Related papers: Another Dirac
This paper has rather a pedagogical meaning. Surprising symmetries in the $(j,0)\oplus (0,j)$ Lorentz group representation space are analyzed. The aim is to draw reader's attention to the possibility of describing the particle world on the…
Using the cubic Dirac operator and an extended notion of Dirac cohomology we generalize results of Huang-Pandzic, which appeared in JAMS (Sept. 6, 2001 electronic) on a conjecture of D. Vogan
In this note a simple extension of the complex algebra to higher dimension is proposed. Using the postulated algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra…
This is a brief introduction to the geometric aspects of aperiodic tiling and the collaboration of John Conway and the author in the decade 1990-2000.
A review of author's work on cyclic inequalities of Shapiro-Diananda type and related optimization problems is presented.
Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived and tweaked, little emphasis has been placed on studying…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
Generally, it is common that cited papers are earlier than citing papers. But we found three different cases, with more undiscovered. In this letter, we attempted to explain the reasons. However, negative time lag between citing and cited…
The article uses two examples to explore the statement that, contrary to the common wisdom, the properties of singular cardinals are actually more intuitive than those of the regular ones.
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrained variational calculus, optimal control, Lagrangian…
The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
In this paper we consider solutions of the Dirac equation at ultra high energies. The study provides new insights including features overlooked thus far and also new ramifications.
Continuing previous work we develop a certain piece of functional analysis on general graphs and use it to create what Connes calls a 'spectral triple', i.e. a Hilbert space structure, a representation of a certain (function) algebra and a…
A non-classical differential calculus on the quantum disc and cones is constructed and the associated integral is calculated.
We discuss the work of Abhyankar on dicritical divisors with a special focus on the algebraic aspects of this work. We also discuss related work on local quadratic transforms, infinitely near points and Rees valuation rings of an ideal.
This study use some philological and historical means in order to understand Fermat's way of thinking.
The problem if existing neutrinos are Dirac or Majorana particles is considered in a very pedagogical way. After a few historical remarks we recall the theoretical description of neutral spin 1/2 particles, emphasizing the difference…
An technically interesting proof of a known theorem.