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We compute in a theoretical quantum field theory framework the effects that a classic environment will have on an elementary one-fermion state, assumed for simplicity to be that of one electron, in the presence of a magnetic field. We consider its total energy and its spin angular momentum as relevant observables of the state. We show that the changes of these quantities produced by the combined environmental and magnetic effects can be expressed in a simple and compact form. We obtain expressions that only depend on the values of the external environment and magnetic fields, and on the special spin features of the free fermion state. We call these effects “fermion epigenetics” and try to motivate this definition discussing possible relevant analogies with the corresponding medical treatment of epigenetics in organic cells.

The process of organic epigenetics is nowadays considered as a fundamental reaction for the possible positive consequence that it might generate on human health. In particular, a great amount of interest has been raised by the study of the effects that a weak magnetic field might have on the organic cell [1-3]. To completely define these effects, a reliable knowledge of the surrounding environment is also requested, and a detailed discussion is available in the medical literature [

From the point of view of physics, a fascinating possibility exists which would be summarized in the statement [

“The evolution of living systems is a continuation of that of the physical world.”

Accepting this statement, we have devoted a very recent paper [

The aim of this paper is to consider the extra effects that would be produced by the presence of a surrounding environment, and by its modification of the “pure magnetic” effects considered in [

To pursue our investigation, we shall begin by writing the expressions of the total energy and of the components of the spin angular momentum

Equations (1.1), (1.22), (1.3) and (1.4) can be re-written in a way that will be more useful for the continuation of this paper. We will define a “spin current” density

Thus, the general expression of the spin vector

In our previous analysis, we have not concentrated on other properties of the chosen fermion state. For the purposes of this paper, we shall consider another feature of the system called “axial charge”,

where

In terms of the four psinon fields, one easily derives that

Quite generally, one can provide a physical meaning to the axial charge

The two currents

In this paper we want to consider the effects that would be produced on the previous free quantities by the simultaneous presence of a magnetic field and of some environment sourcing a classical electric field

Here, we shall consider the simplest case of a timeindependent field. This means that one can properly derive the electric field as the gradient of a static Coulomb potential,

The same equations give a classic magnetic field

In conclusion, we shall treat a process in which the electron state is surrounded by a classic electric field, derived by a Coulomb potential

where

We are now ready to derive the changes of the considered free variables. This can be done by replacing in the relevant expressions the free psinons with the corrected ones, rewriting systematically

where,

A last, but important, detail of our calculation is that we are going to consider only the combined effects of the mutual interaction between the environment and the magnetic field. In this spirit, we shall extract from all possible interaction terms among

To derive the effects of the combined interaction, which we indicate again with the

Euqations (1.21), (1.22) are the main result of this paper, and we shall spend a few final words to remark those features that appear to us particularly impressive. In particular:

1) In Euqation (1.21), the overall change is given by scalar products, where the free electron spin current is one of the components. The second component is given by the magnetic and electric fields and potentials. In other words, the overall effect for a given environment and magnetic field is determined by the spin density of the free electron.

2) In Equation (1.21), two terms appear. One of them, where the scalar product

where

that can be interpreted as a correction to the value

We will define this term as the

3) The spin changes are represented by an expression that depends on the product of the electric and magnetic potential and on the value of the axial current

The main conclusion which could be drawn from our analysis is that all the considered changes of elementary matter components under the combined effect of a surrounding environment and of a magnetic field only depend on the spin properties of the free state (and on the intensity of the electric and magnetic fields). This conclusion is valid in the theoretical framework of quantum field that we adopted under the general and universal assumptions which are nowadays accepted.

In our search of analogies with the fascinating medical treatment of the epigenetic process, we would still propose the correspondence between 1) the electron energy and the space dependent properties of nucleus epigenome; 2) the electron intrinsic and space independent spin and the nucleus DNA.

Accepting our very personal proposal might lead to some more realistic check of its general properties in a proper medical experiment. A possibility that appears to us to be reasonably realistic is the following one. Looking at the Equation (1.21), we see that the “new” term (not of

A last possibility to be considered, in our opinion, is the following one. If the magnetic field is sufficiently weak, more precise and much weaker than the electric field, its contribution to the overall effect might be negligibly small. In this case, the “new” term

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