Stumbling Blocks Against Unification

My new book  Stumbling Blocks Against Unification   was published last month by Word Scientific. Its subtitle is On Some Persistent Misconceptions in Physics. In the book I discuss certain topics of fundamental theoretical physics that are generally considered as being completly understood and show why such an “understanding” is not correct and are obstacles against further progress.

In particular, as stated in Preface, I discuss why the general opinion about the devastating role of negative energies in classical and quantum physics, especially in quantum field theories, should be revised for the benefit of further advances in quantum gravity. To determine under which conditions a physical system is stable or unstable is not so straightforward as it is generally uncritically believed. Once this concept is understood, the doors are opened to welcoming ultrahyperbolic spaces, whose signature has positive and negative signs.

Next, I show that such spaces are associated with Clifford algebras, which have numerous promising applications, discussed throughout the book. Among others, the generators of Clifford algebras in infinite-dimensional spaces play the role of quantum field operators thatcreate particles with either definite momenta or definite positions.

Within quantum field theories, the concept of a particle with a definite position is not quite well understood, and there are confusing ideas about that notion. I show that once this concept is properly formulated, quantum field theories can be employed in creating continuous sets of particles at different positions. In particular, such sets can be strings or branes. The quantization of a generic brane has so far been very difficult and has not yet been completely finished. However, with branes generated by means of the creation operators of a quantum field theory, we have solved the problem of the quantum brane. Now, if we consider the braneworld scenario, which regards our universe as a brane embedded in a higher-dimensional space, with the effective induced metric on the brane being the spacetime metric, we arrive at quantum gravity.

Contents:

• Preface
• Acknowledgement
• About Historical Misconceptions in Physics
• Higher Derivative Theories and Negative Energies
• Upon Quantization — Ghosts or Negatives Energies?
• Transformations of Spinors
• Quantum Fields as Basis Vectors
• Brane Space and Branes as Conglomerates of Quantum Fields
• Particle Position in Quantum Field Theories
• Misconceptions and Confusion About Tachyons
• Ordering Ambiguity of Quantum Operators
• What Have We Learned?
• Bibliography
• Index