A Finite Unified Quantum Field Theory of the Elementary Particle Standard Model and Quantum Gravity Based on New Quantum Dimensions and a New Paradigm in the Calculus of Variations

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This book has a NEW EXPANDED EDITION with ISBN number: 0-9746958-3-1 entitled, "Quantum Theory of the Third Kind: A New Type of Divergence-free Quantum Field Theory Supporting a Unified Standard Model of Elementary Particles and Quantum Gravity based on a New Method in the Calculus of Variations" with important new material on the unitarity of the theory and the relativistic invariance of the theory (and some typo corrections). The reader is strongly urged to obtain the new edition from its web page!
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Product Details

  • ISBN-13: 9780972079594
  • Publisher: Pingree-Hill Publishing
  • Publication date: 5/28/2003
  • Pages: 192
  • Product dimensions: 7.48 (w) x 9.02 (h) x 0.40 (d)

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The Standard Model is a unified model of the electromagnetic, weak and strong interactions. It is formed from Electroweak Theory and an SU(3) color gauge theory of the strong interaction called Quantum Chromodynamics (QCD). Each part is separately renormalizable, as is the combined theory.  This ad hoc theory of all known interactions except gravitation has been remarkably successful in accounting for the experimental data at energies currently accessible at accelerators. There are a number of phenomena that are not understood within the framework of the Standard Model such as dark matter and dark energy, some CP violation phenomena, and the spin dependence observed in certain experiments. There is also an appreciation of the ad hoc nature of the unification of the strong and electroweak sectors. They are “just glued together”. An overall symmetry encompassing both sectors (broken as it would be) would be more reassuring and more elegant. However the theory works, and appears to work well, for most particle physics phenomena.

Superstring theory has become a seriously considered alternative to the Standard Model. It appears to offer a finite theoretical framework without divergences. It offers the hope of a rational grand unification. It is mathematically interesting and elegant. However, it has almost no experimental support. It predicts many particles that remain to be found.  It requires additional dimensions that are not evidenced. It does not have a demonstrable, satisfactory “low energy limit” that resembles the Standard Model. It has the problem of too many possibilities: after thirty years of effort one cannot point to a Superstring theory and say it is THE Superstring theory. Considering that far more theoretical effort has been expended on Superstring theory by more theorists then on any other theory of physics, its physical justification, its nature, and its contact with experiment is still not well understood.

In the hope of developing a sound theory that clearly makes contact with known experimental data, that has a direct connection to the Standard Model, that is finite (no divergences), and that can be directly extended to encompass gravitation, we have developed a two-tier formulation of the Standard Model and its variants. It is admittedly far more modest in its scope than Superstring theory. Yet it allows us to have a finite theory - a major goal of Superstring theory - and to address cosmological issues by its easy unification with two-tier quantum gravity (next chapter) - also a finite theory without divergences.

Thus we have a theory that accounts for all known interactions and yet incrementally extends known successful theories - in a significant way.  With (perhaps) the exception of General Relativity, the growth of particle physics theory in this century has been largely incremental.

The nature of the mechanism that two-tier quantum field theory uses to avoid divergences has the important feature that it does not depend on “magic cancellations”, does not depend on details of the symmetries, and does not depend on details of the form of the theories. Thus all the variations and extensions of the Standard Model have an equivalent two-tier version that is finite. This feature gives the theorist the flexibility to modify and extend the two-tier Standard Model without worrying about the introduction of new divergences.

The other major advantage is that the theory is very much like the world we see at current energies - four dimensions and no large number of new particles. It leaves open the door for new interactions and new particles IF they are found at higher energies. Thus it is not a showstopper. Nor is it a prediction of a vast desert extending to the highest energies. It gives a finite, unified theory with an “Open Door” policy for the future.
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Table of Contents

1. Some Issues Facing Elementary Particle Physics Today
Form of Physically Acceptable Theories
Standard Model
Quantization of Gravity
Correspondence Principle
String and Superstring Theories
Goal: Unified Theory Without Renormalization Issues

2. An Extension of the Calculus of Variations
A New Paradigm in the Calculus of Variations
Simple Physical Example - Strings On Springs
The Composition of Extrema - Lagrangian Formulation
The Composition of Extrema - Hamiltonian Formulation
Translational Invariance
Lorentz Invariance and Angular Momentum Conservation
Internal Symmetries
Separable Lagrangians
Separable Lagrangians and Translational Invariance
Separable Lagrangians and Angular Momentum Conservation
Separable Lagrangians and Internal Symmetries

3. Quantization of Coordinate Systems
Non-commuting Coordinates
Quantization Using C-Number Coordinates
Coordinate Quantization
Particle States
Y Fock Space Imaginary Coordinate States
Y Coherent Imaginary Coordinate States
Hamiltonian for Particle and Coordinate States
Second Quantized Coordinates

4. Scalar Two-Tier Quantum Field Theory
Two-Tier Space
Vacuum Fluctuations
The Feynman Propagator
String-like Substructure of the Theory
Charge Conjugation
Time Reversal

5. Interacting Quantum Field Theory
Y Space Quantum Dimensions
An Auxiliary Asymptotic Field
Model Lagrangian with phi4 Interaction
In-states and Out-States
S Matrix
LSZ Reduction for Scalar Fields
Coherent in and out States

6. Perturbation Theory
The U Matrix
Reduction of Time Ordered Products
The dX Integration
Coherent Y In and out states
Perturbation Expansion
General Form of Propagators

7. Two-Tier Quantum Electrodynamics
A New Quantum Electrodynamics with Non-Commuting Coordinates
The Y Field
Quantization of the Free Dirac Field
Quantization of the Electromagnetic Field
Particle Propagators
Coulomb Interaction
Asymptotic States
S Matrix
LSZ Reduction
Time Ordered Products and Perturbation Theory
Renormalization of Two-Tier QED
Unitarity of Two-Tier QED
Correspondence Principle for Two-Tier QED
Consistency with Precision QED Experiments
Calculational Rules for Feynman Diagrams
Two-Tier Coulomb Potential vs. Conventional Coulomb Potential
Doubly-Charged Dilepton Resonances

8. Two-Tier Standard Model Theory
Formulation of Two-Tier Standard Models
Low Energy Behavior of the Two-Tier Standard Model
High Energy Behavior of the Two-Tier Standard Model
Path Integral Formulation
Two-Tier Yang-Mills Gauge Fields
Two-Tier Massive Vector Fields
General Short Distance (High Momentum) Behavior of Two-Tier Propagator
Higgs Particles
General Form of the Two-Tier Standard Model Path Integral
Renormalization - Finite
Asymptotic Freedom and Quark Confinement
Two-Tier Coordinates

9. Two-Tier Quantum Gravity: Finite
Two-Tier General Relativity
Lagrangian Formulation
The Mass Scale
Planck Scale Physics
Measurement of the Quantum Gravity Field
The Two-Tier Gravitational Potential vs. Newtonian Gravitational Potential
Black Holes

10. A Unified Quantum Field Theory of the Known Forces of Nature
Low Energy Behavior
Negative Degree of Divergence - A Finite Unified Theory
Other General Issues


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  • Anonymous

    Posted August 9, 2003

    New Type of Quantum Field Theory w/o Divergences

    This book introduces a new type of Quantum Field Theory called 'Two Tier QFT' that has no divergences, and thus allows a finite quantum field theory of the Standard Model and Gravitation to be created. It is written like a textbook and goes through the mathematical details thoroughly. It is at the level of a graduate QFT course. But the theory is new and highly original research. Some tidbits: black holes must have a minimal mass - ultra-microscopic black holes are not possible. Maybe that is why they are not created in high energy/cosmic ray experiments. Also massive vector mesons do not create divergences so that the Higgs mechanism is not needed to create a renormalizable electroweak theory. I found this to be a very interesting book that might make QFT a viable alternative to the current monopoly of Superstring theory. I highly recommend it.

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