9 Ergebnisse.

Conformal groups illustrate and emphasise how rich group theory is, something usually not recognised, and they also emphasise how fundamental geometry is in physics (and conversely). Reasons, and implications for physics, are explored as a start to the study of the vast fields of mathematics and physics suggested and required. These groups have non-linear transformations, ones with singularities. Other aspects also show richness beyond what is...

The conformal group is the invariance group of geometry (which is not understood), the largest one. Physical applications are implied, as discussed, including reasons for interactions. The group structure as well as those of related groups are analyzed. An inhomogeneous group is a subgroup of a homogeneous one because of nonlinearities of the realization. Conservation of baryons (protons can't decay) is explained and proven. Reasons for variou...

Quantum mechanics, its properties including wavefunctions, complex numbers and uncertainty, are necessary and completely reasonable and understandable, with no weirdness. Classical physics is impossible. Much uncertainty comes from Fourier analysis. Waves and particles and collapse of wavefunctions are meaningless. Their seeming appearance in analyzed. Reasons and limitations of superposition are considered. Gravitation is an example of nonlin...

Geometry through its fundamental transformations, the Poincaré group, requires that wavefunctions belong to representations. Massless and massive representations are very different and their coupling almost impossible. Helicity-1 gives electromagnetism, helicity-2 gives gravitation, no higher helicities are possible. Basis states, thus the fundamental fields, are the potential and connection. General relativity is derived and is the unique the...

Excision of errors and confusion about quantum mechanics -- and stimulation of thoughtful and adventurous readers are pre-eminent rationales of this entire work, these requiring definitions and analysis of underlying concepts of quantum mechanics, of quantum field theory -- why probability is given by the absolute square, what wavefunctions are and are not and why, and many others -- and also examination of some from the philosophy of science....

Group Theoretical Foundations of Quantum Mechanics

This is a thought-provoking book. Mirman is a crusader for the advancement of a no-nonsense approach to physics. He does not request your complete agreement, but your willingness to think, which is good. I enjoyed the ride." David J. Santos, Mathematical Reviews In-depth analysis of the necessity for quantum mechanics and for its properties. All are (easily) understandable and unavoidable. Geometry, group theory and consistency require wavefun...

Chapters: The Physical Meaning of Poincaré Massless Representations, Massless Representations, Massless Fields are Different, How to Couple Massless and Massive Matter, The Behaviour of Matter in Fields, Geometrical Reasons for the Poincaré Group, Description of the Electromagnetic Field, The Equations Governing Free Gravitation, How Matter Determines Gravitational Fields, Nonlinearity and Geometry, Quantum Gravity.

WHY GOD COULD NOT CREATE THE UNIVERSE WITH A DIFFERENT DIMENSION EVEN IF IT WANTED TO or perhaps anything else. Perhaps the universe must be the way it is. It seems that what is omnipotent is mathematics, elementary arithmetic, just counting. Yet even mathematics is not powerful enough to create a universe¿there are just too many conditions, conflicting. Existence is impossible. Beyond that for there to be structure is quite inconceivable. But...