Hamiltonian for Fermionic Fields

Log in or Sign up to hide all adverts.

Sorry, I was in a rush this morning, and I answered the most important. I will answer them now, hold on.

 

Log in or Sign up to hide all adverts.

Log in or Sign up to hide all adverts.

Now that I recognize what they are supposed to mean, I can say the epsilon_k must be a scalar since it refers to energy. Mu appears to be a chemical potential, is also a scalar. I don't remember where I got the equation - I never saved the page. No - I wondered whether mu related to the muon particle, but that can thankfully be put to rest - it is ~ after a little investigation is the chemical potential. The usual suspects... I thought I answered this part. They are the matrices \(\alpha, \beta\) which have the properties \(\alpha \beta+ \beta \alpha= 0\). M is for mass and c and p are speed of light and momentum, of course.

 

Well, any questions I had on it, no longer apply. The equation I began with, did not have a coupling term for the ZPF, which confused me because I was under the consideration that the electrons gained energy from the ZPF. Apparently such contributions do not happen unless we are talking about sufficiently high enough temperatures. I am now waiting to found out if my last post to Rpenner nips that in the bud, and I have come to the correct understanding. One thing I don't understand is that the total energy of the Fermi gas at absolute zero is larger than the sum of the single-particle ground states. Surely this cannot be tested since absolute zero of the vacuum can never be acheived, so how such a proposition can be made seems more like guess-work.

 

I wish I could give you a more... exhilarating answer. But, essentially, I have simply been reading up a lot on Hamiltonians the other day. Then I came across a seperate link to a book by a PhD that suggested that electrons gain a certain amount of energy from ZPF energy\(_{fluctuations}\). In light of this, I wondered why the simplest of total energy states in field theories did not express this quantity. Apparently, now with a little help from rpenner, the energies required for such a ''difference'' are acquired only at large enough temperatures. Low temperature Fermi gasses are not concerned with coupling interactions from the ZPF. The equation where I coupled the ZPF energy interaction with fermions would only suffice for large enough temperatures, and obviously, that Hamiltonian is not really applicable to our normal day universe in so-called ''empty space''. But of course, space is not really empty. It is teeming with oscillations known as the ZPF.

Now the problem I am facing involves the theory of Fermi gasses. I seem to find an inconsisteny in the understanding of theory. The sum of the ground state of the energy is actually less than that which is found in the total energy of the fermi gas at absolute zero - the statement however cannot be true, or atleast, a proven fact, because absolute zero temperatures can never be attained. Atleast to every oscillation there will be half the energy of a quantum packet left, hence why absolute zero is a myth.

 

If you don't know the connection between the equation of motion and the Hamiltonian then you are, as James R says, delving into areas vastly beyond your abilities. The fact you wondered whether the Dirac equation is[/] the Hamiltonian is bad enough but this is just like watching a car crash in slow motion.

Stop thinking you're deceiving anyone and be a lot more realistic. If you honestly want to spend your time in the future hopefully doing physics, ie being paid to do research, then you're going about it in completely the wrong way. No university is going to be fooled by you (unless you try some creationist degree mill in Alabama), never mind those people who decide on PhD funding, to say nothing of levels of research beyond that, academic or commercial. You're wasting your own time, because ultimately you achieve nothing. Are you any step closer to being able to do the physics of which you speak? No. Are you any step closer to being able to do competent research? No. So what is the point? If you honestly want to do research at some point in your life then you need to change your approach. If you just want to con suckers into thinking you understand stuff you don't then sod off and find a forum which will accept that kind of crap. Either way continuing on your present course is a waste of your time and ours. There's no point explaining the specifics of fermionic Hamiltonians when you can't do basic calculus, upon which variational principles are built, upon which Hamiltonian mechanics is built. No one builds a house starting with the roof, they put the foundations down first and you seem hell bent on skipping the foundations.

 

Whatever happened to the days when people came to forums to ask questions and this was acceptable? Even troll slayers like alphanumeric deter a good discussion.

Boring sod. And I think you will agree, I never ever stated I wanted to take physics to a university level, and even if I was, I would certainly need not fool anyone. I would have to go through the same channels as you once did. Fool.

 

(emphasis added)

So, would it be appropriate to cesspool every thread you start on university-level physics? Please demonstrate your human ability to communicate usefully and explain why or why not.

 

The issue is that you aren't asking out of vague interest. You've said things like you know a lot about the Dirac equation, yet you start this thread.
You want people to think you're competent in this, that you're actually doing work in this stuff and threads like this appear to be attempts to reinforce that appearance.

I know we're not telling you what you want to hear but that's sometimes the best reply. If you truly want to grasp this stuff then those of us who have grasped it are the best people to know what things you must know before tackling this stuff. And every one of us who has done it thinks you've skipped too much and you're not understanding the basics enough. That's a comment you don't want to hear I'm sure but its still honest advice.

A full and detailed reply, including relevant explanations, to your original post would be lost on you because you don't understand the things such an answer would be phrased in terms of. If you want detailed high level answers you're going to have to show you would understand them and you've failed to do that. If you can't be bothered to learn the basics, the essentials upon which any good understanding of physics is built, why should anyone be bothered to provide you with answers? Why should we help you when you won't help yourself? If all any of us did was just provide lengthy answers without regard for the level of understanding the recipient has then it'd be a waste of everyone's time.

I'd say the same to anyone, this isn't some specific thing about you. You can't do quantum field theory if you don't know quantum mechanics and special relativity. You can't do fermionic Hamiltonian mechanics if you don't know Hamiltonian mechanics. You can't do Hamiltonian mechanics if you can't do variational principles. You can't do variational principles if you can't do vector calculus. You can't do vector calculus if you don't know vectors or calculus. See how it builds up?

Like I said, you want to waste your own time asking about topics you don't know to first thing about? Fine, no skin off my nose, its your own time you're wasting. Just don't be surprised if people can't be bothered to answer your questions in any kind of detailed way when they feel the details would be lost on you.

Yes, saying "You need to do the basics before going on to the advanced stuff" is boring but you'll not find a single person doing the advanced stuff who skipped the basic stuff. I've said it before, I know the basic stuff isn't 'cool' but its a necessary evil. Its not really even an evil, having a broad familiarity with mathematical physics topics is what having a well rounded understanding is all about.

I didn't specifically say just university. If you plan to do science in any serious way, regardless of where you do it, you're going about it in completely the wrong manner.

And if you think I'm a fool because I'm offering you honest advice based on personal experience then I think you should get yourself a dictionary, along with a few introductory books on vectors, linear algebra and calculus.

 

What a shameful reason. Free forums for the public should not be run by axiomatic rigid dogmatists who form closed sub-groups cut-off from popular discussions by more niaver posters.

 

No, I think your a fool for thinking I would even try to somehow... evade proper channels to achieve a doctorate in physics, and now we have surcomed to the fact I never said that, in any science will do you now.

Alphanumeric, there has been no harm in my presence here. I have not tried to manipulate anyone to believe in a bad science. If anything, most things I have said I have been able to back up, and most things I say to other people are most of the time, correct. Sure I have made mistakes, we all do.

Secondly, it seems this little conquest you and rpenner are on, where you slay the elite group of trolls is not only pointless in most cases with one individual alone, but its an endless war at that. If you class me as one of these trolls, then just say so, crank maybe? You have never called me these things outright, but I could possibly believe you want to, or are waiting for a very a good reason.

You don't have the necessery forum skills to invite a good dicussion, which goes for many here, unless that discussion is by the small closed nit group I have referenced here before. Not naming names, because I don't want to sound like a broken record, you know?

Please Register or Log in to view the hidden image!

Sad thing is, this place does not belong to you, and you have no right telling anyone to sod off.

 

I never ''wondered'' it per se, Alphanumeric. I linked to a paper on the Dirac Equation... You do this all the time. Why? If the link was incorrect tell me so. Stop making me out to be the bad one all the time. It's disingenuous, harsh and misleading to the facts.

 

Why didn't you just say it was to do with the variational principle? Then I would have understood. It's a bit like me asking what mu was, and no one told me. Instead Rpenner posted a lot of math, totally evading any direct help. Eventually I worked out what her equations meant which is how I found out. You guys drive a hard game.

The expectation value of \(\hat{H}\) is never lower in value than the true ground state energy \(E_0\) which is the expectation value of \(\hat{H}\). I can see how something like that would apply to the claims of the wiki article.

Why oh why, do people dance around making it so difficult. Why don't they cut to the chase and let the person they are telling worry about the answer.

 

Which is why there is always a higher energy, [or should be] a higher energy present [if] the system had managed to reach a zero temperature, [which is still impossible].

 

Who said this forum is free? You, me and almost everyone else are allowed to post at the whim of the moderators, who get their authority from whoever owns the site.

Where did I say that? I said that if you have any plans to do any kind of science in the future then you're going the wrong way about learning it. Academia or commercial or for your own kicks, it makes no difference to the fact your method of learning is deeply flawed.

Actually there is. You've posted a fair few threads where you present your own 'ideas' as sound and viable physics. If someone who didn't know any physics came along and read those posts then they might think what you're saying is accurate and thus they would have their understanding tainted. You obviously thought what you were saying was valid, because even after I went through a large chunk of it and explained error after error you came out with things like "I take it that everything else you agree with", again presenting your personal views or understand as viable physics.

Asking honest questions is not a problem. Putting your own 'original research' forth as accurate when it is not is a problem.

You've rarely backed up your claims. You've shied away from any attempt at a proper discussion. You've ignored a great many corrections.

And it isn't entirely about what you say about physics, its what you say about yourself. You investigate the Dirac equation but you don't know about Pauli matrices. You have looked at vorticity in electromagnetism but you don't know the cross product. You're supposedly familiar with concepts in general relativity but you've never heard of polar coordinates or what covariant means. These things point to you being disingenuous, which makes threads like this seem like nothing more than an attempt for you to appear to be talking about high level stuff. If you're skipping things like polar coordinates and Pauli matrices and jumping to GR and QED then you're not going about learning this stuff properly.

Waiting? As if there hasn't been enough reasons to already?

If someone like QuarkHead had started this thread I'd be a lot more on topic because I'd know he actually wants to learn about it and his current level of knowledge is sufficient to get into the details. With you threads like this only serve to reinforce the view that you're biting off more than you can chew.

If you started threads on things like basic linear algebra and calculus you'd get more replies on topic, as that's the kind of discussion which you'd benefit from, ie people wouldn't be so obviously wasting their time answering you. Asking questions on fermionic Hamiltonians when you don't know the connection between a Hamiltonian and the equations of motion is a waste of your time and anyone who puts in effort to explain the specifics.

What use is you knowing the Hamiltonian for a fermionic field if you don't know the methods which then allow you to actually do something with that information? There's no point someone giving you a canoe if you don't have a paddle to make use of it.

I do, I just see no reason to expend considerably more effort writing a full explanation of concepts you lack the required grounding in. If I explained the specifics of Hamiltonian mechanics within string theory to a 7 year old I'd be wasting my time and theirs. If I explained it to someone whose competent at quantum field theory, general relativity and a slew of mathematical methods then it wouldn't be a waste.

When you can demonstrate you aren't the 7 year old in that analogy then you'll get more in-depth relevant replies. Until then the only piece of advice anyone should be giving you is that if you want to understand the high level stuff properly (ie more than what an afternoon on Wiki can give) then you're going to have to start at the bottom, just like everyone else.

Previous members who did as you are doing, posting pet theories on topics they know nothing about, throwing out mish-mashes of LaTeX code, deluding themselves and being utterly unwilling to accept any correction or advice from anyone, no matter how relevant, have been banned for 'wasting people's time'. Whether or not you're a sock puppet of Reiku, you're displaying precisely the same behaviour as he did and he's the person who got banned for the aforementioned reasons.

I know you don't want to hear advice which isn't just "OMG you're doing really complicated stuff, that's amazing!" but that doesn't make my advice an insult. You won't find a single person who can do the complicated stuff but who skipped the simple stuff, why should you be any different?

 

Ooohhh.. being really nasty with the specifics. Well, yes. Plasma would have had to [pay] for the site. As for me and you, we pay diddly squat, the whole point of being a free forum for the public.

As for posting ideas, you will find theyn were subejcted to psuedoscience, so I would not whine if I was you. If I was subjecting them to the physics subforum, then yes you would have a valiant point.

''I do, I just see no reason to expend considerably more effort writing a full explanation of concepts you lack the required grounding in.''

Taking into consideration all the whining you do about posters whining, I dare say I could have learned a great deal more off you since my time here. You fail to do that with so many - educating those around you is not your primary goal. If anything, slanging matches are more up your street.

And what mish-mash of latex? Are you now accusing me of being out of order because I know how to type latex? I think we should concentrate in this thread, because I think you might be referring to the Hamiltonian. Which one?

 

And don't say I don't have the knowledge to understand your teachings, if you have that capability. I actually prize myself for picking up on these concepts you believe so ''evidently'' elludes me actually quite well. It doesn't take me long at all, so you are my guest at anytime if you want to civily teach me something. I love learning new things.