Scientific Community and Remaining Errors, Physics Examples

The scientific community controls the possible errors by a rigorous process using referees. Consequently the only possible errors are very few, they come from what anyone considers obviously true. Three of these errors are pointed here: the main one is the belief that any quantum state follows a Schrodinger equation. This induces two secondary errors: the impossibility of magnetic charges and the identification between the Lorentz group and SL (2, C).


The Universality of the Schrödinger Equation
Even if Erwin Schrödinger was a physicist working on General Relativity, even if Louis de Broglie introduced his wave for the movement of any particle from relativistic considerations [1], the belief that any quantum state follows a Schrödinger equation is now the basis of the axiomatic quantum theory. The first reason is the fact that the Schrödinger equation was the first one: where H is the Hamiltonian operator. For a single electron this operator reads: where V is the exterior electric potential and ( ) where A µ is the covariant components of the electromagnetic potential spacetime vector. This wave equation was relativistic, it was the awaited wave equation: de Broglie studied all aspects and results of this equation [3]. For high energies, the µ γ matrices are currently chosen as following: ; where ξ is named the right wave and η is named the left wave. With: and with: we get the Dirac equation in

The Impossibility of Magnetic Monopoles
This impossibility is one of the false ideas coming from the previous false postulate. If any quantum state has value into the complex field and follows a Schrödinger equation, then there is only one possible phase to the wave. This phase is the electric gauge, its conservation gives the charge of the particle. There is no place for another phase.
If you disagree with this false postulate you will be able to read the Dirac wave as a function of space and time with value in the Clifford algebra of space. This algebra is non commutative, then several different phases are available. This is the starting point of the Lochak's theory of the leptonic monopole [4]- [9]. There is, aside the i of the electric phase, another object with square −1, the , allowing another gauge that Lochak associates to a magnetic monopole. Actually the 3 Cl algebra contains not only 2 but 4 different and independent i, each giving a particular gauge: .
The Lie algebra generated by these four elements is exactly the Lie algebra of the ( ) ( ) Lie group. This group is the gauge group of the electro-weak Weinberg-Salam model [10]. Then the chiral gauge ( )

The Confusion between Different Lie Group
The main success of the non-relativistic quantum mechanics was the explanation group of rotations around a fixed center. The theory is well understood: if a physical system has a quantum state ψ and if this system is transformed, for instance if we rotate the physical system by a rotation R, the quantum state becomes ( ) The T transformation is linear, since the wave equation is a linear one. Then the f defined by: is an homomorphism from the group ( ) The theory of homomorphisms of Lie group classifies all possible representations, using the properties of the Lie algebras of these Lie groups [28]. In the case of ( ) The true number awaited is x The next oddity is: Then the square of the pseudo-norm of any space-time vector is the determinant of this vector. Let M be any non null element in 3 Cl and let R be the transformation from space-time into itself that associates to any x the space- This gives: So R multiplies by r any space-time distance and we name R a Lorentz dilation with ratio r. Moreover with . = ν µ ν µ x R x′ (21) we get for any And R is a Lorentz transformation belonging to the restricted Lorentz group made of the transformations conserving the orientation of space and time. The Dirac wave satisfies: And we also get, with † M M = : ; .
Since the conjugation M M  is the main automorphism of 3 Cl the group of the N is isomorphic to the group of the M. Next for any M satisfying (20), (21), (23) and (25) We also have and so we get: which allows us to write So the Dirac theory supposes: we can easily see that it is equivalent to (25) and we get Then we must say that, even in the first form of the Dirac theory, the Dirac

Concluding Remarks
The link between the main error in section 1 and the last one is the abuse of methods of approximations in quantum mechanics. The first study of the relativistic invariance of the Dirac equation used infinitesimal operators next the exponentiation of these operators. On the contrary we used here exact and general calculations completely without the ≈ symbol.
The false postulate of the universality of the Schrödinger wave also induced the idea that any true physical formalism was necessary based on the complex field. If you look at the Dirac equation all seem actually based on the complex field. But this is mainly an accident, a coincidence between the Clifford algebra 3 Cl of the real space with dimension 2 3 on  and the complex space of the 2 2 × matrices with dimension 4 on the  field, which is then also an algebra on the real field with dimension 8. This isomorphism is not an isomorphism of complex algebras, only of real algebras. The generator of the electric gauge for the Dirac Equation (8)  quantum physics is totally incredible for any believer of the axiomatic quantum theory [32].