Dirac Definition and 859 Threads

Hello, I have a question concerning the current in the Dirac equation and its corresponding operator. One can construct a current density that is \textbf{j}^{i} = \psi^{\dagger}\gamma^{i}\psi If I want to have the current, I will have to integrate: I = \oint \textbf{j} \cdot \textbf{n} \, dA...

Hi! I can define \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 I know that the four gamma matrices \gamma^i\:\:,\;i=0...3 are invariant under a Lorentz transformation. So I can say that also \gamma ^5 is invariant, because it is a product of invariant matrices. But this equality holds: \gamma...

If yes, how can we find it?

Homework Statement Find <lz> using \Psi, where \Psi=(Y11+cY1-1)/(1+c^2)). Ylm are spherical harmonics, and <lz> is the angular momentum operator in the z direction. Homework Equations <lz> Ylm = hmYlm The Attempt at a Solution The brackets around <lz> are throwing me off...

Hi there, I'm having a problem calculating the energy momentum tensor for the dirac spinor \psi (x) =\left(\begin{align}\psi_{L1}\\ \psi_{L2}\\\psi_{R1}\\ \psi_{R2}\end{align}\right)(free theory). So, with the dirac lagrangian \mathcal{L}=i\bar{\psi}\gamma^\mu\partial_\mu\psi-m\bar{\psi}\psiin...

The Dirac electron in the Higgs vacuum field v and an electromagnetic field with vector potential A_\mu is described by the following equation: i \gamma^\mu \partial_\mu \psi = g v \psi + e \gamma_\mu A^\mu \psi where g is the coupling constant to the Higgs field and e is the coupling...

Alright, so I was wondering if anyone could help me figure out from one step to the next... So we have defined |qt>=exp(iHt/\hbar)|q> and we divide some interval up into pieces of duration τ Then we consider <q_{j+1}t_{j+1}|q_{j}t_{j}> =<q_{j+1}|e-iHτ/\hbar|q_{j}>...

The Dirac electron in the Higgs vacuum field v and an electromagnetic field with vector potential A_\mu is described by the following equation: i \gamma^\mu \partial_\mu \psi = g v \psi + e \gamma_\mu A^\mu \psi where g is the coupling constant to the Higgs field and e is the coupling...

consider a particle in one dimension. there is a dirac delta potential such as V=-a delat(x) the wave functions in two sides(left and right) are Aexp(kx) and Aexp(-kx) respectively. so the differential of the wave functions are not continious at x=0. what is the justification here?

Is this the correct form for a Dirac electron in a Higgs field with scalar potential \phi and an electromagnetic field with vector potential A_\mu i \gamma^\mu \partial_\mu \psi = g \phi \psi + e \gamma_\mu A^\mu \psi where g is the coupling constant to the Higgs field and e is the...

I was wondering which are the properties of functions defined in such a way that ∫dx f(y-x) g(x-z) = δ(y-z) where δ is Dirac delta and therefore g is a kind of inverse function of f (I see this integral as the continuous limit of the product of a matrix by its inverse, in which case the...

Homework Statement http://quantum.leeds.ac.uk/~almut/section2.pdf Please note i am referring to the above notes I basically don't get how the maths works to get (eq(25))(eq(22))(eq(24)) = eq(26) am i missing something interms of the commutator relations ? Homework Equations The Attempt at a...

Hi, How is \frac{1}{\displaystyle{\not}{P}-m+i\epsilon}-\frac{1}{\displaystyle{\not}{P}-m-i\epsilon} = \frac{2\pi}{i}(\displaystyle{\not}{P}+m)\delta(P^2-m^2) ? This is equation (4-91) of Itzykson and Zuber (page 189). I know that \frac{1}{x\mp i\epsilon} =...

I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy. I started with eigenvalue problem H|Psi> = E|psi> H = ? for state a? SO it means that indvdually H= E (|a><a|) for state a and for all three...

Dirac "bubble potential" Homework Statement Consider a radially symmetric delta potential V(r) = −Vo * δ(r − a) with l=0. How many bound states does this system admit? The Attempt at a Solution With l=0, the radial equation reduces to the one dimensional TISE. So, solving the 1D TISE with a...

In the Principles of Quantum Mechanics, Dirac derives an identity involving his delta function: xδ(x)=0. From this he concludes that if we have an equation A=B and we want to divide both sides by x, we can take care of the possibility of dividing by zero by writing A/x = B/x + Cδ(x), because...

Homework Statement We have to give the total charge, dipol and quadrupol moments of a charge constellation, but I seem to be falling at the first hurdle. Q = \frac{1}{4\pi \epsilon_{0}} \int_{vol} \rho(\vec{r}) d^{3}\vec{r} whereby the charge density of the group of particles is...

If I take a modified Dirac Eq. of the form (i\gamma^\mu \partial_\mu -M)\psi=0 where M=m+im_5 \gamma_5, and whish to square it to get a Klein-Gordon like equation would I multiply on the left with (i\gamma^\nu \partial_\nu +m+im_5\gamma_5) or (i\gamma^\nu \partial_\nu +m-im_5\gamma_5)? I was...

Homework Statement I have the state: |\psi>=cos(\theta)|0>+sin(\theta)|1> where \theta is an arbitrary real number and |\psi> is normalized. And |0> and |1> refer to the ground state and first excited state of the harmonic oscillator. Calculate the expectation value of the Hamiltonian...

I need to show that u^{+}_{r}(p)u_{s}(p)=\frac{\omega_{p}}{m}\delta_{rs} where \omega_{p}=\sqrt{\vec{p}^2+m^{2}} [itex]u_{r}(p)=\frac{\gamma^{\mu}p_{\mu}+m}{\sqrt{2m(m+\omega_{p})}}u_{r}(m{,}\vec{0})[\itex] is the plane-wave spinor for the positive-energy solution of the Dirac equation...

Hi all, I was diving into my 3rd year quantum assignment and I saw the following which I have to use for the rest of the question to prove the Cauchy-Schwarz inequality: Homework Statement || a|x> + b|y> ||^2 I only really learned a bit about Dirac notation last year, so please...

The Schrödinger wavefunction for the hydrogen atom scales as r^l for small r, where l is the orbital angular momentum. Is this changed in any dramatic way for the Dirac equation wavefuction? Does the small component of the Dirac spinor have the same small-r asymptotic behaviour as the large...

From dirac, if A=B, then \frac{A}{x}=\frac{B}{x}+c\delta(x) (1) How this formula is derived? Since \frac{dlnx}{dx} = \frac{1}{x}-i\pi\delta(x) We can get \frac{A}{x} = A\frac{dlnx}{dx}+Ai\pi\delta(x) \frac{B}{x} = B\frac{dlnx}{dx}+Bi\pi\delta(x) So if A=B, \frac{A}{x}=\frac{B}{x}...

Homework Statement Normalised energy eigenfunction for ground state of a harmonic oscillator in one dimension is: 〈x|n〉=α^(1/2)/π^(1/4) exp(-□(1/2) α^2 x^2) n = 0 α^2=mω/h suppose now that the oscillator is prepared in the state: 〈x|ψ〉=σ^(1/2)/π^(1/4) exp(-(1/2) σ^2 x^2)...

What actually is the "Dirac Point"? I'm trying to find out what actually is the "Dirac Point"?! I've Googled it and searched around on the internet, looked through books, but haven't actually been able to find a definitive definition and explanation, just general references to it within the...

Hello! I'm trying to write an essay on RQM. The problem I have encountered is the diffrent choices of matrices for the dirac equation. The two choices that I´m mixing up in my equations are: \begin{eqnarray} \gamma^0 = \left( \begin{array}{cc} I & 0 \\ 0 & -I \end{array} \right), \quad...

Let δ(x)=∞ at x = 0, and zero elsewhere. Then δ(x)(1-exp(x)) = ? It seems the above expression is zero. But isn't it zero times infinity at x = 0?

Let u(t) = \begin{Bmatrix} 1, & t \geq 0 \\ 0, & t<0 \end{Bmatrix} and let's have a simple circuit. Solo capacitor, connected to a DC voltage U0, a switch S exists. For purposes of this problem, I can mark the voltage across the capacitor as Vc(t) Vc(t)=u(t)*U0 Current...

Homework Statement Show that \left\langlex|p|x'\right\rangle = \hbar/i \partial/\partialx \delta(x-x') 2. The attempt at a solution \left\langlex|p|x'\right\rangle = i\hbar \delta(x-x')/(x-x') = i\hbar \partial/\partialx' \delta(x-x') = \hbar/i \partial/\partialx \delta(x-x') For...

Hello, I am trying to show that: \delta(x) = \lim_{\epsilon \to 0} \frac{\sin(\frac{x}{\epsilon})}{\pi x} Is a viable representation of the dirac delta function. More specifically, it has to satisfy: \int_{-\infty}^{\infty} \delta(x) f(x) dx = f(0) I know that the integral of...

What is the experimental evidence that a wavefunction will collapse to a dirac delta function, and not something more 'smeared' out?

In the equation for determining the coefficients of eigenfunctions of a continuous spectrum operator, I have trouble understanding the origin of the Dirac delta. a_f = INTEGRAL a_g ( INTEGRAL F_f F_g ) dq dg a is the coefficient, F = F(q) is an eigenfunction. From this it is shown that...

Homework Statement I'll post it as an image since the notation will be tricky to type out. It's problem 4. http://img29.imageshack.us/img29/1228/307hw3.jpg Homework Equations Not sure this really applies hereThe Attempt at a Solution This is for a physics course but as you can see it's...

So I could swear that a few months ago, there were dozens of papers by Dirac available on archive.org -- page after page of them...but now, there's nothing -- even just a search for "dirac" turns up less than one page. Was there some kind of purge, or something like that? Or am I just crazy...

Homework Statement Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 2. The attempt at a solution f(x)=exp[abs(x)+3]*delta(x-2) f(2)=148.4 Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 = 0 [b]3. Why is the answer 0?

Hi, The typical representation of the Dirac gamma matrices are designed for the +--- metric. For example /gamma^0 = [1 & 0 \\ 0 & -1] , /gamma^i = [0 & /sigma^i \\ - /sigma^i & 0] this corresponds to the metric +--- Does anyone know a representation of the gamma matrices for -+++...

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...

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

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...

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?

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...

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...

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...

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...

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...

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

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...

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...

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 =...

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 =...