QuantumPhysics.dvi

20.3 Application to the decay rate of 2p state of atomic Hydrogen The simplest application of the above general formulation of s ...

spectrum of visible light) inside the cavity depends on the temperature. We know from experience with ovens and flames that at m ...

and we find the following formulas for respectively absorption and emission, 〈nα(k)− 1 ,α,k|A(t,x)|nα(k),α,k〉 = (nα(k)) 1 (^2) ε ...

This is clearly a very powerful relation, because it impliesthat the details of the absorption and emission process, encoded in ...

After some simplifications, the internal energy density perunit frequency is given by U(ω) = 8 π ̄h c^3 ( ω 2 π ) 3 1 e ̄hω/(kBT ...

21 Relativistic Field Equations In the preceding chapters matter, such as electrons and nuclei, was treated as non-relativistic ...

s^2 <0, the events are causally related by the propagation of particles of any mass; one may viewτ, defined byτ^2 =−s^2 /c^2 ...

From this it is clear thatβcmust be interpreted as the relative velocity between the twoframes. Indeed, the pointx′= 0, which is ...

In passing from the second to the third line, we have relabeled the summation indices so that as to expose the combinationxμxνin ...

21.3.2 Covariant tensors Every contravariant vector and tensor naturally has an associatedcovariant vectoror tensor of the same ...

21.3.3 Contraction and trace Two vectorsAμ,Bμmay becontractedto form their Minkowski inner product, A·B≡ημνAμBν=AμBμ=AμBμ (21.28 ...

The transformation under rotations is standard, sincepis a vector, whileEis rotation-invariant. Under a boost in the 1-direction ...

Here,pis the momentum of the incoming particle, which is related tothe energy byE^2 =p^2 c^2 + m^2 c^4. Eliminatingp^2 between t ...

is obtained by including amass term, ( ̄h^2 ∂μ∂μ−m^2 c^2 ) φ(x) = 0 (21.44) This equation for a massive scalar field may be solv ...

for any scalar functionθ. The electric and magnetic fields are first order time and space-dervatives of the electric potential a ...

since the derivative∂ρ∂μAνis symmetric inρ,μ, while theεμνρσis antisymmetric in all its indices, and may be normalized toε^0123 ...

A variationδAμofAμthen yields the following variation of the action, δS[A] = ∫ d^4 x ( − 1 2 FμνδFμν+δAμjμ ) = ∫ d^4 x(Fμν∂νδAμ+ ...

Next, we determine the structure relations of the Lorentz algebra. To this end, we consider an arbitrary representationD(Λ) of t ...

coordinates of space-time, but usually, we may ultimately restrict to its real subalgebra when needed. The relevant linear compl ...

result of the complexification, the finite-dimensional representations we will obtain this way may not be unitary. The finite-di ...