Hamiltonian for Fermionic Fields

Discussion in 'Physics & Math' started by Green Destiny, Nov 14, 2010.

  1. AlphaNumeric Fully ionized Registered Senior Member

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    So its my fault you don't show enough understanding to be worth explaining high level topics to? Its my fault you appear to have no interest in honest back and fore discussions? Rpenner made a comment earlier in the thread about you not engaging in actual discussion and I agree with him. Attempts to engage in discussion of the details ends up with you saying something wrong, someone correcting you, you complaining and then the thread never recovers because you have to have the point reiterated 10 times, from multiple people.

    Okay, if you want an actual discussion lets first gauge the appropriate level of any answer. Do you know what a Hamiltonian is? A Lagrangian? Can you go between them? Do you know how they relate to things like the Dirac equation or the Einstein field equations? Are you able to do variational methods (actually do, not quote the Wiki definition)? Are you familiar with functional analysis in any way? To what level of linear algebra are you comfortable with? To what level of calculus are you comfortable with? When answering "to what level" please give examples of things you are comfortable with.

    Once we nail down what you do and don't know we can start filling in the gaps of what you don't know. If you are honest and forthcoming then I'm willing to be pleasant and jolly. Start bullshitting then don't expect a hug from me.
     
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  3. Green Destiny Banned Banned

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    How oh how did you actually extract the above from what I said to you? You said you have no intentions trying to teach me anything on top of all the other things you do here - In which I replied if you actually stopped whining about whiners I dare say you could have actually taught me something worth while. I never said anything was your fault in the context you put it - if anything it is your own failt for wasting your own time.

    Nice. I will return later. I have children to take care of for the next hour and a half. But I will return and then we can construct what we will do - gauging. I will say off hand I only know elementary gauging, like symmetries for instance in a U(1).
     
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  5. AlphaNumeric Fully ionized Registered Senior Member

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    The time I spend on forums is some aside from work, I do not really attempt to use it constructively to further my own understanding of anything, that's what work is for. I 'waste' 15 minutes typing a retort to your lengthy essays, which you've wasted days on. When I want to spend my time constructively I can. If you're thinking you're spending your time constructively with those essays then you're mistaken. That's the difference.

    I didn't say 'gauge' in the sense of 'gauge theory', I said 'gauge' in the context of 'evaluating something', ie gauging someone's understanding. This is quite different from gauge theory. If I thought gauge theory were relevant I'd have listed it in the questions I asked you.

    As for U(1), the example I gave in this thread of how a system can be invariant overall but individual components not be was the U(1) gauge transformation. Your reply strikes me as just quoting definitions, as you just tell me the notation I used, which is superfluous, and then go on to mention an action, which was irrelevant to what point I was making. The Maxwell action is not \(\partial_{a}A_{b}-\partial_{b}A_{a}\), its built from that. \(\partial_{a}A_{b}-\partial_{b}A_{a}\) is gauge invariant but it is not Lorentz invariant. If you're familiar with the notion of U(1) gauge theories then you shouldn't have needed me to spell out that example in that thread.

    When you reply answer specifically the questions I asked, don't just quote it and reply with something barely relevant, which is something you tend to do.
     
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  7. Green Destiny Banned Banned

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    Do you know what a Hamiltonian is? A Lagrangian?

    Yeh.We may differ though on what we class as ''knowing something'' - but yeh, I think I understand the two quite well.

    Can you go between them?

    Not sure what is meant by that statement.

    Do you know how they relate to things like the Dirac equation or the Einstein field equations?

    No.

    Are you able to do variational methods (actually do, not quote the Wiki definition)?

    I know how the principle enters the Hamiltonian, but that is all.

    Are you familiar with functional analysis in any way?

    Bits. I am sure there is a lot more on it, than I currently know, put it that way.

    To what level of linear algebra are you comfortable with?

    Elementary vector spaces.

    To what level of calculus are you comfortable with?

    Not sure. My calculus is quite bad. I understand the basics of summation and integration.
     
  8. Green Destiny Banned Banned

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    I'm not being fair to myself about question 3. I do know of the Einstein Hilbert action which does show up in relativity. And I do know about the Dirac Langrangian, but I've never worked with them, but familiar to me.
     
  9. Green Destiny Banned Banned

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    Don't even think about it AN. I don't even know what I was thinking about - just piss off. I've had just about enough of you stalking every post of mine on this forum.
     
  10. AlphaNumeric Fully ionized Registered Senior Member

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    If you don't know how to go between them, ie given H work out L or vice versa then your answer to my first question is 'no'. My definition of 'knowing' is not "Can you give me the definition" but do you have a working understanding of them, can you actually solve a problem involving them without having to look up every word or equation's meaning.

    Then your 'investigation' of the Dirac equation cannot have amounted to much, since not non-pop science literature on it will not involve its relationship to a Lagrangian or Hamiltonian.

    So the answer is again 'no', since that amounts to no more knowledge than someone looking up the definitions of the terminology would learn in 5 minutes.

    There's a lot more to functional analysis than a 65 year old professor of functional analysis at Oxford would know, as with pretty much any area of science.

    Then you don't know functional analysis or variational principles, since variational principles need a basic understanding of functional analysis, which needs an understanding of calculus.

    Let's be a little more specific, since its easy to say "Yes, a bit" or "Sort of" to questions of the form "Do you know about X?".

    Which, if any, of the follow cannot, even in principle, be a valid Hamiltonian density :

    1. \(\mathcal{H} = (q_{a})^{\mu}(q_{a})^{\nu}\eta_{\mu\nu} - \ln \Big((p_{b})^{\rho}(p_{c})_{\rho}\delta_{bc}\Big) + t\, \sinh \Big( (p_{a})^{\mu}(q_{a})^{\nu}R_{\mu\nu})\\)
    2. \(\mathcal{H} = \epsilon_{ij}(q_{i})^{\mu}(p_{j})^{\nu}\eta_{\mu \nu } - \sin \Big(R^{\sigma}_{\lambda\xi\phi}(p_{b})^{\lambda}(p_{c})^{\tau}(q_{b})^{\phi}(q_{c})_{\sigma}\Big) \delta_{\tau}^{\xi}\)
    3. \(\mathcal{H} = \exp\Big((p_{a})^{\mu}(q_{a})_{\mu}\Big)- (p_{b})^{\rho}(p_{c})_{\rho}\delta_{bc}\)

    Give an explanation for your answer.

    What are the equations of motion for the following Hamiltonian : \(\mathcal{H} = \frac{1}{2}p^{2} + q \,\sin(q^{2})\)

    If you don't know how to do these then say (remember, be honest or don't expect me to play nice), so we can do another iteration and eventually work out at what level of detail any answer to the original post's question should be pitched at. Please don't just dodge the questions or give irrelevant or clearly copied and pasted replies, as I'll deem that to mean you don't know the answers (which isn't a problem) but you're unwilling to admit it (which is a problem).

    And just to nip a possible excuse in the bud, the total amount of time this should take someone who does know about this stuff is under 5 minutes. Including typing up an answer? 10 max. Competent mathematicians might not even need to put pen to paper.

    /edit

    Let me guess, you saw I was replying and you decided to back out. You didn't like my comment in the other thread, where you clearly didn't know what you were talking about but pretended you did and now you want an excuse to run away from a genuine offer of help. If you were honest about your level of understanding you'd get more help because you'd get replies which are appropriate for your understanding. Fermionic Hamiltonians are not something you have enough grounding to understand and this post was meant to be a working backwards till we hit your level of understanding (which is kinder than the opposite, assuming you know nothing and working upwards, even if that would be quicker).

    You don't like it when people give you honest advice when it isn't something you want to hear. That's a very poor way to go through life.
     
  11. Green Destiny Banned Banned

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    Yes I saw you replying. I was going to send you a private message, then I thought no.

    Look, there is no chance in hell we could have a discussion without you trying to spit on the floor I am walking, so you can think again about me doing this. I really thought you would try to be civil, but I can see what frame of mind you are in, and I am not going to feed it.
     
  12. Green Destiny Banned Banned

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    Even if I was honest, by the way. You would still be a dick.
     
  13. AlphaNumeric Fully ionized Registered Senior Member

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    Ah, someone's upset he had his nonsense pointed out in another thread and now wants to pick up his ball and go home.

    You whine and whine about how I'm mean to you and how I'm wrong about you in regards to being a hack and a liar but you never do the simplest thing to shut me up, which is put your maths where your mouth is. 5 minutes work to answer those questions and you'd demonstrate to me and everyone else you're not just full of hot air. Every time I give you a chance to step up you make an excuse and then complain about how its not right I don't believe your claims about understanding this and that. Just like belief in god, why should I believe something for which there is no reason or evidence for?

    The best way to shut up a smart arse who thinks they know it all (which is what you and others view me as) is to prove them wrong, so step up and show I'm wrong about you.
     
  14. Green Destiny Banned Banned

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    Don't be ridiculous. You can't even make a true guess on what kind of emotion I might be feeling. I can assure you, I am not sad, I am angry with you. There is a big difference.
     
  15. Green Destiny Banned Banned

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    Mind you, your PhD is on physics, not psychology.
     
  16. AlphaNumeric Fully ionized Registered Senior Member

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    Your behaviour isn't uncommon, I don't need a PhD in psychology, you're doing what plenty of other cranks do. You want to be seen to talk the talk but when anyone scratches the surface and exposes your ignorance you get all huffy and indignant about how someone dares not believe you, despite you never stepping up or being able to engage in any kind of informed honest discussion.

    If you're angry about how I am short with you and repeatedly rip your posts apart, stop posting crap and actually retort what I say if I'm wrong, as you claim. You've now posted more in this thread about how you won't answer my questions than it would have taken to answer them, if you can do them.

    Which we both know you can't. Go on, prove me wrong.
     
  17. Green Destiny Banned Banned

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    Oh, so you finally call me a crank? It wasn't so long ago I said you have never called me a crank directly, and now you are humoring me. You really do look out for my best interests don't you.

    Just go jump off a bridge, or anything that would make you cease all communication with me, or I will put you on ignore again. Then you'll just be talking to yourself.
     
  18. AlphaNumeric Fully ionized Registered Senior Member

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    Was there any need for me to explicitly say it? Were words like 'fraud', 'liar' and 'hack' not hints enough? Nothing to do with humouring you, if I haven't called you crank before then consider it an oversight on my part.

    So you won't step up then? Instead you expend more energy and time whining about how you are upset I call you a liar and a fraud than it would take to demonstrate I'm wrong. If you could, which you can't, hence why you're just going into hissy fit mode.

    And putting me on ignore won't stop me pointing out your mistakes. And its not like you respond to my corrections anyway, you just mass quote me and then ignore everything I said. Putting me on ignore will just mean people don't have to read you quote entire posts of mine then ignore them.

    Thanks for yet again demonstrating the validity of my criticisms of you.
     
  19. AlphaNumeric Fully ionized Registered Senior Member

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    Having gone quiet for a few days GD PM'd me this evening with a link to my Facebook page and a few choice comments (whether it was some attempt at intimidation I don't know). The URL he provided was of the form facebook.com/[IDnumber]/[my name] but what he didn't realise was that the ID number wasn't mine, it was his and caused a redirect to a URL of the form facebook.com/[his name]/[my name] before redirecting to just facebook.com/[my name]. And low and behold, his real name is the same real name of our old friend Reiku aka gluon aka photino aka NeoNo.1 aka [insert sock puppet here].

    So the suspicion I had, as well as a few others, was bang on and all his whining about me making conspiratorial accusations of sock puppetry was just as dishonest as his claims of understanding physics.

    I'm sure no one here is reeling from the revelation GD is just another of Reiku's sock puppets but now, assuming a mod doesn't show him the door, maybe he'll be a bit more honest about his understanding. And if not then I'm certain a mod will make use of the ban hammer.
     
  20. rpenner Fully Wired Valued Senior Member

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    Finally, Facebook's complete disregard of even trivial privacy concerns works for good and not evil.

    //Edit -- speaking of evil -- what's with those fully illuminated retinas in that Facebook page? Yeesh! "He's got his father's eyes."
     
  21. prometheus viva voce! Registered Senior Member

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    Ha ha! Priceless!
     
  22. James R Just this guy, you know? Staff Member

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    Ok, Green Destiny, as a confirmed sock puppet, is gone.
     
  23. Idle Mind What the hell, man? Valued Senior Member

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    1,200 posts is a pretty good run for a sock that's been banned more than a few times. Oh, what form will he take on next?
     

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