# Quantum electrodynamics

Quiz by Flo Lindenbauer, updated more than 1 year ago
 Created by Flo Lindenbauer about 2 years ago
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## Resource summary

### Question 1

Question
Given the Schrödinger equation, $$i\partial_t |\psi\rangle = H|\psi\rangle,$$ which of the following is true?
• The Schrödinger equation is a purely nonrelativistic equation, as it is not possible to find a relativistic Hamiltonian
• The Schrödinger equation can be made relativistic by chosing a relativistic Hamiltonian
• The Schrödinger equation cannot be Lorentz covariant because of its special role of time
• The Schrödinger equation requires that the time development of $$\psi$$ follows a hermitian operation

### Question 2

Question
What is the problem with the Klein-Gordon equation? Why can't we interpret it as a relativistic single particle equation?
• The probability density is not positive definite
• It is a linear equation, we wan't a nonlinear one
• The Klein-Gordon equation is not relativistic
• The Klein-Gordon equation has no real solutions

### Question 3

Question
Which relation do the Dirac $$\gamma$$-matrices satisfy?
• $$[\gamma^\mu,\gamma^\nu]=2g^{\mu\nu}$$
• $$[\gamma^\mu,\gamma^\nu]=g^{\mu\nu}$$
• $$\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}$$
• $$\{\gamma^\mu,\gamma^\nu\}=g^{\mu\nu}$$
• $$\{\gamma^\mu,\gamma^\nu\}=\delta^{\mu\nu}$$
• $$[\gamma^\mu,\gamma^\nu]=\delta^{\mu\nu}$$

### Question 4

Question
What properties do the Dirac matrices satisfy? $$\gamma^\mu=(\gamma^0,\gamma^m)=(\beta,\beta\alpha_m)$$
• $$\gamma^\mu$$ are hermitian
• $$\gamma^\mu$$ are anti-hermitian
• $$\gamma^i$$ are hermitian
• $$\gamma^i$$ are anti-hermitian
• The eigenvalues of $$\gamma^i$$ are $$\pm i$$
• The eigenvalues of $$\gamma^i$$ are $$\pm 1$$
• The eigenvalues of $$\beta$$ are 0 and 1
• The eigenvalues of $$\beta$$ are 1 and -1
• The eigenvalues of $$\beta$$ are 1

### Question 5

Question
Which operation creates a particle with momentum k?
• $$a^\dagger(k)|0\rangle$$
• $$a(k)|0\rangle$$

### Question 6

Question
The quantization of the free electromagnetic field poses a problem which can be solved by adding a gauge breaking term to the Lagrangian. Which one? $$\mathcal L\to\mathcal L + G$$
• $$G=(\lambda-1)(\partial\cdot A)^2$$
• $$G=-\frac{\lambda}{2}(\partial\cdot A)^2$$
• $$G=-\lambda g^{\mu0}(\partial\cdot A)$$
• $$G=-(1-\lambda)\partial_\mu(\partial\cdot A)$$
• $$G=\langle\psi|\partial\cdot A|\psi\rangle$$

### Question 7

Question
Which field is given by this Lagrangian $$\mathcal L=(\partial_\mu \varphi^\ast)(\partial^\mu\varphi)-m^2\varphi^\ast\varphi$$?
• a free scalar field
• a fermionic field
• the photon field

### Question 8

Question
What is the canonical quantization procedure for a scalar field $$\varphi(t,\vec x)$$ with conjugate momentum $$\pi(t,\vec y)$$?
• $$[\varphi(t,\vec x),\pi(t,\vec y)]=i\delta(\vec x-\vec y)$$
• $$\{\varphi(t,\vec x),\pi(t,\vec y)\}=i\delta(\vec x-\vec y)$$
• $$[\varphi(t,\vec x),\pi(t,\vec y)]=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)$$
• $$\{\varphi(t,\vec x),\pi(t,\vec y)\}=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)$$

### Question 9

Question
What gives $$\gamma^0\gamma^\mu\gamma^0$$?
• $$\gamma^\mu$$
• $$\gamma^{\mu\dagger}$$
• $$-\gamma^\mu$$
• $$-\gamma^{\mu\dagger}$$
• $$-\gamma^{\mu T}$$
• $$\gamma^{\mu T}$$

### Question 10

Question
In order for the Dirac equation to be covariant, a spinor has to transform according to $$\psi'_\alpha(x')=S_{\alpha\beta}(L)\psi_\beta(x)$$ under a Lorentz transformation. Which relation must these matrices S satisfy?
• $$S^{-1}\gamma^\mu S={L^\mu}_\nu\gamma^\nu$$
• $$S\gamma^\mu S^{-1}={L^\mu}_\nu\gamma^\nu$$

### Question 11

Question
Choose the right name for basis elements of Dirac field bilinears: $$1$$: [blank_start]scalar[blank_end] $$\gamma^5$$: [blank_start]pseudoscalar[blank_end] $$\gamma^\mu\gamma^5$$: [blank_start]axial vector[blank_end] $$\gamma^\mu$$: [blank_start]vector[blank_end] $$\frac{i}{2}\[\gamma^\mu,\gamma^\nu]$$: tensor
• scalar
• pseudoscalar
• axial vector
• vector
• antisymmetric tensor

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