**Fundamental
Interactions in New Physical Perspective (FINePP)**

(Invariance in the Presence of Kintetic Gauge Fields)

Motto:

The physicist Leo Szilard once announced to his friend Hans Bethe that he was thinking of keeping a diary:

“ I don't intend to publish. I am merely going to record the facts for the information of God.”

“ Don't you think God knows the facts?” - Bethe asked.

“ Yes,” said Szilard,

“ He knows the facts, but He does not knowthis version of the facts.”

**Introductory lectures**

*1. Conservation laws – invariances – symmetries.*

A simple question that you wanted, but have missed
to put: Why do we need to derive the conservation of the electric charge
from the gauge invariance of
the EM interaction, while we had derived it from the classical Maxwell equations?

What does Noether’s 2nd theorem tell to field theories?

What is the relation between invariance principles and symmetries?

Classification of invariances – half century after Wigner.

Why are conservation laws considered to be symmetries?

Are there physical symmetries, which do not express conservation?

*2. Relativity theories as invariance principles. *

Invariances in different reference frames.

Aren’t there preferred (distinct) reference frames? Is conservation invariant
under change of reference frame?

Similarities of, and differences between electricity and gravitation.

Field charges and their conservation.

The role of transformation groups to describe invariances.

*3. Equivalence principles.*

A philosophical consideration: Equivalence is not identity.

Physical examples for the distinction between identity and equivalence.

The identity-equivalence problem on the example of the isotopic spin.

What does it mean for physics that equivalence does not mean identity?

The equivalence principle. The equivalence of the masses of gravity and inertia.

Distinction between isotopes of field charges (on the example of masses of
gravity and inertia).

Conservation of which mass?

(*Textbook, Sections I.1-2*)

**Special considerations**

*4. Velocity dependent phenomena.*

Examples. Field
charges and isotopic field
charges.*
*Lorentz force. Lorentz transformation.

Equivalence principle for electric charges.

Preliminary consequences of distinction between isotopic field charges of the electromagnetic field.

(

*5. A look at the history of interaction theories.*

Structure of Hamiltonians. Velocity dependence of the
kinetic part of the Hamiltonian.

A short adventure in the history of QED (1928-1932):

Perturbation strategies.

Interaction models by Dirac, Fermi, Breit vs. Møller, and their interpretation
by Bethe and Fermi.

Asymmetry in the scattering matrix? Difference in the roles of two interacting
particles? What is behind, what is the property in which they may differ?

(*Textbook, Sections II.7, III.1* )

*6. Examples for the distinction between isotopic
field charges.*

Writing isotopic field charges in the formulas of physical
quantities and equations.

Isotopic field charges destroy the symmetry and invariance properties
of field tensors: Loss of Lorentz invariance? How to restore it?

What do we insist on: The absolute role of Lorentz transformation, or invariance
of our equations and physical laws under a transformation?

Replace or extend our existing theories? Search for a combined transformation,
which extends the standard body of physics.

Can isotopes of field charges interact with each other?

The isotopic field charge spin assumption.

(*Textbook, Sections III.4-6*)

**Interaction models**

*7. Possible models of interaction between field
charges and between isotopic
field charges.*

Single particle’s isotopic field charge states:

Probabilistic model;

Harmonic oscillator model;

Flip-flop model;

Intermediate particle model.

Discussion of the possible intermediate model of interaction between two particles.

(*Textbook, Sections III.2-3*)

*8. Evidences for the two kinds of isotopic field
charges.*

The Dirac equation for QED and the Einstein equation
for gravity in the presence of isotopic field charges.

Once again on the assumption of the existence of isotopic field charges:
classical evidences based on the examples of physical forces.

Discussion of conservation laws in different source interaction fields
(gravitational, electroweak, strong).

Historical references to the formation of the Standard Model.

(*Textbook, Sections III.4-7*)

**Proof of an interaction model in a velocity
dependent perspective**

*9-10. Mathematical
derivation of the isotopic field charge spin conservation*

Prehistory: the example of Yang-Mills fields and derivation
of the isospin conservation.

Introduction to mathematical tools to be applied.

Why can the chosen mathematical tools describe the proposed phenomenological
model of interaction?

Assumption on the presence of a velocity dependent gauge
field.

Noether's currents for gauge invariance localised in the velocity space.

Derivation of two conserved Noether currents in a general interaction field
in the presence of a velocity dependent gauge field.

(*Textbook, Sections IV.1-2.1*)

*11. Discussion of the mathematical results.
Discussion of the physical considerations. Conservation of the Isotopic
Field
Charge Spin.*

Two conserved physical quantities.

First conserved quantity: Conservation of the field charge.

Second conserved quantity: Conservation of the isotopic field charge spin.

Coupling of the two conserved quantities.

(*Textbook, Sections IV.2.2-3.3*)

**Mechanism of physical interactions in the
presence of a velocity dependent gauge field**

*12. Mediating gauge bosons.*

Physical
interpretation
of the isotopic field charge spin conservation.

The lost invariance has been restored.

The derived conservation law involves the existence of gauge quanta
associated with the conserved quantity (which carry the isotopic
field charge spin):

Prediction of the gauge quanta of the isotopic field charge field.

(*Textbook, Sections IV. 3.4-3.5*)

*13. Mechanism of the interaction
between isotopic field charges and the isotopic field charge spin.*

Mechanism
of the isotopic
field charge spin interaction.

Feynman diagrams. Exchange of two bosons?

Physical consequences of the discussed possible mechanism.

Isotopic field charges assign fermionic twin brothers to each
fermionic field charge; the conservation of the isotopic field
charge spin
assigns a bosonic
twin brother to each intermediate boson (of the Standard Model). Comparison
of SUSY and IFCS models.

The isotopic field charge spin conservation involves a mechanism
that may extend the Standard Model in the presence of the assumed
velocity
dependent
gauge
field.

Ten consequences of the model.

(*Textbook, Sections IV. 4, and V*)

*14. Application of the obtained
results in physical situations*.

Valence electrons in chemical
bounds and phase
transitions.

Extra boson exchange in interactions between fermions.

Velocity dependent Finsler geometry in gravitational field
and its curvature tensor.

Additional terms in the gravitational equation; modification
of the Schwarzschild solution and consequently, e.g., the
rotation angle
of the Mercury perihelion.

**Textbook**: G. Darvas (2012) *Another
Version of Facts. On Physical
Interactions,* 134 p.

Proposed reading:

http://arxiv.org/abs/0811.3189v1

http://www.springerlink.com/content/g28q43v2112721r1/

**______________________________
**

**INTRODUCTION to the Textbook**

This book treats fundamental physical interactions starting from two preliminary assumptions.

(a) Although mass of gravity and mass of inertia are equivalent quantities
in their measured values, they are qualitatively not identical physical entities.
We will take into consideration this difference in our equations.

Later we will extend this ‘equivalence is not identity’ principle
to sources of further fundamental interaction fields, other than gravity.

(b) Physical interactions occur between these qualitatively different entities.

These two assumptions do not contradict to any known physical theory, however, they allow another interpretation of facts built in our explanations of physical experience.

First we interpret the mentioned preliminary assumptions. Then we will sketch in main lines a picture of fundamental physical fields influenced by the distinction between the two qualitative forms of the individual field-charges and interaction between them. A next part will demonstrate the existence of an invariance between the two isotopic forms of the field charges, and will formulate certain consequences in our view on the physical structure of matter. Finally we will discuss how can these results potentially change our approach to a few open questions of physics, including the effects of a family of intermediate bosons to be predicted by the proven invariance between the assumed isotopic states of the individual field charges.

The proposed conceptual framework and assumption on the interaction mechanism goes beyond the Standard Model (SM). Many physicists are convinced that SM does not hold eternally alone and is not untranscendable; there will appear new, more precise theories that will partially include the SM, and answer those questions that are left open by the SM. However we do not certainly know how, at least at present.

CERN organised three workshops to discuss possible theoretical candidate models beyond the SM to base a “new physics” in accordance with fine scale anomalies and symmetry breakings in high energy experiments, in 2005-2007 (CERN workshop, 2008a; CERN workshop, 2008b; CERN workshop, 2008c). They agreed that SM holds, it needs only some extensions. So do we as well. Section IV of the present work provides an alternative extension theory, still not discussed in those three working group reports.

This work (started in January 2001) is an attempt to exceed a couple of the limits of the Standard Model. Gerard ‘t Hooft expressed his view on the physics after the SM: “What is generally expected is either a new symmetry principle or possibly a new regime with an altogether different set of physical fields.” ( See in: Hooft, 2005, Sec. 12). The isotopic field charge spin conservation and the D field, being introduced in this book, are candidates (Darvas, 2011).

The presented idea is based on the same facts like those considered in the SM, only on “another version” of them. It clusters the observations in another way. Unlike existing alternative theories, e.g., the SUSY, which renders a new (“supersymmetric”) brother to each particle, this model clusters the observed sources of fields in two-eggs twin pairs, regarding them as isotopic states of each other, and there is left “only” the twin brothers of the bosons mediating their interactions to be observed. It covers gravitational, electroweak and strong interactions. In contrast to the SUSY, which renders fermion-boson pairs as new-born brothers to each other, the Isotopic Field Charge Spin (IFCS) assumption, proposed in the present work, renders fermion-fermion and boson-boson twins to each other.

This assumption does not assume new fermions; the twin brothers of fermions originate in splitting the existing ones. Fermions split as a result of a newly interpreted property. The assumption is mathematically based (Darvas, 2009) on an invariance of interactions under rotation of the isotopic field charges’ spin (a property that distinguishes the field charge twins from each other) in a still hypothetical gauge field, that means, on the conservation of the isotopic field charge spin.

The bosonic twin brothers should appear as the quanta of the D field (cf., Section IV.3.2) that mediate between the split fermion states, that means, between isotopic states of field charges. The prediction of bosonic twin brothers will be discussed in Section IV.3.5.

The IFCS assumption theory does not give a clue to everything, (e.g., mass). It is a modest attempt to answer a few open questions of contemporary physics (Darvas, 2011).

Section I provides a conceptual introduction to the theme, Section II treats
the introduced concepts in classical approaches and conjectures interaction
between isotopic states of field charges, while the next one (III) discusses
historical roots of the topic and their approaches from classical through quantum
physics to field theories. Appearance of two different variants of the individual
field charges in our physical equations would cause so far not experienced
distortion in symmetries, unless another invariance does not counterbalance
the apparently lost symmetries in our laws of nature. Section IV demonstrates
the existence of this invariance, presents its exact mathematical proof and
the physical consequences in field theory, then Section V derives conclusions.