# What is Dirac: Definition and 897 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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4. ### 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...
5. ### 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}...
6. ### 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*}
7. ### 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...
8. ### 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...
9. ### 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 } +...

12. ### 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...
13. ### 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...
14. ### 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 ?
15. ### 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...
16. ### 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:
17. ### 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}...
18. ### 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}...
19. ### 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.
20. ### 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?
21. ### 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.
22. ### 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...
23. ### 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
24. ### 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...
25. ### 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...
26. ### 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...

31. ### 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...
32. ### 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’)##?

47. ### 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 $$\mathscr{L}=\bar{\psi}(x)(i\not{\!\partial}-m)\psi(x) \tag{5.1}$$...
48. ### I Rewriting Feynman amplitudes and the Dirac equation

I was studying the photon polarization sum process (second edition QFT Mandl & Shaw,https://ia800108.us.archive.org/32/items/FranzMandlGrahamShawQuantumFieldTheoryWiley2010/Franz%20Mandl%2C%20Graham%20Shaw-Quantum%20Field%20Theory-Wiley%20%282010%29.pdf) and got stuck in how to get certain...
49. ### I Dirac Lagrangian and Covariant derivative

This is from Griffiths particle physics, page 360. We have the full Dirac Lagrangian: $$\mathcal L = [i\hbar c \bar \psi \gamma^{\mu} \partial_{\mu} \psi - mc^2 \bar \psi \psi] - [\frac 1 {16\pi} F^{\mu \nu}F_{\mu \nu}] - (q\bar \psi \gamma^{\mu} \psi)A_{\mu}$$ This is invariant under the joint...
50. ### A Relation between Dirac's equation density matrix and current with spin

After computind dirac 1D equation time dependant for a free particle particle I get 2 matrixs. From both,them I extract: 1) the probablity matrix P =ps1 * ps1 + psi2 *psi2 2) the current matrix J = np.conj(psi1)*psi2+np.conj(psi2)*psi1 I think that current is related to electricity, and...