QED propagators of virtual particles are unreal, based on wrong math trick.

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QED is wrong.
Quantum field theory

All QED calculations such as anomalous magnetic moment rely on unphysical propagators based on wrong math trick that diverge to infinities, invalidating QED.

(Fig.1)  Virtual electron (= fermion ) propagator used in QED is just an unphysical math irrelevant to the real phenomena or real particles.

QED propagators lack real particle picture.

All QED calculations use the unphysical equations called propagators allegedly representing virtual electrons (= fermions ) and photons violating Einstein relativity ( this-middle ) and diverging to meaningless infinities.

Fig.1 shows the fermion propagator consisting of two unphysical Dirac wavefunctions ( this-p.2,  this-p.4 ) expressing (virtual) electrons and photons just as nonphysical math symbols (= c, c^† d,.. ) with No real particle shape.

The p² shows Einstein relativistic energy relation (= this page uses -1,+1,+1,+1 version of notation, and approximately, c = ℏ = 1 ) where p⁰ = E = -p₀ is relativistic energy, p^j = p_j ( j = 1, 2, 3 ) is relativistic momentum ( this-p.11 ).

This fermion propagator containing virtual electrons is expressed as two Dirac spinors ψ(x)bar-ψ(x') when the time t > t' (= x⁰ > x'⁰ ) or -bar-ψ(x')ψ(x) when t' > t.

(Fig.2)  Artificial change of fermion propagator utilizing unphysical infinities.

QED propagators rely on unrealistic integration of infinite virtual particles' energy.

The unphysical fermion propagator Fig.1 can be changed into equations surrounded by the square of Fig.2 using Cauchy integration residue theorem and ±∞ infinities (of illusory virtual particles' energy ).

In the case of ① x⁰ > x'⁰ (= or t > t' ) of Fig.2, when p⁰ → -i∞, the exponential function e^{-ip0(x - x' )} becomes zero (and the upper integrated numbers become zero also in p⁰ → ±∞ ). which means the upper integration becomes equal to Cauchy clockwise integration (= real number integration from -∞ to +∞ and the integration from +∞ back to -∞ through imaginary number part of -i∞ ) around the solution of p⁰ = square root of p²_j + m² - iε (= ε is a very small positive number close to zero ).

In the case of ② x⁰ < x'⁰ (= or t < t' ) of Fig.2. when p⁰ → i∞, the exponential function becomes zero, which means the upper integration becomes equal to Cauchy counter-clockwise integration around p⁰ = -square root of p²_j + m² +iε where the momentums of  p_j ( j = 1, 2, 3 ) are also changed into -p_j.

See this-p.8-p.14,  this-p.2-5,  this-p.3,  this.

(Fig.3)  Cauchy formula from -∞ to +∞ applied to unphysical electron propagator.

In Cauchy integral formula, when the integration surrounds some complex value (= in Fig.3, p⁰ = E-iε  ε → +0 ), this (complex) value can be inserted into other function like f(p⁰) → f(E).

The sign of the counter-clockwise (or clockwise ) Cauchy integration is plus (or minus ).

In the upper Fig.3, the integral from -∞ to +∞ can be interpreted as the sum of integral of the real numbers of p⁰ from -∞ to +∞ and the integral of complex numbers of p⁰ from +∞ → -i∞ → -∞

↑ This equation is valid only when the integrated values become zero in p⁰ → ±∞ or p⁰ → -i∞ (= corresponding to the case of x⁰ - x'⁰ > 0  ← e^{-ip0( x0 - x'0 )} → 0 when p⁰ → -i∞ ).

See this-p.8-p.9,  this-p.19-p.22

(Fig.4)  Unphysical QED propagators lack real particle picture.

Using the unphysical Dirac electron-antiparticle wavefunctions, The first part (= ψ-bar-ψ ) of the fermion propagator of Fig.1 becomes like Fig.4

They use the artificial wrong 4 × 4 matrix expression consisting of u (= 4×1 matrix, this-p.10 )-bar-u (= 1×4 matrix called adjoint ), which cannot become the normal number.

(Fig.5)  ↓ Unreal wrong matrix is used in QED propagator.

As shown in the upper Fig.5. QED fermion propagators rely on the unrealistic wrong 4×4 matrix (= called projection operator,  this-p.26,  this-p.24-lower ) consisting of u (= 4× matrix) and bar-u (= 1×4 matrix ), which is Not a normal matrix calculation nor becoming a normal number.

This artificial wrong matrix of 4×1 matrix + 1×4 matrix = 4×4 matrix is also one of QED illegitimate math tricks.

(Fig.6)  Fermion propagators are wrong, based on inconsistent rules.

QED propagator illegitimately changes the rule, so invalid.

When inserting Dirac wavefunctions into the latter part of fermion propagator (= -bar-ψψ,  this-p.13-(7.81),  this-p.4-4.25 ), we originally obtain bar-v (= 1×4 matrix )-v (= 4×1 matrix) which is just the normal number ( this-p.24-(10.169),  this-p.4-(7.22),  this-p.10-(5.34) ), unlike u-bar-u case.

But QED illogically changes this original bar-v v (= number ) into v-bar-v (= wrong artificial 4×4 matrix, like u-bar-u ) to artificially obtain the fermion propagator for QED calculation ( this-p.12 ).

This illogical artificial change of Fig.6-lower is clearly wrong, inconsistent, invalidating all the QED calculations based on this electron (= fermion ) propagator.

This-p.27-(3.45) shows bar-ψ including bar-v, but its p.29-(3.63) illogically changes bar-ψ (= bar-v ) into ψ = v ( see also this-p.8-(5.27) and p.10-(5.34),  this-p.168-p.169,  this-p.1-lower ).

(Fig.7)  Unphysical QED virtual photons.

QED propagators need paradoxical virtual photons with unreal longitudinal polarization.

In the same way as the unphysical fermion propagator, they obtain QED photon propagators ( this-p.8-p.9,  this-p.18 this-p.5 ) which need the imaginary virtual photons with longitudinal polarization and negative probability.

As shown here, QED propagators of electrons (= fermion ) and photons rely on wrong inconsistent rules and unrealistic particles, which invalidates all the (artificial) QED calculations based on infinite virtual particles.

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