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. F

    Is Dirac delta function dimensionless?

    Probably a trivial question, but does Dirac delta function has (to have always) a physical dimension or is it used just as a auxiliary construct to express e.g. sudden force impulse, i.e. Force = Impulse \times \delta, where 'Impulse' carries the dimension? Any comments would be highly...
  2. F

    Dirac Delta: Finite Height in Fourier Analysis

    Hi, if the definition of a dirac delta (impulse) function is just a sinc function with an infinite height and 0 width, why is it that they are shown and used in Fourier analysis as having a finite height? for example g(t) = cos(2*PI*f0*t) has two impulses of height = 1/2 at f=+/-f0
  3. I

    Dirac Delta Integral Homework: Proving Equations

    Homework Statement For some reason these are just messing me up. I need to prove: 1. \delta(y)=\delta(-y) 2.\delta^{'}(y) = -\delta^{'}(-y) 3.\delta(ay) = (1/a)\delta(y) In 2, those are supposed to be first derivatives of the delta functions Homework Equations Use an integral...
  4. S

    Dirac particle in a spherical potential box

    Hello, I'm studyng relativistic quantum mechanics by the book Relativistic quantum mechanics. Wave equations - Greiner, W. and I'm trying to derive the energy eingenvalues for s1/2 states, so I have the equation that I uploaded with the name eq1.jpg. In the text the author says, "If we assume R0...
  5. A

    Using Dirac Bracket: Books & References for Examples

    I have searched in web and go through some papers. But the use of Dirac Bracket in constraint still unclear to me. It would be better if I have some examples. Can anyone please help me by suggesting books/references where I can find details about using Dirac Bracket?
  6. N

    Why there is 2[itex]\pi[/itex] in every dirac delta function

    in QF, every dirac delta function is accompanied by 2\pi,i.e.(2\pi)\delta(p-p_0) or (2\pi)^3\delta(\vec{p}-\vec{p_0}) the intergral element in QF is \int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_P}, it comes from the integral element \int\frac{d^4p}{(2\pi)^4}(2\pi)\delta(p^2-m^2),I want to know why...
  7. M

    Quantum mechanics and Minimal coupling of Dirac field

    Hi I have a simple question: We know from non-relativistic quantum mechanics that the spin of an electron couples only to the magnetic field, i.e. it processes around the magnetic field. How is this resolved in the relativistic context where it would seem that the spin should couple to...
  8. D

    Too few examples to explain The principles of quantum mechanics by dirac.

    Too few examples to explain "The principles of quantum mechanics" by dirac. Hi! I studied my first course of quantum physics without a technical formalism (I'm studying physics engineering). I find some hindrances in paragraph 20. It says (I'm translating from Italian): After a few...
  9. M

    The Dirac equation with anomalous magnetic moment term

    Hi could someone please explain the story (if there is one) about the Dirac equation with an anomalous magnetic moment term, I have seen this in several old papers but it never seems to be mentioned in textbooks. Was this an old confusion in formulating QFT. In this context I believe the Dirac...
  10. Jim Kata

    Understanding Dirac Spinor Question in QED

    In Qed they replace the current vector J^{\alpha} by ie\overline{\Psi}\gamma^{\alpha}\Psi. I don't understand how this is done. I understand that J^{A\dot{A}}=J^{\alpha}{\sigma^{A\dot{A}}_\alpha} but if J^{A\dot{A}} is a rank two matrix then...
  11. A

    Is f(x)δ(x) Equal to f(2)δ(x)?

    Homework Statement Homework Equations The Attempt at a Solution Can I write, say, f(x) \delta(x)=f(2)\delta(x)? Since \delta(x) =0 for x\neq0
  12. D

    Prove that derivative of the theta function is the dirac delta function

    let θ(x-x') be the function such that θ = 1 when x-x' > 0 and θ = 0 when x-x' < 0. Show that d/dx θ(x-x') = δ(x - x'). it is easy to show that d/dx θ(x-x') is 0 everywhere except at x = x'. To show that d/dx θ(x-x') is the dirac delta function i also need to show that the integral over the...
  13. M

    How Do Dirac Gamma Matrices Satisfy Their Anticommutation Relations?

    Homework Statement Given that \gamma^{\mu}\gamma^{\nu}+\gamma^{\nu}\gamma^{\mu}=2g^{\mu\nu}*1 where 1 is the identity matrix and the \gamma are the gamma matrices from the Dirac equation, prove that: \gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu}=2g_{\mu\nu}*1 Homework Equations...
  14. J

    Dirac Delta Integration for Exponential Functions

    Homework Statement find \int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt for x(t) = e^{a t} u(t) there is no information conserning a, β, or t_{0}... The Attempt at a Solution assuming that t_{0} is a constant\int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt =...
  15. J

    Why Does the Free-Field Dirac Hamiltonian Calculation Seem Incorrect?

    Homework Statement This is a simple problem I thought of and I'm get a nonsensical answer. I'm not sure where I'm going wrong in the calculation. Find the value of <-,p',v';+,q',r'|H|-,p,v;+,q,r> where H is the free-field Dirac Hamiltonian H =...
  16. Rasalhague

    Exploring Dirac Delta Functions in QM Theory

    I'm reading Daniel T. Gillespie's A QM Primer: An Elementary Introduction to the Formal Theory of QM. In the section on continuous eigenvalues, he admits to playing "fast and loose" with the laws of calculus, with respect to the Dirac delta function. I'd like to understand it better, or, if such...
  17. P

    Solve Dirac Delta Function IVP: y''-2y'-3y=2\delta (t-1)-\delta (t-3)

    Homework Statement Solve the given symbolic initial value problem: y''-2y'-3y=2\delta (t-1)-\delta (t-3) ;y(0)=2,y'(0)=2 The attempt at a solution Let Y(s):= L{y(t)}(s) Taking laplace transform of both sides: [s^{2}Y(s)-2s-2]-2[sY(s)-2]-3Y(s)=2e^{-s}-e^{-3s}...
  18. M

    Free particle in quantum mechanics, Dirac formalism

    The problem is very easy, maybe just something about eigenvectors that I'm missing. Go to the first two pages of the 5th chapter of ''Principles of Quantum Mechanics'', by Shankar, 2nd edition. Homework Statement Shankar wants to find the solution for a free particle in Quantum Mechanics...
  19. Z

    Zeta regularization and product of dirac delta distribution

    using the convolution theorem with power functions x^{m} we may define via the convolution theorem the product of 2 dirac delta distribution then main idea is to consider the convolution integral \int_{R}dt(x-t)^{m}t^{n} and then apply the Fourier transform with respect to variable 'x'...
  20. A

    A problem with a Dirac delta function potential

    Homework Statement An ideal particle of energy E is incident upon a rectangular barrier of width 2a and height V_{0}. Imagine adjusting the barrier width and height so that it approaches V(x)=\alpha \delta(x). What is the relationship between V0, alpha and a? Homework Equations The...
  21. K

    Lagrangian, Hamiltonian and Legendre transform of Dirac field.

    In most of the physical systems, if we have a Lagrangian L(q,\dot{q}), we can define conjugate momentum p=\frac{\partial L}{\partial{\dot{q}}}, then we can obtain the Hamiltonian via Legendre transform H(p,q)=p\dot{q}-L. A important point is to write \dot{q} as a function of p. However, for the...
  22. 0

    Dirac Notation and completeness relation

    I am confused about two minor things right now. The following illustrates both which I pulled from my QM book: <x|p_{op}|0>=\int_{-\infty}^{\infty}dp<x|p_{op}|p><p|0>=\int_{-\infty}^{\infty}dp~p<x|p><p|0>...
  23. L

    Difference Equation and Dirac Delta

    Homework Statement y[n] - (2/3)y[n-1] = x[n] what is y[n] if x[n] = diracdelta[n] The Attempt at a Solution for some reason, i argued that y[n-1] = diracdelta[n-1] so y[n] = diracdelta[n] + (2/3)diracdelta[n-1] Im pretty sure this is wrong, anybody can help?
  24. K

    This is the Hilbert space for the Dirac spinor and state vector.

    I believe Dirac spinors are not in any Hilbert space since it has no positive definite norm. However one QM axiom I learned told me any quantum state is represented by a state vector in Hilbert space, so what is happening to Dirac spinor?Or is it just that the axiom is not for relativistic QM?
  25. R

    Quantizating a symmetric Dirac Lagrangian

    As is well known, a Dirac Lagrangian can be written in a symmetric form: L = i/2 (\bar\psi \gamma \partial (\psi) - \partial (\bar\psi) \gamma \psi ) - m \bar\psi \psi Let \psi and \psi^\dagger be independent fields. The corresponding canonical momenta are p = i/2 \psi^\dagger...
  26. T

    Theory Behind Dirac Lagrangian: Reasons Nature Didn't Choose Mine

    We all know that the free Lagrangian for a spin-1/2 Dirac field is \mathcal{L}=\bar\psi(i\gamma_\mu\partial^\mu-m)\psi. But, if I were to invent a Lagrangian, I would have tried \mathcal{L}=\partial_\mu\bar\psi\partial^\mu\psi-m^2\bar\psi\psi. What's wrong with this second Lagrangian? Why...
  27. T

    Scaling Property of the Dirac Delta Function

    Homework Statement Prove that \displaystyle \int_{-\infty}^{\infty} \delta (at - t_0) \ dt = \frac{1}{ | a |} \int_{-\infty}^{\infty} \delta (t - \frac{t_0}{a}) \ dt For some constant a. The Attempt at a Solution Edit: Looking at this again, I really don't understand where this is coming...
  28. Orion1

    Are these matrix definitions correct for the Dirac equation?

    Hydrogen normalized position wavefunctions in spherical coordinates: \Psi_{n \ell m}\left(r,\theta,\phi\right) = \sqrt{{\left( \frac{2}{n r_1} \right)}^3 \frac{\left(n - \ell - 1\right)!}{2n\left[\left(n + \ell\right)!\right]}} e^{-\frac{r}{n r_1}} \left({2r \over {n r_1}}\right)^{\ell} L_{n -...
  29. L

    Proof of Dirac delta sifting property.

    Homework Statement Prove the statement http://www.mathhelpforum.com/math-help/vlatex/pics/60_32c8daf48ffa5f233ecc2ac3660e517e.png The Attempt at a Solution I am clueless as to how I would go about doing this, I know the basic properties. I think it has to do with using epsilon...
  30. E

    Note to the derivation of Dirac equation

    In book Quantum Electrodynamics, Feynman wrote that the Dirac equation is a relativistic form of the Pauli equation, not a correct form of Klein-Gordon equation. But, I think that the electron spin is only assumed in Pauli equation, but Dirac equation derives it? I went through derivation in...
  31. M

    Confused about Dirac particles

    I'm really confused! The Dirac equation describes spin -1/2 particles - i.e. particles of definite spin. And yet the spin operator does not commute with the Dirac Hamiltonian! The reason I'm confused is because I thought if you were going to describe particles of a given kind - that is...
  32. O

    QFT Dirac Chiral Equations of Motion

    Homework Statement From Mandl and Shaw (exercise 4.5): Deduce the equations of motion for the fields: \psi_L(x)\equiv{1 \over 2} (1-\gamma_5)\psi(x) \psi_R(x)\equiv{1 \over 2} (1+\gamma_5)\psi(x) for non-vanishing mass, and show that they decouple in the limit m=0. Hence show that the...
  33. A

    Fine structure, exact formula. Dirac.

    Hello all, I'm still plugging away at the meaning of spin, and spin orbital coupling. I am at the stage where I am testing out various formulations of corrections to Schrodinger's equation and beginning to test my ideas against data. Right now I am looking at Hydrogen spectra because being a...
  34. B

    Discourse on Dirac Delta Function in Spherical/Polar Coordinates

    Anyone know where I can find a discourse on the dirac delta function in spherical or polar coordinates, in particular why it is the form it is with correction coefficients? Thank you.
  35. C

    What is the probability associated with a Dirac delta-like distribution?

    Hi all, I have a question about the actual value associated with the probability p(r) where p(r) is infinite for r=0. I realize that this p(r) can only be a distribution and only exist under an integral, and can't represent a pdf. My p(r) is a radially symmetric laplace distribution in 2d...
  36. L

    Using MATLAB to get the fourier transform of dirac delta function

    Homework Statement Dear all, I have a problem when I using MATLAB to get the Fourier transform of dirac delta function. below is my code.Homework Equations clear all; clc; close all; % t=0:0.002:2; t=0:0.002:4; dt=t(2)-t(1); u=zeros(size(t)); pos0=find(t>=1,1); u(pos0)=1/dt...
  37. J

    What is the result of taking the integral of δ(τ+2) - δ(τ-2)?

    hi guys i want to find i took the integral of δ(τ+2) and I said that it's basically u(t+2) δ(τ-2) is u(t-2) so we have u(t+2) - u(t-2) = 2 from -2 to 2.. well after that i need to get the absolute value of this and then the power of two, i don't know how to do this.. my book...
  38. D

    Trace Theorems and Dirac Matrices

    I think I'm missing something real simple on trace theorems and Dirac matrices, but am just not seeing it. In the Peskin and Schroeder QFT text on page 135 we have: gamma^(mu)*gamma^(nu)*gamma_(mu) = -2*gamma^(nu) But, why can't we anti-commute and obtain the following...
  39. K

    Find an orthogonal quantum state: introduction to dirac notation.

    Homework Statement Suppose we have a spin 1/2 Particle in a prepared state: \left|\Psi\right\rangle = \alpha \left|\uparrow\right\rangle + \beta\left|\downarrow\right\rangle where \left|\uparrow\right\rangle \left|\downarrow\right\rangle are orthonormal staes representing spin up and...
  40. G

    Commutators with the Dirac Equation

    Homework Statement (Introduction to Elementary Particles, David Griffiths. Ch 7 Problem 7.8 (c)) Find the commutator of H with the spin angular momentum, S= \frac{\hbar}{2}\vec{\Sigma}. In other words find [H,S] Homework Equations For the Dirac equation, the Hamiltonian...
  41. N

    Do higher spin particles obey Klein-Gordon or Dirac equations?

    Please teach me this: We know that 0-spin particles obey Klein-Gordon equation and 1/2spin particles obey Dirac equation.But I do not know whether higher integer spin particles obey Klein-Gordon equation or not.Similarly,do higher half integer spin particles obey Dirac equation?Because if we...
  42. Q

    What is the purpose of the Dirac delta function in three dimensions?

    i don't really understand the dirac delta function in 3D. is it right that integral of f(r)d3(r-a)dt = f(a) where a = constant ,r is like variable x in 1D dirac delta function? so why when i have f(r')d3(r-r') , it picks out f(r)? where r is now a constant and r' is a...
  43. C

    Dirac delta function under integral?

    Hello all, I joined this amazing forum just today.I hope that my question will get answered soon. So here it is.I am unable to understand a some steps in calculation. Please help me understand. Here is a linear homogeneous first order differential equation whose solution a research...
  44. N

    Dirac delta, generalizations of vector calculus and sigh vagueness

    Although I am an aspiring physicist, I cannot cope with the physicist's love for vagueness when it comes to yielding math. Exactness is simply not a luxury that can be ignored, certainly not in theoretical physics. But okay, I realize the dirac delta function can be made exact by the use of...
  45. T

    Why is the product of Dirac spinors a 4x4 matrix?

    Hi togehter. I encountered the following problem: The timeordering for fermionic fields (here Dirac field) is defined to be (Peskin; Maggiore, ...): T \Psi(x)\bar{\Psi}(y)= \Psi(x)\bar{\Psi}(y) \ldots x^0>y^0 = -\bar{\Psi}(y)\Psi(x) \ldots y^0>x^0 where \Psi(x) is a Dirac...
  46. A

    Understanding the Dirac Delta Distribution

    So I've been told that the Dirac delta functional is a distribution, but I don't see why that's the case. I had an introduction to distributions in my calculus IV course, but as I remember it, a distribution involves and integral containing a the product of a function from the Schwartz space and...
  47. M

    Laplace transform - Dirac delta

    i need help trying to find the laplace transform of te-t\delta(t) i know the laplace transform of te-t is 1/(s+1)2 but i don't know how to find the laplace transform of a product with the Dirac delta
  48. A

    Can Particles Described by Dirac and Klein-Gordon Equations Exist Independently?

    The component solutions of the Dirac equation are also solutions of the Klein-Gordon equation. But these solutions are not scalars since the coefficients contain quantities like energy and momentum[the phase part is of course an invariant] These are neither zero spin nor half spin...
  49. J

    Three dimensional dirac function

    Homework Statement Show that if r = \sqrt{x^2 + y^2 + z^2} then \nabla^2 \left( \frac{1}{r} \right) = -4 \pi \delta^3(r) Homework Equations I've heard Green's theorem should help me... not quite certain how. The Attempt at a Solution I took the divergence of the left hand side...
  50. S

    Is the Dirac Delta Function Even?

    Hi this is my first post here so I'm sorry if my question seems trivial. I haven't worked a lot with the dirac delta function before, so i always thought that the shifting property would only work as: \int\delta(x-h)\;f(x)\;dx=f(h) Now I've been reading some articles and I came across...
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