By Alexander Kuznetsov, Nickolay Mikheev

This booklet explores the intersection of particle physics, astrophysics, and cosmology referred to as astroparticle physics. severe electromagnetic stipulations found in puslars and different stars enable for investigations of the function of quantum techniques within the dynamics of astrophysical gadgets and within the early Universe. dependent partially at the authors' personal paintings, this booklet systematically describes a number of tools of calculation of the consequences of sturdy electromagnetic fields in quantum strategies utilizing analytical suggestions of the Dirac equation and Feynmann diagrams at either the loop and tree degrees. the distinction is emphasised on the restricting instances: the case of a really robust magnetic box, and the case of a crossed box. The presentation will entice graduate scholars of theoretical physics with earlier realizing of Quantum box idea (QFT) and the traditional version of Electroweak Interactions, in addition to experts in QFT wishing to grasp extra concerning the difficulties of quantum phenomena in exterior electomagnetic fields.

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3) are ε(O) = α (qϕ)α , 2 q⊥ ε(E) = α (q ϕ) ˜α q2 . 9) Substituting the polarization vector of the O-mode photon, one obtains Tr[ρ(p )ˆ ε(O) ρ(−p)ˆ ε(O) ] = 0. By this means the O-mode photon cannot decay into the electron–positron pair with both electron and positron being produced in the ground Landau level. Performing the similar calculation for the E-mode photon one obtains Tr[ρ(p )ˆ ε(E) ρ(−p)ˆ ε(E) ] = 4m2 . The resulting S matrix element squared for the decay of the E-mode photon takes the form e2 (2π)3 m2 T 3 |Sif |2 = δ (.

If, in addition, the current jV appears to be the photon polarization vector, the tensor fαβ has the meaning of the strength tensor of the photon electromagnetic field. 16) ∞ dt e−iΩ , du 0 1 − cos βt cos βtu −iΩ . 17) 0 where (f ϕ) = fαβ ϕβα , (f ϕ) ˜ = fαβ ϕ˜βα . 1 The Amplitude j → f f¯ → j in a Magnetic Field (2) u sin βtu q2 1 − u2 cos βt − ⊥ cos βtu − 2 2 tan βt 2 u sin βtu q cos βtu − , = 2 tan βt = qα jV β − qβ jV α , fαβ = qα jV β − qβ jV α . 19) mf jP 4π 2 1 ∞ du 0 0 βt dt (jA ϕϕq)(cos βtu − cos βt) t sin βt − (jA q) cos βt e−iΩ + (jA q)e−iΩ0 .

52) Substituting the matrix element, one should take into account, that, as usual, δ 2 (Q⊥ = 0) = Ly Lz , (2π)2 δ(kQ = 0) = T , 2πk0 where Lx , Ly , Lz are the typical scales along the axes OX, OY , and OZ, and T is the total interaction time. Integration over the positron momenta with the δ functions yields d3 p 2 κ δ (Q⊥ )δ(kQ){. } = 2 {p → q − p − sk; χ2 → χ − χ1 }. E m χ2 For the integration over the electron momenta it is convenient to insert the variables τ and u as follows τ= e(q F˜ p) , m4 χ u=1−2 χ1 = 1−u χ, 2 χ2 = χ1 .

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