Stumbling Blocks Against Unification: On Some Persistent Misconceptions In Physics

Contents
Preface
Acknowledgement
1. About Historical Misconceptions in Physics
2. Higher Derivative Theories and Negative Energies
	2.1 Negative energies and stability
	2.2 Unequal masses, unequal tension: Special cases of generic metric
	2.3 Collision or scattering of two particles
	2.4 Positive and negative masses
	2.5 Discussion
3. Upon Quantization — Ghosts or Negatives Energies?
	3.1 Illustrative example: The system of two equal frequency oscillators
	3.2 Interacting quantum oscillator
	3.3 On the stability of higher derivative field theories
	3.4 Conclusion
4. Transformations of Spinors
	4.1 Transformations of Clifford numbers
	4.2 Clifford algebra and spinors in Minkowski space
	4.3 Four independent spinors
	4.4 Behavior of spinors under Lorentz transformations
		4.4.1 Rotation
		4.4.2 Space inversion
	4.5 Generalized Dirac equation (Dirac-K¨ahler equation)
5. Quantum Fields as Basis Vectors
	5.1 Introduction
	5.2 Clifford space as an extension of spacetime
	5.3 Generators of Clifford algebras as quantum mechanical operators
		5.3.1 Orthogonal and symplectic Clifford algebras
		5.3.2 Equations of motion for a particle’s coordinates and the corresponding basis vectors
		5.3.3 Supersymmetrization of the action
	5.4 Basis vectors, Clifford algebras, spinors and quantized fields
		5.4.1 Spinors as particular Clifford numbers
		5.4.2 Quantized fields as generalized Clifford numbers
		5.4.3 The action and field equations
	5.5 Towards quantum gravity
		5.5.1 Gravitational field from Clifford algebra
		5.5.2 Fermion creation operators, branes as vacuums, branes with holes, and induced gravity
	5.6 Quantized fields and Clifford space
	5.7 Conclusion
6. Brane Space and Branes as Conglomerates of Quantum Fields
	6.1 Introduction
	6.2 Brane as a point in the brane space M
	6.3 Special case: Flat brane space M
	6.4 An interacting bunch of scalar fields
	6.5 Generalization to arbitrary configurations
		6.5.1 Non interacting case
		6.5.2 Bunch of Stuckelberg fields interacting in a particular way
		6.5.3 Self interacting Stueckelberg field in configuration space
	6.6 Conclusion
7. Particle Position in Quantum Field Theories
	7.1 Manifestly covariant formulation of a scalar field quantum theory
	7.2 States with indefinite position or momentum
		7.2.1 Wave packet profiles for a Hermitian and non Hermitian scalar field
		7.2.2 The action principle for the wave packet profiles and conserved currents
		7.2.3 Working with field operators
		7.2.4 The action principle for creation operators and conserved currents
		7.2.5 The action principle for states
		7.2.6 The scalar product between states at different times: The propagator
	7.3 Motion of wave packets
	7.4 What about causality violation?
8. Misconceptions and Confusion About Tachyons
	8.1 Introduction
	8.2 The superluminal transformations of extended relativity
	8.3 Formulating extended relativity in real spacetime M4,4
	8.4 Klein-Gordon equation in Clifford space
	8.5 Tachyons and causality
	8.6 Conclusion
9. Ordering Ambiguity of Quantum Operators
	9.1 Introduction
	9.2 Geometric definition of momentum
	9.3 The equations of motion for the expectation value of momentum
	9.4 On the integration of vectors in curved space
	9.5 Conclusion
10. What Have We Learned?
Bibliography
Index