__The Quantum Field Theory of the Fundamental Interactions__

__The Quantum Field Theory of the Fundamental Interactions__

## A Theory Beyond the Standard Model

### to explain the origin of the fundamental fermions.

This theory currently being researched by Nova Software, Inc. has the goal of
explaining how all the known fundamental fermions* (and only those fermions) arise from the
three known fundamental particle interactions. The Standard Model assumes the
existence of the observed fundamental particles, and then is extremely successful
in predicting the physics that ensues. It does not, however, constrain
the Universe to that observed set of fermions and their eigenvalues.
Many others are possible within the confines
of that model.

Theories "Beyond the Standard Model" often are based on
additional interactions (forces) and/or fields (particles) beyond those currently part of it.
Some mechanism is typically included to explain why the added
element(s) are not already readily apparent to us. That mechanism must be overcome
in experiments to confirm the "new physics." This theory
is different: It assumes that the interactions and particle spectrum are only those
already known. There is new physics waiting to be found, but not via the presently
explored types of extensions. There is
some evidence for this point of view from the fact that none of the many
experimental searches based on the ideas to date has conclusively indicated new physics
beyond the standard model.
A lesson from history may be the unsuccessful search for the Ether, Newton's absolute frame,
for many years. The answer to today's conundrum may likewise come from changes to
one or more fundamental hypotheses.

In that spirit this
theory goes beyond the Standard Model in a different direction by postulating a
revised form of quantum field theory. It adds a hypothesis that enhances the role of the internal symmetry group smooth manifolds and their U(1) X SU(2) X SU(3) product to the foundations of space-time. The observed sets of the
fundamental fermions* and bosons** emerge as derived objects in a natural way
from these hypotheses and their mathematical consequences. Those results then help
to insure that the theory will be able to match the Standard Model's successes
while providing a deeper understanding of
how it arises and give possibly new, heretofore unsuspected, testable results.

In its current form, in addition to QFT and the Standard Model, the Interaction Theory draws most heavily on results from the theories of topological groups and manifolds, homotopy theory, Lie groups and Lie algebras and differentiable manifolds. When complete the theory will be posted on a public pre-print server, published in an established physics theory journal, and made available by free download here to enable and encourage other researchers to further investigate its potential.

- The pattern of the fundamental particle quantum numbers is somewhat intricate and subtle,
with some
irregularities which may not appear in simplified presentations of its structure.
It is the complete pattern, given here, that Interaction Theory
takes as its goal to derive and explain.
- *
There are 12 distinct fermions (fields) based on mass alone. When their quantum numbers are taken into account there are 24 fundamental fermions with the 12 distinct masses. These 24 consist of 8 different sets of various strong, E&M, weak and global quantum numbers. These 8 sets are then replicated twice more at higher masses, for some as yet unknown reason outside the Standard Model. These three otherwise identical mass levels, the generations or families of the fundamental fermions and anti-fermions, may be assigned additional pairs of generation "quantum numbers", such as +-1, +-2, +-3, to distinguish them. The ordinary matter in the Universe consists entirely of generation +1 fermions, without anti-fermions. This absence of anti-fermions is also unexplained in the Standard Model, which is nearly symmetric between the two types of fermions, and thus favors an approximately equal distribution of the two.__Fermions:__

Chirality is a binary property that can only be defined for fermions and anti-fermions. It is closely related to the field's behavior under transformations between right and left handed coordinate systems, i.e. to parity changes. It is not even an approximately conserved quantum number for Standard Model fermions with mass, but is nonetheless crucial for understanding the weak interaction. It splits the 24 fermion fields into 48 left and right chirality fields that must be considered when specifying which field particpates in which interaction, and into 96 fields when fermion--anti-fermion duality is accounted for. The left-chirality fermion fields and right-chirality anti-fermions are the only ones participating in the weak interaction. That then results in 36 (quarks) of those 96 chiral fermions and anti-fermions responding to all three interactions, while 42 respond to two interactions (36 quarks to strong + EM, & 6 charged leptons to weak + EM ), 12 respond to only one (left-chirality neutrinos and right-chirality anti-neutrinos only to the weak interaction; right-chirality charged leptons and left-chirality charged anti-leptons only to the EM interaction), and 6 have no known interaction at all (Right-chirality neutrinos and left-chirality anti-neutrinos). These 6 might be considered artifacts only needed to balance the theoretical books of the Standard Model, without physical significance, as their existence has never been confirmed. Their gravitational interaction, if they were to have a typical mass, would be far too weak to detect. Gravity is approximately 10^-32 weaker than the weak interaction. Results from neutrino oscillation experiments do imply however, that an originally left-chiral neutrino in flight will eventually become right-chiral for a while, and then transition back to left again, and so on indefinitely. It will only interact with other matter from the left-chiral state.

The 100% chiral selectivity of the weak interaction causes it to not conserve parity 100%. Some unknown aspect of the weak interaction causes it to also violate CP conservation at the ~4% level in certain higher generation processes. This result is embodied in the CKM matrix supplement to the Standard Model. Both fermion and anti-fermion chiralities participate in the strong and EM interactions equally, so these two interactions exhibit no chiral, no parity, preference. The Standard Model also allows for the strong interaction to violate CP conservation up to 100%, but it does no do so. Attempts to remedy this disagreement have not been successful. It remains an open question, unresolved within the the Standard Model. CPT is conserved by all the interactions, universally.

Fermions have spin 1/2, anti-fermions spin -1/2. All have a non-zero mass. These mass values cover a wide range of 1:10^10 or greater. A particle and its anti-particle have the same mass including sign: Gravity does not distinguish between the two types. Charged lepton generation masses approximately satisfy the empirical Koide mass formula. Quark generation masses depart from it significantly. Neutrino mass measuremens have only established upper limits to date and are continuing. Their status is summarized in the PMNS mass matrix adjuct to the Standard Model. The Standard Model extension of the see-saw model of neutrino oscillations is also treated here as part of the Standard Model. - **
There are 4 fundamental vector bosons (spin 1) for the three interactions based on mass alone. When their quantum numbers are taken into account there are 12. 8 vector bosons (gluons) mediate the strong interaction, 1 (photon) mediates the electromagnetic interaction, and 3 (W+- and Z0) mediate the weak interactions of the left-chiral fermions and right-chiral anti-fermions. The W- and W+ are each other's anti-particle. The Z0 boson, having all zero quantum numbers, is its own anti-particle The gluons and photons are self-conjugate, their own anti-particles too, and mediate their interactions for both fermions and anti-fermions, of both chiralities. In addition the charged weak vector bosons, W- and W+, participate in the electromagnetic interaction by virtue of their electric charges, although they are not its primary carriers, uniquely among the vector bosons.__Bosons:__

The other fundamental boson is the scalar Higgs boson (spin 0) which does not mediate any interaction and is of a vastly different character than the vector bosons of the interactions. The Higgs we observe today might be called the reduced Higgs, without any charge or other quantum numbers, and thus its own anti-particle. It's a single particle remnant of the expanded Higgs particle, a weak isospin doublet and anti-doublet that existed only in the ultra-high energy fundamental particle plasma of the first moments of the Universe. In those moments only the Higgses had rest mass. All the other fundamental particles were massless according to the Standard Model. By means of a quasi-phase transition in that plasma (spontaneous symmetry breaking) and by direct contact (Yukawa interactions) the Higgs' kinetic energies were gradually transferred into the rest masses of the other fermions and bosons with which they interacted. Within a short time the average energy of the Higgs field fell to the current value (246 Gev) and stablilized there. Only the reduced Higgs remained after that phase transition. The expanded Higgs carried weak isospin, weak hypercharge, and integer or zero electric charge. All the Higgs fields are unique among the fundamental particles in having a substantial non-zero average value (energy) throughout the Universe in a form that makes possible the spontaneous symmetry breaking. The gluon field do not have any weak chiral interaction nor weak hypercharge, so could not interact directly with the expanded Higgs field. The photon field likewise has neither interaction, but only arose as a consequence of the Higgs-induced phase transition. Consequently neither particle acquired mass from the expanded Higgs and both travel at the speed of light. - Many other fundamental particles with a wide variety of properties have been proposed and are being actively searched for. The above are the only ones unequivocally confirmed by the Particle Data Group thus far and thus the only subjects for the Standard Model and Interaction theory.

** Summmary for a general audience:** The current physics theory of the
known fundamental particles, the Standard Model, explains extremely well
how they interact via their strong, electromagnetic and weak interactions and
the Higgs field.
It does not, however,
explain how the particular combination of observed fundamental particles
and the pattern of their
interactions, and only that combination and pattern, occurs. These facts are
inserted into the theory "by hand" from what we see, rather than being derived
from fundamental hypotheses.
The Quantum Field Theory of the Fundamental Interactions is being researched at Nova
Software, Inc., to address this question, to see if there is a
theory that can
successfully explain those facts in more fundamental terms. If successful
the theory
will be made available in the usual physics locations for such work, and at this site
in the hope that others will find it a worthwhile subject for further study.