Dirac Definition and 900 Threads

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. Kostik

    A Making sense of Dirac's rotation operator in "General Theory of Relativity"

    In Dirac's "General Theory of Relativity", Chap. 34 on the polarization of gravitational waves, he introduces a rotation operator ##R##, which appears to be a simple ##\pi/2## rotation, since $$R \begin{pmatrix} A_0 \\ A_1 \\ A_2 \\ A_3 \end{pmatrix} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 &...
  2. arivero

    I The components of Dirac Equation -- Bosonic Lagrangian?

    The four components of Dirac equations obey the Klein-Gordon equation for a particle of mass m. This is always explained when introducing Dirac equation, but it is never exploited further. I am wondering: Can we then write a bosonic lagrangian for these four "particles"? Is this related to the...
  3. J

    Where can I find chemistry experiments that are accurately described with the Dirac equation?

    Let's say we can solve the Dirac equation numerically with a powerful computer. What experiments do you recommend to take a look at to compare the result of the simulations with the real data. Maybe chemical reactions?
  4. Steve Zissou

    A Dirac Delta: Normal -> Lognormal?

    Hello shipmates, Instead of imagining a Dirac Delta as the limit of a normal, like this: $$ \delta\left ( x \right ) = \lim_{a \to 0}\frac{1}{|a|\sqrt{2\pi}}\exp\left [ -\left ( x/a \right )^2 \right ] $$ Could we say the same thing except starting with a lognormal, like this? $$ \delta_{LN}...
  5. Kostik

    A What does Dirac mean by "the suffixes would not balance"?

    In Dirac ("GTR") p. 39 he says, "For a covariant vector ##A_\mu##, we have $$A_{\mu;\nu}-A_{\nu;\mu} = A_{\mu,\nu} - \Gamma^\rho_{\mu\nu} A_\rho - \left( A_{\nu,\mu} - \Gamma^\rho_{\nu\mu}A_\rho \right) = A_{\mu,\nu} - A_{\nu,\mu}.$$ This result may be stated: covariant curl equals ordinary...
  6. Kostik

    A Dirac's coordinates ##(\tau, \rho)## for the Schwarzschild metric with ##r \le 2m##

    Dirac in his "GTR" (Chap 19, page 34-35) finds a coordinate system ##(\tau, \rho)## which has no coordinate singularity at ##r=2m##. Explicitly, the transformation looks like (after some algebra): $$\tau=t + 4m\sqrt{\frac{r}{2m}} + 2m\log{\frac{\sqrt{r/2m}-1}{\sqrt{r/2m}+1}}$$ $$\rho=t +...
  7. Kostik

    I Dirac comment on covariant derivatives

    Dirac in "General Theory of Relativity" (top of p. 20) says "Even if one is working with flat space ... and one is using curvilinear coordinates, one must write one's equations in terms of covariant derivatives if one wants them to hold in all systems of coordinates." This comment follows his...
  8. DuckAmuck

    A Anti-symmetric tensor question

    The sigma tensor composed of the commutator of gamma matrices is said to be able to represent any anti-symmetric tensor. \sigma_{\mu\nu} = i/2 [\gamma_\mu,\gamma_\nu] However, it is not clear how one can arrive at something like the electromagnetic tensor. F_{\mu\nu} = a \bar{\psi}...
  9. ergospherical

    What is the Wave Function for a Particle in One Dimension in Dirac Formalism?

    What is ##<x|P|x'>##? (for particle in 1d, and ##\hbar = 1##)?\begin{align*} <x|P|x'> &= \int dp' <x|P|p'><p'|x'> \\ &= \int dp' \ p' <x|p'> <p'|x'> \\ &= \int dp' \ p' \frac{1}{\sqrt{2\pi}} e^{ip'x} \frac{1}{\sqrt{2\pi}} e^{-ip'x'} \\ &= \frac{1}{2\pi} \int dp' \ p' e^{ip'(x-x')} \end{align*}
  10. D

    I Dirac Notation for Operators: Ambiguity in Expectation Values?

    Hi If A is a linear operator but not Hermitian then the expectation value of A2 is written as < ψ | A2| ψ >. Now if i write A2 as AA then i have seen the expectation value written as < ψ | A+A| ψ > but if i only apply the operators to the ket , then could i not write it as < ψ | AA | ψ > ? In...
  11. Demystifier

    A Found a new formula of Dirac calculus

    I have found a new formula in Dirac calculus. The formula is elementary, so probably I'm not the first who found it. Yet, I have never seen it before. As many other formulas in Dirac calculus, it is not rigorous in the sense of functional analysis. Rather, it is a formal equality, which is only...
  12. topsquark

    A Solving the Radial Equation for the Dirac Hydrogen Atom Solution

    I'm going to be a bit sketchy here, at least to start with. If you want me to show you exactly where I am I might post a pdf, if that's okay. (Only because it will simplify coding several pages of LaTeX.) Briefly, what I'm trying to do is take this system of equations: ##F^{ \prime } +...
  13. S

    A Covariant four-potential in the Dirac equation in QED

    Under the entry "Quantum electrodynamics" in Wikipedia, the Dirac equation for an electron is given by $$ i\gamma^{\mu}\partial_{\mu}\psi - e\gamma^{\mu}\left( A_{\mu} + B_{\mu} \right) \psi - m\psi = 0 ,\tag 1 $$ or $$ i\gamma^{\mu}\partial_{\mu}\psi - m\psi = e\gamma^{\mu}\left( A_{\mu} +...
  14. James1238765

    I How Is the Matrix V Related to Dirac Spinors and Tensor Products?

    Could anyone help with some of the later parts of the derivation for Dirac spinors, please? I understand that an arbitrary vector ##\vec v## $$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} $$ can be defined as an equivalent matrix V with the components $$ \begin{bmatrix} z & x - iy \\ x + iy...
  15. J

    I Understanding the Equations of Motion for the Dirac Lagrangian

    I'm having trouble following a proof of what happens when the Dirac Lagrangian is put into the Euler-Lagrange equation. This is the youtube video: and you can skip to 2:56 and pause to see all the math laid out. I understand the bird's eye results of the Dirac Lagrangian having an equation of...
  16. Math Amateur

    I Dirac Notation for Vectors and Tensors (Neuenschwander's text ....)

    I am reading Tensor Calculus for Physics by Dwight E. Neuenschwander and am having difficulties in confidently interpreting his use of Dirac Notation in Section 1.9 ... in Section 1.9 we read the following: I need some help to confidently interpret and proceed with Neuenschwander's notation...
  17. Delerion24

    Help with the derivative of the Dirac delta

    My goal is to develop the equation 21. You should asume that \delta(r_2-r_1)^2 =0. These is named renormalization. Then my question is , do my computes are correct with previous condition ?
  18. guyvsdcsniper

    How Do You Convert Linear Operators to Dirac Notation?

    I am trying to convert the attached picture into dirac notation. I find the LHS simple, as it is just <ψ,aφ>=<ψIaIφ> The RHS gives me trouble as I am interpreting it as <a†ψ,φ>=<ψIa†Iφ> but if I conjugate that I get <φIaIψ>* which is not equiv to the LHS. *Was going to type in LaTex but I...
  19. Graham87

    Intro Quantum Mechanics - Dirac notations

    I am learning Dirac notations in intro to quantum mechanics. I don’t understand why the up arrow changes to down arrow inside the equation in c). My own calculation looks like this:
  20. H

    Sifting property of a Dirac delta inverse Mellin transformation

    Hi, I have to verify the sifting property of ##\frac{1}{2\pi i} \int_{-i\infty}^{i\infty} e^{-sa}e^{st} ds## which is the inverse Mellin transformation of the Dirac delta function ##f(t) = \delta(t-a) ##. let ##s = iw## and ##ds = idw## ##\frac{1}{2\pi} \int_{-\infty}^{\infty} e^{-iwa}e^{iwt}...
  21. H

    Mellin transform of Dirac delta function ##\delta(t-a)##

    Hi, I found Laplace transform of this Dirac delta function which is ##F(s) = e^{-st}## since ##\int_{\infty}^{-\infty} f(t) \delta (t-a) dt = f(a)## and that ##\delta(x) = 0## if ##x \neq 0## Then the Mellin transform ##f(t) = \frac{1}{2 \pi i} \int_{\gamma - i \omega}^{\gamma +i \omega}...
  22. Salmone

    A Prove a formula with Dirac Delta

    Why is the Laplacian of ##1/r## in spherical coordinates proportional to Dirac's Delta, namely: ##\left(\frac{\partial^2 }{\partial r^2}+\frac{2}{r}\frac{\partial }{\partial r}\right)\left(\frac{1}{r}\right)=-\frac{\delta(r)}{r^2}## I get that the result is zero.
  23. P

    Scattered State Solutions of a Repulsive Dirac Delta Potential

    I feel that this problem can be directly answered from the E>0 case of the attractive Dirac delta potential -a##\delta##(x), with the same reflection and transmission coefficients. Can someone confirm this hunch of mine?
  24. R

    I Does anyone have a collection of the Dirac Equations?

    I am working on my physics paper and just realized that after explaining everything I did not add the equasion. Now I am wondering where I can find a good source on them, so that I can add them.
  25. snoopies622

    I What do the psi_3 and psi_4 components of the Dirac equation represent?

    Forgive me if you've heard this song before, but I don't understand how to interpret the \psi_3 and \psi_4 components of the Dirac equation. For instance, at 8:27 of this video we see that while an electron at rest can be in a state like [1,0,0,0], the same electron as viewed from a...
  26. K

    I What is unique about the bra in Dirac bra-ket notation?

    It's said that every ket has a unique bra. For any vector ##|v> ∈ V## there is a unique bra ##<v| ∈ V*##. I'm not sure what that means. What is unique? Can anyone please help me understand. Thank you
  27. L

    A Interaction between matter and antimatter in Dirac equation

    I'm new to relativistic quantum mechanics and quantum field theory and was trying to learn about the Dirac equation. Unfortunately, I got a little stumped by the interaction between matter and antimatter. It seems like the time derivative of matter is dependent on the spatial derivative of...
  28. A

    I References for Hamiltonian field theory and Dirac Brackets

    I'm looking for complete and detailed references on constrained Hamiltonian systems and Dirac brackets. While my main interest is electrodynamics, I would prefer a complete exposition of the theory from the ground up. So far, my knowledge about the topic comes from books in QFT, like Weinberg...
  29. Leo Liu

    I What is the Definition of the Delta Function?

    I came across it in the derivation of Gauss' law of electric flux from Coulomb's law. I did some research on it, but the wikipedia page about it was slightly confusing. All I know about it is that it models an instantaneous surge by a distribution. However I am still perplexed by this concept...
  30. M

    I Dirac equation in the hydrogen atom

    Hello! I went over a calculation of the hydrogen wavefunction using Dirac equation (this one) and I am a bit confused by the angular part. The final result for the wavefunction based on that derivation is this: $$ \begin{pmatrix} if(r) Y_{j l_A}^{m_j} \\ -g(r)...
  31. Viona

    Operator acts on a ket and a bra using Dirac Notation

    Summary:: Operator acts on a ket and a bra using Dirac Notation Please see the attached equations and help, I Think I am confused about this
  32. F

    Conservation of charge with Dirac delta

    Hello, I was reviewing a part related to electromagnetism in which the charge and current densities are defined by the Dirac delta: ##\rho(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} - \underline{x}_n(t))## ##\underline{J}(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} -...
  33. tworitdash

    I Can a Gaussian distribution be represented as a sum of Dirac Deltas?

    We know that Dirac Delta is not a function. However, I just talk about the numerical version of it that we use every day. We can simply represent the Dirac delta function as a limiting case of Gaussian distribution when the width of the distribution ##\sigma->0##. $$ \delta(x - \mu) =...
  34. Haorong Wu

    The representation matrix for alpha and beta in Dirac equation

    In the 4-dimensional representation of ##\beta##, ## \beta=\begin{pmatrix}\mathbf I & \mathbf 0 \\ \mathbf0 & -\mathbf I\end{pmatrix} ,## and we can suppose ## \alpha_i=\begin{pmatrix}\mathbf A_i & \mathbf B_i \\ \mathbf C_i & \mathbf D_i\end{pmatrix} ##. From the anti-commutation relation...
  35. U

    A question on the Dirac delta distribution

    Is it correct to say that $$\int e^{-i(k+k’)x}\,\mathrm{d}x$$ is proportional to ##\delta(k+k’)##?
  36. A

    Writing the charge density in the form of the Dirac delta function

    Hey guys! Sorry if this is a stupid question but I'm having some trouble to express this charge distribution as dirac delta functions. I know that the charge distribution of a circular disc in the ##x-y##-plane with radius ##a## and charge ##q## is given by $$\rho(r,\theta)=qC_a...
  37. snypehype46

    Exercise involving Dirac fields and Fermionic commutation relations

    I'm trying to the following exercise: I've proven the first part and now I'm trying to do the same thing for fermions. The formulas for the mode expansions are: What I did was the following: $$\begin{align*} \sum_s \int d\tilde{q} \left(a_s(q) u(q,s) e^{-iq \cdot x}+ b_s^\dagger(q) v(q,s)...
  38. Haorong Wu

    I Could this function be approximated by Dirac delta function?

    hi, there. I am doing some frequency analysis. Suppose I have a function defined in frequency space $$N(k)=\frac {-1} {|k|} e^{-c|k|}$$ where ##c## is some very large positive number, and another function in frequency space ##P(k)##. Now I need integrate them as $$ \int \frac {dk}{2 \pi} N(k)...
  39. R

    A Dirac Notation: Why is order reversed in ket expasion?

    Shankar Prin. of QM 2nd Ed (and others) introduce the inner product: <i|V> = vi ...(Shankar 1.3.4) They expand the ket |V> as: |V> = Σ vi|i> |V> = Σ |i><i|V> ...(Shankar 1.3.5) Why do they reverse the order of the component vi and the ket |i> when they...
  40. M

    I Probability: why can we use the Dirac delta function for a conditional pdf?

    Hi, I have a quick question about something which I have read regarding the use of dirac delta functions to represent conditional pdfs. I have heard the word 'mask' thrown around, but I am not sure whether that is related or not. The source I am reading from states: p(x) = \lim_{\sigma \to...
  41. redtree

    I Integrating with the Dirac delta distribution

    Given \begin{equation} \begin{split} \int_{y-\epsilon}^{y+\epsilon} \delta^{(2)}(x-y) f(x) dx &= f^{(2)}(y) \end{split} \end{equation} where ##\epsilon > 0## Is the following also true as ##\epsilon \rightarrow 0## \begin{equation} \begin{split} \int_{y-\epsilon}^{y+\epsilon}...
  42. thaiqi

    I What is the relation between the Dirac equation and QED?

    Hello, everyone. Need I understand Dirac equation if I plan to learn QED?
  43. B

    A Geometry of matrix Dirac algebra

    Indeed, if we take a vector field which dual to the covector field formed by the gradient from a quadratic interval of an 8-dimensional space with a Euclidean metric, then the Lie algebra of linear vector fields orthogonal (in neutral metric) to this vector field is isomorphic to the...
  44. peguerosdc

    A Getting particle/antiparticle solutions from the Dirac Equation

    Hi! I am studying Dirac's equation and I already have understood the derivation. Following Griffiths, from factoring Einstein's energy relation with the gamma matrices: ## (\gamma^\mu p_\mu + m)(\gamma^\mu p_\mu - m) = 0 ## You take any of the two factors, apply quantization and you arrive to...
  45. Antarres

    A Dirac delta function confusion

    As a part of a bigger problem, I was trying to evaluate the D'Alambertian of ##\epsilon(t)\delta(t^2-x^2-y^2-z^2)##, where ##\epsilon(t)## is a sign function. This term appears in covariant commutator function, so I was checking whether I can prove it solves Klein-Gordon equation. Since there's...
  46. rannasquaer

    MHB Dirac Delta and Fourier Series

    A beam of length L with fixed ends, has a concentrated force P applied in the center exactly in L / 2. In the differential equation: \[ \frac{d^4y(x)}{dx^4}=\frac{1}{\text{EI}}q(x) \] In which \[ q(x)= P \delta(x-\frac{L}{2}) \] P represents an infinitely concentrated charge distribution...
  47. patric44

    Quantum Dirac notation based quantum books?

    hi i am recently following the nptel course in quantum mechanics (The Course ) and it seems like a really good course , but i can't find the book that it based on . my question is : had anyone saw that course before to suggest a QM book related to it ? - she began by an introduction to vector...
  48. entropy1

    I The significance of the Dirac notation

    If we have the wavefunction ##|ab \rangle##, what do the a and b stand for? In particular, do a and b signify an outcome of some pending or possible measurement, or do they signify some aspect of the wavefunction, and if so, which aspect?
  49. M

    I Condtion on transformation to solve the Dirac equation

    The problem is given in the summary. My attempt: Assume that ##\psi^\prime (x^\prime)## is a solution of the Dirac equation in the primed frame, given the transformation ##x\mapsto x^\prime :=\Lambda^{-1}x## and ##\psi^\prime (x^\prime)=S\psi(x)##, we have $$ \begin{align*} 0&=(\gamma^\mu...
  50. JD_PM

    I Understanding the wrong way to quantize the Dirac Field | Part 1

    I've been studying Tong's beautiful chapter (pages 106-109; See also Peskin and Schroeder pages 52-58), together with his great lectures at Perimeter Institute, on how to quantize the following Dirac Lagrangian in the wrong way $$\mathscr{L}=\bar{\psi}(x)(i\not{\!\partial}-m)\psi(x) \tag{5.1}$$...
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