

r/3amjokes for real weird and alot of OC

r/cleandadjokes If your really sick of seeing not dad jokes in r/dadjokes

Punchline !

Edit: this is not a post about NSFW , This is about jokes, knock knock jokes, blonde jokes, political jokes etc being posted in a dad joke sub

Edit 2: don't touch the thermostat

Do your worst!

How the hell am I suppose to know when it’s raining in Sweden?

Mathematical puns makes me number

We told her she can lean on us for support. Although, we are going to have to change her driver's license, her height is going down by a foot. I don't want to go too far out on a limb here but it better not be a hack job.

The nurse asked the rabbit, “what is your blood type?”

“I am probably a type O” said the rabbit.

Ants don’t even have the concept fathers, let alone a good dad joke. Keep r/ants out of my r/dadjokes.

But no, seriously. I understand rule 7 is great to have intelligent discussion, but sometimes it feels like 1 in 10 posts here is someone getting upset about the jokes on this sub. Let the mods deal with it, they regulate the sub.

I'm surprised it hasn't decade.

They were cooked in Greece.

He lost May

Now that I listen to albums, I hardly ever leave the house.

Two muffins are in an oven, one muffin looks at the other and says "is it just me, or is it hot in here?"

Then the other muffin says "AHH, TALKING MUFFIN!!!"

Don't you know a good pun is its own reword?

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

And now I’m cannelloni

Because she wanted to see the task manager.

And boy are my arms legs.

But that’s comparing apples to oranges

Put it on my bill

Heard they've been doing some shady business.

but then I remembered it was ground this morning.

Edit: Thank you guys for the awards, they're much nicer than the cardboard sleeve I've been using and reassures me that my jokes aren't stale

Edit 2: I have already been made aware that Men In Black 3 has told a version of this joke before. If the joke is not new to you, please enjoy any of the single origin puns in the comments

They’re on standbi

BamBOO!

A play on words.

Amy

Me again. I got loads of helpful feedback on my last post. Again, goal is to build a Dewsci MMUE that's as close to "canon" as possible (i.e. phasers/photorps/quantums, etc).

So here we go, this is a heavily revised version based off Jaylie's MMUUE. While I've retained the DECS from my original build, all the polaron stuff is replaced in favour of phaser synergy and moar console clickies. Traits remain the same, since I don't have the ones that Jaylie does, but the Boff powers have also been modified. Bear in mind that some boff powers could be replaced (like maybe SSV instead of TR), but this is a starter build, and then maybe I can swap certain consoles/boff powers out in the future for things which are more effective.

Unlike Jaylie, this one has no hull heals, instead opting for a more offensive config. Healies come from threat reduction and Unconventional systems coupled with DPRM. The idea being that despite the cannon focus, this is actually supposed to be a more standoff build, engaging at 10-7 km and using control abilities to maintain enemy positions while shredding them with cannon fire/secdef/anomalies.

Anyway, have at it!

Player Information

Skill Tree

Hello, and on todays episode of "I have no idea what the fuck I'm doing", I am a basic bitch DEW tactical captain who is attemptong to do SCIENCE.

The skinny: Space magic looks cool, and I have been specifically wanting to use the T6 Multi-mission explorer pack (Palatine/Esquiline/Brigid) because lets face it, those ships look dope. Better than a Somerville, anyway. While I technically wouldn't mind going full EPG, I lean towards Dew rather than torps because a) I have a lot of cool stuff for Dew and b)can't be bothered grinding all the good meta stuff out for torps. Oh, and c) because I absolutely ADORE cannons, they are just the most fun thing ever.

So I've read (note: not necessarily absorbed) the revisiting exotic series, and found a couple of relevant guides/builds Guide to DEWSci and another Palatine Dewsci boat. But I'm still new to science stuff in general, having flown almost exclusively escorts and cruisers.

The nice thing is I managed to pick up quite a lot of good stuff during the sales for fairly cheap, so I THINK I'm pretty well equipped.

So without further ado, I'll paste up what I've got so far, and feel free to rip it apart - I'll put the hard requirements/constraints in at the top, and you guys can mull it over. Anywhere you see: "???" is a hole - as in, I have no idea what goes here, and I need your advice.

BIG NOTE: I also have the mirror Engle, which means I have Superior Area Denial and the mirror shuttles - I have left this out of the build currently, because IDK if you guys have anything better to suggest.

#READ ME FIRST

##Hard requirements:

• MUST be a ship from the Starfleet Multi-Mission Explorers Bundle - I've used the Palatine here, but if there's a better pick, go for it.
• Weaponry MUST be mostly DEWSci, preferably cannons/turrets - Polaron has been slotted here (grudgingly) because of the set bonuses, but honestly, I've got all the kit for phasers too.
• Hangar Pets left unslotted because I'm looking for the best Fed/Mirror Fed pets to feel like a starfleet boat. I can sort of rationalise starfleet outfitting a ship with experimental polaron weaponry, but elite scorpion fighters are just taking the piss.

##Notes: