The Foundations of Physical Law - Rowlands, Peter (Singapore ; World Scientific Pub. Co., 2015)
The book originated in a series of lectures given at Liverpool in 2013 to a group that included postgraduate and undergraduate students and staff of the Physics Department. They followed from two very successful lectures given to the undergraduate Physical Society. It seemed that there was a very large interest among the students in investigating the foundations of physics in a way that was never done in physics courses, and was not available in books or other outlets. However, the idea was to create a framework in which students (and interested staff) could develop their own thinking relative to the ideas in the lectures. So it was important to create both conceptual and mathematical structures on the issues that are important at this level. The book has the right sort of technical content to allow for this development, but doesn't lose itself in excessive details. The ideal use for this book would be on postgraduate courses where students would be encouraged to think about the foundations in a way that is well beyond the superficial. However, a course on aspects of this material would also be valuable at the undergraduate level, where students could be stimulated into believing that creative thinking could solve the problems that emerge when we confront foundational problems.
1. Introduction to foundational physics. 1.1. What do we mean by foundations of physics?. 1.2. How do we study it? 1.3. Avoiding the arbitrary. 1.4. Totality zero. 1.5. What questions should we ask? -- 2. Mathematical ideas and methods. 2.1. Quaternions and octonions. 2.2. Clifford algebra. 2.3. Groups. 2.4. Nilpotents and idempotents. 2.5. Standard and non-standard analysis. 2.6. Topology. 2.7. Key numbers in duality, anticommutativity and symmetry-breaking. 2.8. Some significant group tables -- 3. The most primitive concepts. 3.1. What are the most primitive concepts in physics?. 3.2. Measurement. 3.3. Conservation and nonconservation. 3.4. Real and imaginary. 3.5. Commutative and anticommutative -- 4. A fundamental symmetry. 4.1. A key group. 4.2. Visual representations. 4.3. Two spaces? 4.4. A unified algebra. 4.5. Nipotency. 4.6. The symmetry-breaking between charges. 4.7. The parameters in the dual group. 4.8. Conservation of angular momentum and conservation of type of charge -- 5. Nilpotent quantum mechanics I. 5.1. The Dirac equation. 5.2. The nilpotent Dirac equation. 5.3. Using discrete differentiation. 5.4. Idempotents and nilpotents. 5.5. Pauli exclusion. 5.6. Vacuum. 5.7. Quantum mechanics and the quantum field. 5.8. Spin and helicity. 5.9. Zitterbewegung and Berry phase. 5.10. CPT symmetry -- 6. Nilpotent quantum mechanics II. 6.1. Bosons. 6.2. Baryons. 6.3. Partitioning the vacuum. 6.4. Local and nonlocal. 6.5. The Coulomb (electric) interaction. 6.6. The strong interaction. 6.7. The weak interaction -- 7. Nilpotent quantum field theory. 7.1. A perturbation calculation. 7.2. Cancellation of loops. 7.3. Propagators. 7.4. A weak interaction calculation. 7.5. BRST quantization. 7.6. Mass generation. 7.7. String theory. 7.8. One-fermion theory. 7.9. Dualities in nilpotent quantum theory -- 8. Gravity. 8.1. General relativity or quantum mechanics?. 8.2. Gravity and quantum mechanics. 8.3. General relativity and Newtonian theory. 8.4. The effect of observation on nonlocal gravity. 8.5. The aberration of space. 8.6. Gravitomagnetic effects. 8.7. Maxwell's equations for gravitomagnetism. 8.8. Mach's principle. 8.9. Can we quantize gravitational inertia? 8.10. Extended causality and quantized inertia -- 9. Particles. 9.1. Particle structures from nilpotent quantum mechanics. 9.2. Phase diagrams. 9.3. Dirac equation for charge. 9.4. Fermionic states from the algebra. 9.5. Equation for specifying particle states. 9.6. Tables of particle structures. 9.7. SU(5). 9.8. Quarks. 9.9. Grand unification : a prediction. 9.10. The Higgs mechanism and fermion masses. 9.11. Larger group structures for fermions and bosons -- 10. Return to symmetries. 10.1. A universal rewrite system. 10.2. Mathematical representation. 10.3. Physical application. 10.4. Entropy and information. 10.5. Duality and the factor 2. 10.6. Anticommutativity and the factor 3. 10.7. Symmetry and self-organization.
Includes bibliographical references (p. 225-226) and index.
Electronic reproduction.
Keywords: Physics; Mathematical physics; Quantum theory; Electronic books