Dirac Definition and 859 Threads

  1. Spinnor

    A Pauli and a Dirac electron, momentum density and spin.

    In the article, "What is spin", by Hans C. Ohanian we are shown how to take the wave-function for a Dirac electron with spin up and localized in space and then determine the momentum density in the Dirac field. The momentum density divides into two parts, a part that depends on the motion of the...
  2. S

    What's a thorough QM book besides Dirac?

    Hi, PF. I've got a question for you. Maybe this would be better posted in the science education or discussion sections, but it's directly related to QM. I'm just finishing up my undergrad coursework and I've taken QM using Griffiths. It's an okay book, but it does a bit of jumping around, and...
  3. S

    Is the delta in the commutation relations of QFT a dirac delta or a kronecker?

    If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.
  4. Spinnor

    How to graph Dirac equation, some complex numbers?

    Say we a have a sum of spin up plane wave solutions to the Dirac equation which represent the wave-function of a localized spin-up electron which is 90% likely to be found within a distance R of the origin of a spherical coordinate system. Four complex numbers at each spacetime point are needed...
  5. F

    Variation of Dirac delta function

    Is it possible to take the variation of the Dirac delta function, by that I mean take the functional derivative of the Dirac delta function?
  6. J

    Brain freeze on Dirac EQ v. Dirac Hamiltonian

    Alright. So the Dirac Eq is (i \gamma^{\mu} \partial_{\mu} - m) \psi = 0 or putting the time part on one side with everything else on the other and multiplying by \gamma^0 , i \partial_t \psi = (i \gamma^0 \vec{\gamma} \cdot \nabla + \gamma^0 m) \psi I would think that this is the...
  7. L

    Derivative of Dirac Delta function

    Hello I'm trying to figure out how to evaluate(in the distribution sense) \delta'(g(x)). Where \delta(x) is the dirac delta function. Please notice that what I want to evaluate is not \frac{d}{dx}(\delta(g(x))) but the derivative of the delta function calculated in g(x). If anyone could post...
  8. F

    Algebraic structure of Dirac delta functions

    OK, the Dirac delta function has the following properties: \int_{ - \infty }^{ + \infty } {\delta (x - {x_0})dx} = 1 and \int_{ - \infty }^{ + \infty } {f({x_1})\delta ({x_1} - {x_0})d{x_1}} = f({x_0}) which is a convolution integral. Then if f({x_1}) = \delta (x - {x_1}) we get...
  9. Xezlec

    Why doesn't the energy come out right in the Dirac Equation?

    Hello, I'm looking at the Dirac Equation, in the form given on Wikipedia, and (foolishly) trying to understand it. \left( c \boldsymbol{\alpha}\cdot \mathbf{\hat{p}}+\beta mc^2 \right ) \psi = i\hbar\frac{\partial \psi}{\partial t}\,\! So I picture a wavefunction in an eigenstate of the...
  10. E

    Solving an equation with Dirac delta functions

    Hello, I'm dealing with the following equation: A e^{jat} + B e^{jbt} = C e^{jct} \forall t \in \mathbb{R} My book says: given nonzero constants A,B,C, if the above equation yelds for any real t, then the a,b,c constants must be equal. The above statement is prooved by taking the Fourier...
  11. K

    Dirac delta function with contineous set of zeros

    hi! i have a question regarding the delta function. if i have a delta distribution with an argument that is a function of multiple arguments, somthimg like: ∫δ(E-p^{2}_{i}/2m)dp^{N}, ranging over +-∞ now, the argument of the delta function vanishes on a sphere. i can evaluate the...
  12. N

    The Schrödinger equation as the non-relativistic limit of the Dirac equation

    Hello, I'm reading Griffiths' introduction to elementary particles and he seems to claim that the Schrödinger equation can be seen as a non-relativistic limit of the Dirac equation. I was wondering how one could deduce this, e.g. how do we go from \mathcal L = \bar{\psi} \left( i \gamma^\mu...
  13. N

    Charge conjugation for Dirac particles (error in problem?)

    Homework Statement Show that if \psi is a down-spin anti-electron, and we apply charge conjugation, then \psi^C is an up-spin electron. The Attempt at a Solution My calculations suggest that the anti-electron indeed becomes an electron; however, spin does not change for me. Is it possible...
  14. F

    Comparing Dirac and Schrodinger Equations for the Hydrogen Atom

    The Schrodinger equation solved for the hydrogen atom gave good agreement with spectral lines, except for line doublets. To account for these electron spin theory was grafted onto the theory, despite the problem of electron being a point particle. In 1928 Dirac gives his different answer...
  15. S

    Delta Dirac: Showing it's a Distribution

    I realize it's not a function in the classical sense, but how would one show that the delta dirac function is a distribution i.e. how do I show it's continuous and linear given that it's not truly a function?
  16. N

    Neglected solutions to the (free) Dirac equation?

    So it is said that a basis for the plane wave solutions to the Dirac equation are of the form (p denotes the four-momentum vector) e^{-i p \cdot x} u^{(s)} (for particles) and e^{i p \cdot x} v^{(s)} (for antiparticles), with s = 1 or 2 (and u and v having predetermined structure). I'm...
  17. B

    Why does Dirac Equation describe spin 1/2 particles?

    Hi, Everybody! Currently, I am reading the book "Lectures on Quantum Field Theory" (by Ashok Das) But I am a bit confusing. Why does Dirac Equation describe spin 1/2 particles? I have already known that Dirac Equation bears some angular momentum structure, but why it just describe spin...
  18. T

    Can we interchange the Dirac Matrices?

    Ok, first off I will admit that I really am pretty much ignorant of proper QM, as I am a first year undergraduate at a UK university. Today our lecturer, in the final lecture of a Vibrations and Waves course, demonstrated how the Schrodinger equation is derived from applying the Energy and...
  19. snoopies622

    Looking for a Dirac book on qft

    I just happily bought a used copy of Dirac's Lectures on Quantum Mechanics from Amazon.com. I also want his Lectures on Quantum Field Theory but they don't carry it. Anyone know where I can find a copy?
  20. T

    Problem on integrating dirac delta function

    Hi there, I am trying to integrate this: http://imm.io/oqKi I should get the second line from the integral, but I can't show it. This should somehow relate to the Heaviside step function, or I am completely wrong. Any ideas? Sorry about the url, I fixed it.
  21. J

    Property of the dirac delta function

    Hello team! I saw the other day in a textbook that the Dirac delta function of the form d(x-a) can be written as d(a-x) but the method was not explained. I was wondering if anyone know where this comes from. I've been googling but can seem to find it out. Any help would be appreciated...
  22. L

    Dyade Dirac Notation: Why Last Equation?

    \{\vec{A},\vec{B}\}\cdot \vec{C}=\vec{A}(\vec{B}\cdot \vec{C}) \vec{C} \cdot \{\vec{A},\vec{B}\}=(\vec{C}\cdot \vec{A}) \vec{B} I want to write dyade in Dirac notation. (|\vec{A}\rangle\langle\vec{B}|)|\vec{C}\rangle= |\vec{A}\rangle\langle\vec{B}|\vec{C}\rangle...
  23. X

    What does couples as the 4th component of a vector mean in the Dirac equation?

    What does "couples as the 4th component of a vector" mean in the Dirac equation? I'm doing an exercise regarding the spin-orbit operator and the Dirac equation/particles, and I'm having trouble understanding the link between terminology and mathematics. The particular phrase I'm having trouble...
  24. R

    Dirac formulation of QM, motivation for SE

    In Dirac's "The Principles of Quantum Mechanics", in chapter V on the equations of motion Dirac proceeds with a line of reasoning that is something along the following lines (I've modified it a bit to coincide with what's taught in the course I'm taking) 1. We assume that the motion...
  25. F

    What Are the Positive and Negative Energy Solutions of the Dirac Equation?

    Hi! Homework Statement 1. Substituting an ansatz \Psi(x)= u(p) e^{(-i/h) xp} into the Dirac equation and using \{\gamma^i,\gamma^j\} = 2 g^{ij}, show that the Dirac equation has both positive-energy and negative-energy solutions. Which are the allowed values of energy? 2. Starting...
  26. M

    Dirac Delta Function (electrodynamics)

    I'm having a hard time grasping when I should use this little "function". I'm using Griffith's Intro to Electrodynamics and either he doesn't touch on it enough or I'm missing the point. From what I think I understand I'm to use it when there would be a singularity in a result or calculation(?)...
  27. E

    Harmonic Oscillator in Dirac Theory

    Hello everyone, i'm looking for anypaper or such kind of thing that explain the resolution of the harmonic oscillator in the Dirac Theory. I have worked with the exact spin symmetry. I feel like a fish out the water and I'm sure that there are lot of bibliography about this area, but i...
  28. B

    Integrating the following delta dirac function should yield min(t,s), but how?

    Homework Statement I need to understand how to integrate \int_{0}^{t}\int_{0}^{s} \delta(\tau-\tau')d\tau d\tau' The solution is min(t,s) Homework Equations See aboveThe Attempt at a Solution min(t,s)
  29. J

    Dirac Notation: Am I doing this right?

    Homework Statement Find <P>. P = i√(mhw/2)(a†-a). Note a† and a are the ladder operators. P is the momentum operator of the harmonic oscillator. |ψ > = (1/sqrt(2))[ |1> - i |2>] The answer should be zero, can someone check my work?Homework Equations a† |n> = sqrt(n+1)|n+1> a |n> =...
  30. E

    Dirac equation and gamma factor

    I am reading about Dirac's equation for relativistic electron in Feynman's book "Quantum Electrodynamics". Factor \gamma =(1-v^2)^{-1/2} (units c=1) is almost always presented in non quantum calculations of Special relativity. But in his book I also find it on page 44 in lecture "Relativistic...
  31. R

    What are the properties of Dirac notation and operators?

    Homework Statement [A^{+}A]=1 A|a>=\sqrt{a}|a-1> A^{+}|a>=\sqrt{a+1}|a+1> <a'|a>=\delta_{a'}_{a} Homework Equations what is 1 <a|A|a+1> 4. <a+1|A^{+}|a> 3. <a|A^{+}A|a> 4. <a|AA^{+}|a> The Attempt at a Solution 1. <a|A|a+1> =<a|\sqrt{a+1}|a+1-1>=\sqrt{a+1}<a|a> since a=a and...
  32. P

    Covariant Bilinears: Fierz Expansion of Dirac gamma matrices products

    Homework Statement So my question is related somehow to the Fierz Identities. I'm taking a course on QFT. My teacher explained in class that instead of using the traces method one could use another, more intuitive, method. He said that we could use the fact that if we garante that we have the...
  33. B

    How to incorporate the neutral current into the Dirac equation

    Hi Everyone, I'm a math grad student working on numerical procedures for the Dirac equation, and I'd like to be able to incorporate the neutral current interaction neutrino + fermion -> Z bozon -> neutrino + fermion <- poorly impersonated Feynman diagram into the Dirac equation as a...
  34. J

    Proving the Delta Function Identity Using the Local Behavior of Functions

    Homework Statement See http://mathworld.wolfram.com/DeltaFunction.html I want to show (6) on that page. I can show it using (7), but we aren't supposed to do that. I already proved (5), and my prof says to use the fact that (5) is true to get the answer. Homework Equations The...
  35. andrewkirk

    Dirac Delta function as a Fourier transform

    It is fairly easy to demonstrate that the Dirac delta function is the Fourier transform of the plane wave function, and hence that: \delta(x)=∫_{-∞}^{∞}e^{ikx}dk (eg Tannoudji et al 'Quantum Physics' Vol 1 p101 A-39) Hence it should be the case that ∫_{-∞}^{∞}e^{ik}dk = \delta(1) = 0...
  36. T

    The Limitations of the Dirac Sea in Explaining Particle Motion

    I'm not sure if my interpretation is correct, but this Dirac Sea interpretaton does as far as I understand this, tell us that every energy level from -infinity to a certain energy level E<0 is filled with anti-particles. And this should be true for every single location in the universe. If...
  37. A

    Dirac delta and fourier transform

    In my book the dirac delta is described by the equation on the attached picture. This realtion is derived from the Fourier transform, but I'm not sure that I understand what it says. If u=t it is clear that one gets f(u) in the Fourier inversion theorem. But why wouldn't u=t? In the derivation...
  38. A

    Why is the Dirac delta function written as δ(x-x') instead of just δ(x')?

    What's the reason that you write δ(x-x') rather than just δ(x') both indicating that the function is infinite at x=x' and 0 everywhere else? For me that notation just confuses me, and in my opinion the other notation is easier.
  39. T

    Limit involving dirac delta distributions

    Hey All, I am trying to evaluate the limit: \lim_{x\to 0^{+}} \frac{\delta''(x)}{\delta''(x)} Where \delta'(x) is the first derivative of the dirac distribution and \delta''(x) is the second derivative of the dirac distribution. I thought about the fact that this expression...
  40. T

    The Dirac equation and its conjugate

    This isn't really a homework problem, just a form of writing I don't quite understand. The Dirac equation is: ("natural units") (i\gamma^{\mu}\partial_{mu}-m)\Psi = 0 When I try to build the conjugated equation, where \bar{\Psi} := \Psi^{+}\gamma^{0}, I get...
  41. V

    Demonstration of Dirac equation covariance

    Demonstrations of Dirac equation covariance state: The Dirac equation is (i γ^{μ} ∂_{μ} - m)ψ(x) = 0. \ \ \ \ \ \ \ \ \ \ [1] If coordinates change in a way that x \rightarrow x' = Lx, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [2] where L is a Lorentz transformation, [1] should...
  42. S

    A simple application of dirac delta shift theorem help

    A "simple" application of dirac delta "shift theorem"...help Homework Statement show that for a, b, c, d positive: δ(a/b-c/d) = bdδ(ad-bc) Homework Equations ∫f(x)δ(x-a)dx = f(a) The Attempt at a Solution Ok so I start with ∫δ(a/b-c/d)f(x)dx But I am not sure how to apply the shift...
  43. M

    Global U(1) invariant of Dirac Lagrangian

    Does anybody know what interpretation the invariant corresponding to the global U(1) invariance of the Dirac Lagrangian is? I have always had it in my head that it's charge, but then I realized that uncharged free particles such as neutrinos satisfy this equation too! Any thoughts much...
  44. N

    The Dirac delta in squere root of the absolute value

    Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon
  45. J

    Generating Noether charges for Dirac Lagrangian

    I have been calculating the currents and associated Noether charges for Lorentz transformations of the Dirac Lagrangian. Up to some spacetime signature dependent overall signs I get for the currents expressions in agreement with Eq. (5.74) in http://staff.science.uva.nl/~jsmit/qft07.pdf . What...
  46. X

    Angular Momentum Problem in Dirac Notation

    Homework Statement http://img857.imageshack.us/img857/2079/dirac.png Homework Equations H|ψ> = E|ψ> L^{2}|ψ> = l(l+1)\hbar^{2}|ψ> L_{z}|ψ> = m_{l}\hbar|ψ> The Attempt at a Solution I know this problem is very simple since I've seen a very similar problem a while ago but I've completed forgot...
  47. I

    Dirac algebra (contraction gamma matrices)

    I would like to have a general formula, and I am quite sure it must exist, for: \gamma^{\mu}_{ab}\gamma_{\mu \,\alpha\beta} but I didn't succeed at deriving it, or intuiting it, I am troubled by the fact that it must mix dotted and undotted indices.
  48. N

    Dirac delta wave function impossible?

    Hello, I was under the impression that a dirac delta was a "legitimate" state for a particle: maybe not mathematically, but least physically. But I was recently told by a post-doc in QM that if your particle is in a dirac delta state at one moment, the very next moment the particle is...
  49. C

    Is the Kronecker Delta Related to the Dirac Delta in Quantum Mechanics?

    Hello PF, When I was studying Quantum mechanics, I realized that this equality should be true, <{\psi}_{n} \mid {\psi}_{m}>=\int {\psi}_{m}^*{\psi}_{n}dx={\delta }_{mn} So {\psi}_{m}^*{\psi}_{n} must be equal to dirac delta function so that we provide the kronecker delta as a solution of...
  50. J

    The Principles of Quantum Mechanics (Dirac)

    How advanced is this text? The only exposition I've had to quantum mechanics is through "The Quantum Universe" by Brian Cox and Jeff Forshaw. That book was a nice introduction but now I'm looking for something a lot more in depth. Would someone with a strong mathematical background but only a...
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