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

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

5.0 1
by Stephen Blaha
     
 

ISBN-10: 0972079599

ISBN-13: 9780972079594

Pub. Date: 05/28/2003

Publisher: Pingree-Hill Publishing

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

Overview

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!

Product Details

ISBN-13:
9780972079594
Publisher:
Pingree-Hill Publishing
Publication date:
05/28/2003
Pages:
192
Product dimensions:
7.48(w) x 9.02(h) x 0.40(d)

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
Introduction
Two-Tier Space
Vacuum Fluctuations
The Feynman Propagator
String-like Substructure of the Theory
Parity
Charge Conjugation
Time Reversal

5. Interacting Quantum Field Theory
Introduction
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
Unitarity
Perturbation Expansion
General Form of Propagators

7. Two-Tier Quantum Electrodynamics
Formulation
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
Introduction
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
Unitarity
Anomalies
Asymptotic Freedom and Quark Confinement
Two-Tier Coordinates

9. Two-Tier Quantum Gravity: Finite
Introduction
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
Formulation
Low Energy Behavior
Negative Degree of Divergence - A Finite Unified Theory
Unitarity
Other General Issues

REFERENCES
INDEX

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A Finite Unified Quantum Field Theory of the Elementary Particle Standard Model and Quantum Gravity Based on New Quantum Dimensions and a New Paradigm 5 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
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.