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. R

    Understanding the Dirac Equation: Showing \gamma^{\mu} Must Be Square Matrices

    Yep, another quick question on the Dirac Equation! I've become slightly more clued about the use of the DE now in illustrating the negative energy problem in relativistic QM as well as the existence of spin, however one thing is still puzzling me. I've read this excerpt in a text: I'm...
  2. R

    Solve the Dirac Equation: Unraveling Anticommutator Mystery

    [SOLVED] The Dirac Equation I'm trying to understand the following property of the Dirac equation: (i \gamma^{\mu}\partial_{\mu} - m)\Psi(x) = 0 Acting twice with (i \gamma^{\mu}\partial_{\mu} - m): (i \gamma^{\mu}\partial_{\mu} - m)^{2} \Psi(x) = 0 = [ -...
  3. F

    Dirac delta, math of implication?

    So what we have so far is that any and all subsets are implied by a set. If there exist a set, then all the subsets within it are implied to exist also. This includes the elements of a set. The elements of a set are implied by the existence of a set. One of the most natural things to do with...
  4. E

    Dirac, Majorana & a missing factor of 2

    A question concerning Feynman rules for Dirac vs Majorana neutrinos. Take e.g. the scattering process: electron + positron -> electron neutrino + electron antineutrino. Following the electroweak Feynman rules we can calculate an expression for the unpolarized differential cross section...
  5. Q

    The exact meaning of the 4 components of the Dirac Spinor

    \PsiHow to intepret the four components of the dirac spinor? the volume integral of the \Psi^T*\Psi give the probability of finding the releativistic electron in a given volume of space but what exactly do the four components really mean. I have read in many Pop physics books that the 4...
  6. M

    How to Solve an IVP Involving Dirac Delta Function?

    Dirac Delta Function: If, at time t =a, the upper end of an undamped spring-mass system is jerked upward suddenly and returned to its original position, the equation that models the situation is mx'' + kx = kH delta(t-a); x(0) = x(sub zero), x'(0) = x(sub 1), where m is the mass, k is the...
  7. S

    Solving Dirac Delta Function Beam Problem

    1. The ProblemHomework Statement 4 Parts to the Assignment. Finding the Displacement of a beam assuming w to be constant. 1. Cantilever beam, free at one end. Length =l, Force P applied concentrated at a point distance rl from the clamped end. Boundary Conditions y(0)=0, y'(0)=0, y"(l)=0, and...
  8. T

    Does Weak Convergence Hold for Sequences Approaching Infinity?

    Homework Statement Show that if {x_k} is any sequence of points in space R^n with |{x_k}| \rightarrow \infty , then \delta(x-x_k) \rightarrow 0 weakly Homework Equations The Attempt at a Solution I'm still trying to grasp the concept of weak convergence for distributions. It...
  9. J

    Solving simple dirac delta function

    [b]1. Homework Statement \int x[delta(x)-delta(x/3+4)] dx Homework Equations so I'm supposed to use this principle: \int f(x)delta(x-xo)dx=f(xo) The Attempt at a Solution So it seems simple but I just want to make sure that I'm applying the above principle correctly. I...
  10. Q

    Proving the Spin Half Nature of Dirac Quanta

    but I am confused how do you proof that the dirac field describes spin half quanta when quantized? please refer me to a link on the net where this derivation is shown if possible i can't find it in any of the books on quantized field theory
  11. J

    Help converting dirac delta function

    Homework Statement SO I'm given a dirac delta function, also known as a unit impulse function. d(t-t'_=(1/P) sum of e^[in(t-t')], for n from negative to positive infinity. I need to graph this. Homework Equations I understand that at t', there is a force made upon the system which...
  12. R

    Writing M(x,x') in Dirac Notation: A Guide

    Hey guys, I am having difficulty interpreting M(x,x') into dirac notation. How do i write M(x,x') in dirac notation? The actual problem is to write the following in dirac notation: int { int { m(x)* M(x,x') g(x') } dx} dx' I would appreciate your help.
  13. M

    The Dirac Equation and the Neutrinos

    Does the Dirac equation predicts the fact that there are no right handed neutrinos?
  14. E

    Understanding the Dirac Delta Function: Solving the Integral of Delta(x-b)

    Q: Integral of Delta(x-b)dx and the lower limit is (-) infinity and upper is a Please help me in steps tried my best to solve.Note this is not homework I was doing the book problems or my practice Thanks
  15. Hans de Vries

    Deriving the Dirac propagator 'purely' from causality

    I figured out this one, just thought it was quite nice... We start with the only requirement that the Green's function of the propagator is causal in the sense that it propagates stricktly forward in time, so that the Green's function is zero at t<0. Using the Heaviside step function we can...
  16. E

    Proving the Limit of Dirac Delta from Normal Distribution

    Homework Statement How would one show that dirac delta is the limit of the normal distribution? http://en.wikipedia.org/wiki/Dirac_delta using the definition \delta(k) = 1/(2\pi)\int_{-\infty}^{\infty}e^{ikx}dx Homework Equations The Attempt at a Solution
  17. L

    Klein-Gordon-Schrodinger and Dirac equations

    Homework Statement I need to solve the Klein-Gordon-Schrodinger and the Dirac equation for the Coulombian potential.Homework Equations KGS: [(\partial^{\mu}\partial_{\mu} + m^2c^2/h^2)\Psi=0 I don't know how I can add the potential term... Dirac: [\gamma^{\mu}(ih\partial_{\mu} - (e/c)...
  18. I

    How Does Chirality Impact the Dirac and Weyl Equations?

    What results in Chirality? And what is the physical implication of chirality in Dirac equation?
  19. C

    Are spinors just wavefunctions in the dirac field?

    are spinors just wavefunctions in the dirac field?
  20. radou

    Dirac delta function confusion

    OK, I'm currently reading Hughes' Finite Element Method book, and I'm stuck on a chapter the goal of which is to prove that the Galerkin solution to a boundary value problem is exact at the nodes. So, the author first speaks about the Dirac delta function: "Let \delta_{y}(x) = \delta(x-y)...
  21. E

    Fourier transform formulation of the dirac delta

    I have seen two formulations of the dirac delta function with the Fourier transform. The one on wikipedia is \int_{-\infty}^\infty 1 \cdot e^{-i 2\pi f t}\,dt = \delta(f) and the one in my textbook (Robinett) is 1/2\pi \int_{-\infty}^\infty 1 \cdot e^{-i f t}\,dt = \delta(f) I...
  22. F

    How do you interpret derivatives of the Dirac function in Maple?

    hi! I have a system from which i want to compute a expression for a time domain impulse response. The expressions for modulus and phase of the system is quite complicated and I'm using maple in order to do the inverse transforming. now, maple tells me the inverse transform is an expression...
  23. K

    Kronecker delta and Dirac delta

    I do not know if it is true but is this identity true \frac{\delta _{n}^{x} }{h} \rightarrow \delta (x-n) as h tends to 0 ?, the first is Kronecker delta the second Dirac delta. i suspect that the above it is true but can not give a proof
  24. S

    Exploring the Nature of Virtual Particle Annihilation in the Dirac Sea

    If the universe is a Dirac Sea, then wouldn't the light generated from virtual particle annihilation be detectable? Not only this, but wouldn't it drown out all other light sources? I can't find any good explanations so far for why virtual particle annihilation does/doesn't produce photons or...
  25. M

    Understanding the Equivalence of Dirac Delta Functions in Quantum Mechanics

    Dirac developed his delta function in the context of QM. But there are various functions under the integral that give the delta function. My question is does one Dirac delta function equal any other? Are all ways of getting the Dirac delta function equivalent? Thanks.
  26. P

    Dirac delta in Fourier transforms?

    Fourier transforms were invented before dirac delta functions but hidden in every Fourier transform is a dirac delta function. But it went unnoticed until dirac came along? Then they argued for the legitamacy of the delta function but it is present in every Fourier transform which is legitamate.
  27. N

    .Decomposing a 4x4 Matrix into Dirac 16 Matrices

    Dear All, Could you pls remind me how do I decompose arbitrary 4x4 matrix into Dirac 16 matrices... I ve forgotten. Thank you
  28. M

    Harmonic Oscillator, Ladder Operators, and Dirac notation

    Defining the state | \alpha > such that: | \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C}; Now, | \alpha > is an eigenstate of the lowering operator \hat{a}, isn't it? In other words, the statement that \hat{a} | \alpha >\ =\ \alpha | \alpha >...
  29. P

    Dirac Delta Function: Integral at x=a

    Homework Statement int[d(x-a)f(x)dx]=f(a) is the dirac delta fn but is int[d(a-x)f(x)]=f(a) as well? If so why?The Attempt at a Solution Is it because at x=a, d(0)=infinite and integrate dirac delta over a region including x=0 when d(0) is in the value in the integral will produce 1 hence f(a).
  30. J

    Exploring Analogue of Spin Angular Momentum for Classical Dirac Fields

    I've had some trouble with the argument "spin angular mometum has no classical analogue", that everyone seems to be repeating. I used Noether's theorem to calculate angular momentum of a classical Dirac's field, and found that it has internal angular mometum density, that cannot be written as a...
  31. A

    Cumulants and moments of Dirac Delta distribution

    For my statistical mechanics class I need to find the cumulants of a special distribution of which all moments are constant and equal to a. I followed two different approaches and obtained imcompatible results, something is wrong but I couldn't figure it out. Here's what I did: Since all...
  32. G

    Dirac Delta function as a limit

    Dear all, I need a simple proof of the following: Let [tex]u \in C(\mathbb{R}^3)[\tex] and [tex]\|u\|_{L^1(\mathbb{R}^3)} = 1[\tex]. For [tex]\lambda \geq 1[\tex], let us define the transformation [tex]u\mapsto u_{\lambda}[\tex], where [tex] u_{\lambda}(x)={\lambda}^3 u(\lambda...
  33. T

    Index notation vs Dirac notation

    A professor of mine recently remarked that dirac notation is easily the best in physics & we'd quickly realize this once we take a course in relativity. I've already taken the course & I find myself disagreeing with him, but maybe that's only because I enjoy relativity more. Curious what you...
  34. S

    Question on Dirac Delta and functional derivatives

    Suppose that we have a compact manifold \mathcal{M} with a positive definite metric g_{ij}. The volume of the manifold is then V = \int_\mathcal{M} d^3x \sqrt{g(x)}, where x^i are coordinates on \mathcal{M} and \sqrt{g(x)} is the square root of the determinant of the metric. Suppose now that...
  35. P

    A question of Dirac Delta function

    A vector function V(\vec{r}) = \frac{ \hat r}{r^2} If we calculate it's divergence directly: \nabla \cdot \vec{V} = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{1}{r^2} \right) = 0 However, by divergence theorem, the surface integral is 4\pi . This paradox can be solved by...
  36. J

    What's the best book/website on the Dirac equation?

    Did Feynman write about the Dirac Equation? I would like to see how to derive it, and how it reduces to the Schrodenger equation.
  37. M

    Dirac Postulate: Understanding Measurement in Quantum Mechanics

    There is many projection (or measurement) postulates in quantum mechanics axioms: von Neumann measurement, Luders postulate... But does anybody know sth. about DIRAC POSTULATE? Thx
  38. S

    Is There a Simpler Definition for the Dirac Delta Function?

    https://www.physicsforums.com/showthread.php?t=73447 I saw the above tutorial by arildno and looked at how he defined the Dirac Delta "function" as a functional. But isn't there a more easier way to do this. I have seen the following definition in a lot of textbooks. \delta(t) \triangleq...
  39. Q

    What is a Dirac Delta function?

    I often see this in electrodynamics in the form of a point charge density function. There are some rules on how to manipulate the thing in integrals. But what is it mathematically?
  40. T

    Dirac delta functions integration

    I can't figure out how to integrate this: \int_{0}^{\infty} \frac{x}{\sqrt{m^2+x^2}}sin(kx)sin(t\sqrt{m^2+x^2}) dx m, k and t are constants. The book has for m = 0, the solution is some dirac delta functions.
  41. T

    Deriving the Dirac Delta Function Equation in Field Theory

    I found this equation in a field theory book, which I can't figure how it was derived: \delta(x-a) \delta(x-a) = \delta(0) \delta(x-a)
  42. W

    Rotating Dirac particle current

    There is a step that bothers me in my book (Ryder) on QFT and I can't seem to figure it out. It concerns the (spatial) rotation of the spatial part of the Dirac four current: \bar{\psi} \gamma \psi The crucial step here is \frac{1}{4}(\vec{\sigma} \cdot \vec{\theta})...
  43. K

    Solving Dirac Delta Potential: Reflection & Transmission Coefficients

    Question: Consider the motion of a particle of mass m in a 1D potential V(x) = \lambda \delta (x). For \lambda > 0 (repulsive potential), obtain the reflection R and transmission T coefficients. [Hint] Integrate the Schordinger equation from -\eta to \eta i.e. \Psi^{'}(x=\epsilon...
  44. P

    Dirac Delta Function vs probability distribution

    Hello, What is the dirac delta function and how is it different from a probability distribution?
  45. S

    Dirac delta function homework help

    Suppose that we take the delta function \delta(x) and a function f(x). We know that \int_{-\infty}^{\infty} f(x)\delta(x-a)\,dx = f(a). However, does the following have any meaning? \int_{-\infty}^{\infty} f(x)\delta(x-a)\delta(x-b)dx, for some constants -\infty<a,b<\infty.
  46. E

    Dirac delta and exponential

    Let be the exponential: e^{inx}=cos(nx)+isin(nx) n\rightarrow \infty Using the definition (approximate ) for the delta function when n-->oo \delta (x) \sim \frac{sin(nx)}{\pi x} then differentiating.. \delta ' (x) \sim \frac{ncos(nx)}{\pi x}- \frac{\delta (x)}{\pi x}...
  47. F

    Exploring the Delta Dirac Function: What Happens if We Have Two?

    This isn't really homework, I'm just curious. So I'm dealing with the delta dirac function, and I was just wondering what would happen if we had two functions. So the sampling property, \int_{-\infty}^{\infty} f(t)\delta(t-a)\,\,dt = f(a) Now what if we had: \int_{-\infty}^{\infty}...
  48. pellman

    Dirac Lagrangian not invariant under rotations?

    First, I need to be able to do equations in my post but it has been a long time since I posted here. Someone please point me to a resource that gives the how-to. If you make a infinitesimal rotation of the free-field Lagrangian for the Dirac equation, you get an extra term because the Dirac...
  49. S

    Help About charge conjugation of Dirac spinor

    The following formula appears in P J Mulders's lecture notes http://www.nat.vu.nl/~mulders/QFT-0E.pdf {\cal C}~b(k,\lambda)~{\cal C}^{-1}~=~d(k,{\bar \lambda}) (8.18) where {\cal C} is charge conjugation operator. \lambda is helicity. I don't know why there is {\bar {\lambda}} on the...
  50. naima

    Can the Dirac Distribution be Proven Using Integrals?

    bonjour from france, I thought that sum of dirac(x - xi)/g'(xi), where the xi verify g(xi) = 0, was a definition for dirac(g(x)). It was proposed, as an exercise, to prove the equality of the 2 terms. can one help me thanks ps : can i write this in latex?
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