This book, 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, develops a new formulation of quantum field theory. Within this framework, a finite unified quantum field theory of the known forces of nature - electromagnetism, the weak interactions, the strong interactions and gravity - is created. The conventional Standard Model is the large distance limit of the elementary particle sector of the unified theory. The Quantum Gravity sector is finite in this formulation. Its large distance limit is Einsteinian gravity. This unified theory contains no divergences - thus solving a major problem that has bedeviled quantum field theory for the past seventy years. The theory is based on a new form of hidden dimensions: Quantum Dimensions, that only manifest themselves at ultra-high energies. Some new phenomena that result are: * Unification of QED, Weak Interactions, Strong Interactions and Quantum Gravity.* Finite - No divergences.* Finite also with massive vector bosons: No need for Higgs mechanism.* Low Energy Limit: Approximates Standard Model (and QED) to arbitrary accuracy.* Suggests possible doubly charged dilepton resonances.* Large Distance limit of Quantum Gravity: Newtonian gravitational potential.* No ultra-microscopic Black Holes.* A New form of hidden dimensions: Quantum Dimensions.* A New form of interaction: Dimensional Interactions.* A New paradigm (type of problem) for the Calculus of Variations.

This groundbreaking book develops a new form of quantum theory. First there was quantum mechanics. Then there was quantum field theory. Now we have quantum theory of the third kind: a new form of quantum field theory with quantum coordinates in the imaginary part of a complex space-time. This book is the second edition of ?A Finite Unified Quantum Field Theory of the Elementary Particle Standard Model and Quantum Gravity? with major additions on unitarity, relativistic invariance and the nature of space-time. Some major new results in this books are: A Unified Theory of QED, Weak Interactions, Strong Interactions and Quantum Gravity; A General Formulation of Divergence-free Quantum Field Theories (Detailed discussions of unitarity and special relativity showing these theories are physically acceptable.). A divergence-free quantum field theory for massive vector bosons: No need for the Higgs mechanism. The "Low Energy" Limit of elementary particle sector of unified theory approximates the Standard Model (& QED) to extreme accuracy. It suggests possible doubly charged dilepton, and other exotic, resonances. The "Large Distance", classical limit of Quantum Gravity sector is General Relativity. It suggests no ultra-light Black Holes exist. Gravity is repulsive (anti-gravity) at ultra-short distances. Two-tier gravity ?saves? the concept of a space-time point by evading Wigner?s classic argument against it. Based on experimental data a preferred local reference frame defined by Cosmic Background Radiation is shown to exist in each locale. (Preferred local inertial frames are used in two-tier quantum gravity whose dynamical equations are invariant under general relativistic transformations but whose ?ground state? breaks the invariance down to invariance under special relativity.) A New form of hidden dimensions is defined ? Quantum Dimensions ? dimensions implemented via a quantum gauge field. A New method in the Calculus of Variations ? composition of extrema ? is described.

ACCOUNTING PRINCIPLES Meeting the need for a coherently written and comprehensive compendium combining field theory and particle physics for advanced students and researchers, this volume directly links the theory to the experiments. It is clearly divided into two sections covering approaches to field theory and the Standard Model, and rounded off with numerous useful appendices. A timely work for high energy and theoretical physicists, as well as astronomers, graduate students and lecturers in physics. From the contents: Particles and Fields Lorentz Invariance Dirac Equation Field Quantization Scattering Matrix QED: Quantum Electrodynamics Radiative Corrections and Tests of Qed Symmetries Path Integral : Basics Path Integral Approach to Field Theory Accelerator and Detector Technology Spectroscopy The Quark Model Weak Interaction Neutral Kaons and CP Violation Hadron Structure Gauge Theories Appendices Volume 2 (2013, ISBN 3-527-40966-1) will concentrate on the main aspects of the Standard Model by addressing its recent developments and future prospects. Furthermore, it will give some thought to intriguing ideas beyond the Standard Model, including the Higgs boson, the neutrino, the concepts of the Grand Unified Theory and supersymmetry, axions, and cosmological developments.

This book derives Standard Model of Elementary Particles from thirteen postulates. In addition Dark Matter and Dark Energy naturally emerge upon the addition of two more postulates. The key postulate is that Nature has a U(8) symmetry broken to a U(4)xU(4) symmetry. One U(4) representation is compactified and its only remnants are the three known generations of fermions, and a fourth generation that we postulate constitutes Dark Matter. If the fourth generation has a separate ElectroWeak sector we identify Dark Energy with its ¿dark photons¿. The other U(4) symmetry is broken to a complexified Lorentz group that supports exactly four fermion species. Two species comprise the leptons. Lepton doublets consist of a charged lepton and a tachyon (neutrino). The other two species we identify with up-type and down-type quarks. This assignment leads directly to the SU(2)xU(1) form of the ElectroWeak sector. The quark species manifestly embody a natural global SU(3) symmetry that we generalize to color SU(3). As part of the development we show how to create canonical tachyon Quantum Field Theories. The result of these efforts is a theory that brings particle physics to a new depth of understanding and provides a detailed understanding of the reasons for the Standard Model¿s unusual form. The Standard Model unites with Quantum Gravity to form a unified finite theory using Tier Quantum Field Theory. The book entitled, Quantum Theory of the Third Kind, that describes Two-Tier Quantum Field Theory, is also included in this volume. All diagrams calculated in perturbation theory finite.

Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a reference for active researchers in the field.

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

This book describes a new area of physics: the metatheory of physics theories. It develops a mathematical description of the nature of physics theories which it applies to the Theory of Everything or the Final Theory. It also develops quantum Turing machine and Quantum Computer formulations of the Standard Model of Elementary Particles and SuperString Theories.