What is Dirac: Definition and 896 Discussions

Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.
Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful." In another letter he wrote, "I don't understand Dirac at all (Compton effect)."He was the Lucasian Professor of Mathematics at the University of Cambridge, was a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.

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  1. D

    Confusion with Delta Dirac Function's First Property: Why Does Infinity Equal 1?

    I had just reviewed back the properties of Delta Dirac Function, however I'm having a little confusing about the first property as stated : \delta\left(x-a)\right = 0 if x \neq a, \delta\left(x-a)\right = \infty if x = a;Here is my problem : when integrate over the entire region (ranging from...
  2. H

    Integral of Exp(I x) and the Dirac Delta

    I am trying to see why exactly the momentum eignenstates for a free particle are orthogonal. Simply enough, one gets: \int_{-\infty}^{\infty} e^{i (k-k_0) x} dx = \delta(k-k0) I can see why, if k=k0, this integral goes to zero. But if they differ, I don't see why it goes to zero. You have...
  3. R

    A Dirac field can be written as two Weyl fields

    A Dirac field can be written as two Weyl fields stacked on top of each other: \Psi= \left( \begin{array}{cc} \psi \\ \zeta^{\dagger} \end{array}\right) , where the particle field is \psi and the antiparticle field is \zeta. So a term like P_L\Psi=.5(1-\gamma^5)\Psi=\left( \begin{array}{cc}...
  4. S

    Simplifying the integral of dirac delta functions

    hello all, i am unaware of how to handle a delta function. from what i read online the integral will be 1 from one point to another since at zero the "function" is infinite. overall though i don't think i know the material well enough to trust my answer. and help on how to take the integral of...
  5. G

    Proving lorentz invariance of Dirac bilinears

    I'm trying to work through the proof of the Lorentz invariance of the Dirac bilinears. As an example, the simplest: \bar{\psi}^\prime\psi^\prime = \psi^{\prime\dagger}\gamma_0\psi^\prime = \psi^{\dagger}S^\dagger\gamma_0 S\psi = \psi^{\dagger}\gamma_0\gamma_0S^\dagger\gamma_0 S\psi =...
  6. E

    How do I convert f(x) into its Fourier Transform?

    Homework Statement I am really confused in my electrodynamics class. I have the following function. f(x) = \delta (x + \alpha ) + \delta(x -\alpha) How do i convert this into Fourier Tranform ? Those are dirac delta functions on either sides of the origin. Homework Equations...
  7. H

    Understanding Dirac Delta Squares: Clarifying Doubts

    hi, may someone help me to clarify my doubts... in my work, i encounter diracdelta square \delta(x-x_1)\delta(x-x_2) i am not sure what it means... it seems if i integrate it \int dx \;\delta(x-x_1)\delta(x-x_2) = \delta(x_1-x_2) is either zero of infinity. is this correct? thanks
  8. I

    Square root of Dirac Delta function

    Homework Statement I wonder how to deal with the square root of Dirac Delta function, \sqrt{\delta(x)}. Actually, this comes from a problem which asking readers to calculate the wave function of a free particle and of a harmonic oscillator at time t, provided that the wave function at time...
  9. A

    Line of charge as a volume charge dist. (w/ Dirac delta fcn.)

    How would you write an infinite line charge with constant charge per unit length \lambda as a volume charge density using Dirac delta functions? Perhaps in cylindrical coordinates? I'm confused because if you integrate this charge distribution over all space, you should get an infinite amount...
  10. S

    Dirac delta and divergence

    I know that this question was posted before but I just couldn't get it using another way around. So your comments are highly appreciated. In the textbook, \nabla\bullet\left(\widehat{r}/r^{2}\right)=4\pi\delta^{3}\left(r\right). But when I want to calculate the divergence using Catesian...
  11. G

    Moving from Dirac equation to Lagrangian density

    Hi all, As a blind follower of QFT from the sidelines (the joys of the woefully inadequate teaching of theory to exp. particle physics students...), I have just realized that I've never actually gone further than deriving the Dirac equation, and then just used the Dirac Lagrangian density as...
  12. I

    Alternate formulation of Dirac Notation

    I was reading some more quantum mathematics, and a question occurred to me. In the current treatment of the topic, the bra-ket notation is defined as a shorthand notation for more complex mathematical operations. But couldn't bra-ket notation be defined separately from quantum physics? In other...
  13. N

    Dirac Equation Derivation with Inhomogeneous Lorentz Group in QFT Book

    I've seen the derivation of Dirac Equation using Inhomogeneous Lorentz Group in L H Ryder's QFT book.Can anybody give some comprehensible descriptions of this method?
  14. A

    Dirac delta function is continuous and differential

    since dirac delta function is not a literally a function but a limit of function,does it mean that dirac delta function is continuous and differentiable through out the infinity? is there any example of dirac delta function if yes then give meeeeeeee?
  15. S

    Non relativistic limit for dirac propagator

    Hi everybody, I don't know if this is the right section to ask for such a question but I have been dealing with this problem for a while and there's something I still cannot grasp... Let us suppose that we have a dirac free particle with propagator (i'm sorry but I'm not able to obtain the...
  16. pellman

    Dirac conserved current vs Klein-Gordon conserved current

    The conserved current for a field \phi obeying the Klein-Gordon equation is (neglecting operator ordering) proportional to i\phi^{\dag}\partial_\mu \phi-i\phi\partial_\mu \phi^{\dag}. The conserved current for a four component field \psi obeying the Dirac equation is...
  17. T

    Integral over a sphere with the dirac delta function

    Homework Statement \[ \underset{\left|\underline{\xi}\right|=1}{\int}\delta_{0}\left(\underline{\xi}\cdot\underline{z}\right)dS_{\xi}=\intop_{0}^{2\pi}d\varphi\intop_{-r}^{+r}\delta_{0}\left(\varsigma\right)\frac{d\varsigma}{r}=\frac{2\pi}{r}\] The \delta_{0} is the dirac delta function.the...
  18. T

    Integral Over a Sphere with dirac delta function

    Hi, I am not really sure whether its over the surface of the sphere or the Volume, the problem and the solution are given below, I want to know how it has been solved. The \delta_{0} is the dirac delta function. \[...
  19. G

    How Do You Construct the Dual Basis in Dirac Notation?

    Homework Statement my apologies if this question should be posted in the math forum 3-d space spanned by orthonormal basis: (kets) |1>, |2>, |3>. Ket |a> = i|1> - 2|2> - i|3>. Ket |b> = i|1> + 2|3>. The question is to construct <a| and <b| in terms of the dual basis (kets 1,2,3)...
  20. J

    An identity involving a Dirac delta function.

    I have been reading papers for my research and I came across this equation twice: \lim_{\eta\to 0+}\frac{1}{x+i \eta} = P\left(\frac{1}{x}\right) - i \pi \delta(x) Where P is the pricipal part. It has been quite a while since I have had complex variables, but might it come from the...
  21. G

    Is there a paradox involving the Dirac equation and commutation with time?

    I was hoping someone could help me with a seeming paradox involving the Dirac equation. I have taken a non-relativistic QM course, but am new to relativistic theory. The Dirac equation is (following Shankar) i\frac{\partial}{\partial t}\psi = H\psi where H = \vec{\alpha}\cdot...
  22. maverick280857

    Lorentz Algebra in Boosts for the spin-1/2 Dirac Field

    Hi, What is the origin of the following commutation relation in Lorentz Algebra: [J^{\mu\nu}, J^{\alpha\beta}] = i(g^{\nu\alpha}J^{\mu\beta}-g^{\mu\alpha}J^{\nu\beta}-g^{\nu\beta}J^{\mu\alpha}+g^{\mu\beta}J^{\nu\alpha}) This looks a whole lot similar to the commutation algebra of...
  23. M

    Dirac Delta Integration Problem

    Homework Statement \int_{-\infty}^t (cos \tau)\delta(\tau) d\tau Evaluate the integral. I'm supposed to evaluate this for all t I believe, so I'm concerned with t<0, t=0, t>0. Homework Equations \int_{-\infty}^{\infty} f(x)\delta(x) dx = f(0) The Attempt at a Solution...
  24. J

    Derivative in Dirac Notation

    Hi everybody, I am trying to get the partial derivative of the following with respect to Si[t] and Phi[t] separately: Integrate[<Phi[t]|H|Si[t]>] The operator H is the partial derivative with respect to t. I tried this in Mathematica, calling Needs["Quantum`Notation`"] but I...
  25. M

    How to handle the Dirac delta function as a boundary condition

    Using perturbation theory, I'm trying to solve the following problem \frac{\partial P}{\partial \tau} = \frac{1}{2}\varepsilon^2 \alpha^2 \frac{\partial^2 P}{\partial f^2} + \rho \varepsilon^2 \nu \alpha^2 \frac{\partial^2 P}{\partial f \partial \alpha} + \frac{1}{2}\varepsilon^2 \nu^2...
  26. Spinnor

    A pair of 2D harmonic oscillators at a point and Dirac eq.

    A two-dimensional harmonic oscillator is associated with the group Su(2). What is that association? Solutions to the Dirac equation require a pair of spinors at each point? Can we think think of spacetime as having pairs of 2D harmonic oscillators at each point? Thanks for any help.
  27. T

    Two dirac cones are described by two bi-spinors of different chirality

    Is is right to say that the two dirac cones are described by two bi-spinors of different chirality?... Is it right to say that each of the dirac cones contains quasi-particles of different helicity (electrons of positive elicity and of holes negative elicity for one dirac cone and the...
  28. S

    Understanding Dirac Notation: A Simplified Explanation for Scientists

    Hello, I'm fuzzy on how Dirac notation works especially when operators are added in. Does anyone have a clear explanation (the simpler the better) that they can give to me, and or a website or book that does a good job of explaining it?
  29. P

    Double integral using the dirac delta

    Homework Statement Need to integrate using the dirac delta substitution: \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\!x^2\cos(xy)\sqrt{1-k^2\sin^2(y)}\, dx\, dy Homework Equations \cos(xy) = \frac{1}{2}\left(e^{ixy} + e^{-ixy}\right) \delta\left[g(t)\right] =...
  30. T

    Are Dirac Eigenstates Helicity Eigenstates?

    Hi people, I was asking myself... is it true that the elements of the base of solutions of the dirac equation usually used are eigenstates of elicity? Yesterday I tried the calculation following the notation of this site (it uses the dirac representation) and its set of solutions...
  31. V

    Help with EM Fields and Dirac Delta Needed

    Hi guys. I play now a bit with EM fields and I have encountered some problems connected with Dirac delta. By coincidence I visited this forum and I thought I could find some help in here. The problem is that in order to get a potential in some point from a single charge you need to just...
  32. F

    When were Bose-Einstein and Fermi-Dirac statistics first defined?

    Hi everyone I need the historical articles that bose and fermi integrals were defined for the first time. Can anyone help me?
  33. S

    Why is the integral of the Dirac delta distribution equal to unity?

    Previously I posted a question on the Dirac delta function and was informed it was not a true function, but rather a distribution. However, I have to admit I still did not understand why its integral (neg inf to pos inf) is unity. I've thought about this and came up with the following...
  34. J

    Property of the Dirac Delta Function

    Homework Statement How do you show that int[delta(t)]dt from negative infinity to infinity is 1? Homework Equations Dirac delta function defined as infinity if t = 0, 0 otherwise The Attempt at a Solution My teacher said that it has to do with m->infinity for the following...
  35. Z

    How can integration by parts be used to prove the Dirac delta function?

    1. The problem statement Show that: \int_{-\infty}^{\infty} f(x) \delta^{(n)}(x-a) dx = (-1)^n f^{(n)}(a) The Attempt at a Solution I am trying to understand how to prove: \int_{-\infty}^{\infty} f(x) \delta '(x) dx =- f'(x) I know that we need to use integration by parts, but I'm...
  36. A

    Question about lorentz-covariance of Dirac equation

    ψ(x) is the four-component wave function of the Dirac equation，that is ψ(x) can be expressed by a column vector (ψ1(x) ψ2(x) ψ3(x) ψ4(x)） ,under a lorentz transformation,it will become ψ'(x').I am confused that how ψ'(x') can be expressd in the form which is stated by textbooks: ψ'(x')=S(a)ψ(x)...
  37. C

    Can someone explain the 3D Dirac Delta Function in Griffiths' Section 1.5.3?

    Griffiths' section 1.5.3 states that the divergence of the vector function r/r^2 = 4*Pi*δ^3(r). Can someone show me how this is derived and what it means physically? Thanks in advance.
  38. S

    Starting with the definition of the Dirac delta function,

    Homework Statement Starting with the definition of the Dirac delta function, show that \delta( \sqrt{x}) um... i have looked in my book and looked online for a problem like this and i really have no clue where to start. the only time i have used the dirac delta function is in an integral...
  39. P

    Integration on the way to Generating Functional for the free Dirac Field

    Hi, if I want to calculate the generating functional for the free Dirac Field, I have to evaluate a general Gaussian Grassmann integral. The Matrix in the argument of the exponential function is (according to a book) given by: I don't understand the comment with the minus-sign and the...
  40. J

    Dirac delta function - its confusing

    Hi I have been trying to learn dirac delta function. but its kind of confusing. I come across 2 contrasting definitions for it. The first one states that the function delta(x-xo) is infinite at x=x0 while the other states that delta(x-x0) tends to infinite as x tends to x0. Now both of them...
  41. H

    Dirac Equation for a moving square potential well

    Hi, I have learned the Dirac equation recently and I managed to solve it for a free particle (following Greiner book “relativistic quantum mechanics” and Paul Strange book “Relativistic Quantum Mechanics”). I was asked to solve the Dirac equation in the stationary frame for a free particle (no...
  42. B

    Deriving the Dirac equation from an action principle

    Some confusions from some recent lectures; I asked the prof, but I still don't fully understand what is going on. We began with the action (tau is some worldline parameter, dots indicate tau derivatives; they are hard to see): S = \int d\tau \; \left\{ \dot x^{\mu} p_{\mu} - \frac12 e(\tau)...
  43. S

    1D wave equation with dirac delta function as an external force.

    Hey there! I'm faced with this problem: http://img7.imageshack.us/img7/4381/25686658nz9.png It's a 1D nonhomogeneous wave equation with a "right hand side" equaling to the dirac delta function in x * a sinusoidal function in t. I have to find its general solution with the constraints...
  44. J

    Factor of 'i' and antisymmetrization in Dirac Lagrangian

    Hello everyone, I'm not sure if these questions are really trivial or of they're a little subtle... but here goes. 1. In Ramond's text (Field Theory: A Modern Primer), he explains that the Lagrangian for fermions should have the derivative operator antisymmetrized in order for the kinetic...
  45. L

    Dirac delta function definition

    By definition of the Dirac delta function, we have: \int f(x) \delta(x-a) dx=f(a) This is fair enough. But in ym notes there is a step that goes like the following: \mathbf{\nabla} \wedge \mathbf{B}(\mathbf{r})=-\frac{\mu_0}{4 \pi} \int_V dV'...
  46. Y

    Is the Dirac Delta Function Defined at Zero or Infinity?

    I cannot get the answer as from the solution manuel. Please tell me what am I assuming wrong. Thanks
  47. S

    The math of the Dirac delta function?

    I'm posting this here because I'm asking about the mathematical properties of the Dirac delta function, delta(x) which is zero for all non-zero real values of x and infinite when x is zero. The integral (-inf to +inf) of this function is said to be 1. How is this derived?
  48. T

    Calculus with Dirac notation

    I am working through a problem relating to the conservation of probability in a continuity equation. However, I end up with a contradiction when trying to put the following into the Time-Dependent Schrodinger Equation \frac{\partial\psi(x)}{\partial t}=\frac{\partial\left\langle...
  49. F

    Negative energy in Dirac theory

    Can anyone explain what's negative energy mean in Dirac theory? Does it imply anti-particle travel backward in time?
  50. K

    Heaviside function and dirac delta

    Homework Statement Hi there, i am trying to do a proof that H'(t)= δ(t) Homework Equations We have been given the following: F is a smooth function such that lim (t-->±∞)F(t)=0 Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0 I understand it up until this point...
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