arXiv subjects

Peter Rowlands

Publications and source records attributed to Peter Rowlands.

15 recordsLinked to original sources

arXiv2020

The Dirac Equation and the Majorana Dirac Equation

We discuss the structure of the Dirac equation and how the nilpotent and the Majorana operators arise naturally in this context. This provides a link between Kauffman's work on discrete physics, iterants and Majorana Fermions and the work on nilpotent structures and the Dirac equation of Peter Rowlands. We give an expression in split quaternions for the Majorana Dirac equation in one dimension of time and three dimensions of space. Majorana discovered a version of the Dirac equation that can be expressed entirely over the real numbers. This led him to speculate that the solutions to his version of the Dirac equation would correspond to particles that are their own anti-particles. It is the purpose of this paper to examine the structure of this Majorana-Dirac Equation, and to find basic solutions to it by using the nilpotent technique. We succeed in this aim and describe our results.

physics.gen-ph↗

arXiv2013

A critical value for dark energy

Experimental evidence over a number of recent years has shown the density parameter of the universe omega converging to the critical value of 1, which defines a flat, Euclidean universe. No such calculations have defined a critical value for the most significant component of omega, that for the dark energy, omega lambda, but the new data provided by the Planck probe open up the previously unconsidered possibility that a particular value with special physical significance occurs at omega lambda = 2/3. If future observations should converge on exactly this value, then we may have the first indication that the explanation for this phenomenon lies in necessary constraints provided by fundamental laws of physics on possible cosmologies for the universe.

physics.gen-ph↗

arXiv2010

Physical Interpretations of Nilpotent Quantum Mechanics

Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.

physics.gen-ph↗

arXiv2009

Are there alternatives to our present theories of physical reality?

Our notions of what is physically 'real' have long been based on the idea that the real is what is immediately apprehended, that is the local or observable, the physically tangible, though there has always been an alternative philosophical notion that the 'real' is some kind of ontological structure beyond immediate apprehension, and so inaccessible through physics. However, quantum mechanics, with its intrinsic nonlocal correlations, has seemingly left us with a dilemma by showing that fundamental physical theories cannot be both real and local. Reality cannot be reconstructed as a deterministic projection from physical observations. Many people think that the problem lies with quantum mechanics, but, in fact, it is more likely to be a result of unrealistic expectations. We have assumed that fundamental physics ought to be compatible with normal (macroscopic) experience. If, however, we go beyond our current high-level physical theories to the basic elements from which they are constructed, we see that a pattern emerges that gives us a very different and much more coherent understanding of what is meant by physical 'reality'.

physics.gen-ph↗

arXiv2008

What is vacuum?

Vacuum can be defined with exact mathematical precision as the state which remains when a fermion, with all its special characteristics, is created out of absolutely nothing. The definition leads to a special form of relativistic quantum mechanics, which only requires the construction of a creation operator. This form of quantum mechanics is especially powerful for analytic calculation, at the same time as explaining, from first principles, many aspects of the Standard Model of particle physics. In particular, the characteristics of the weak, strong and electric interactions can be derived from the structure of the creation operator itself.

physics.gen-ph↗

arXiv2005

Removing redundancy in relativistic quantum mechanics

It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac equation can be developed which remove the redundancies and singularities from many areas of quantum physics while giving quantum representations to specific particle states.

physics.gen-ph↗

arXiv2003

The nilpotent Dirac equation and its applications in particle physics

The nilpotent Dirac formalism has been shown, in previous publications, to generate new physical explanations for aspects of particle physics, with the additional possibility of calculating some of the parameters involved in the Standard Model. The applications so far obtained are summarised, with an outline of some more recent developments.

quant-ph↗

arXiv2002

A universal alphabet and rewrite system

We present two ways in which an infinite universal alphabet may be generated using a novel rewrite system that conserves zero (a special character of the alphabet and the symbol for that character) at every step. The recursive method delivers the entire alphabet in one step when invoked with the zero character as the initial subset alphabet. The iterative method with the same start delivers characters that act as ciphers for properties that the developing subset alphabet contains. These properties emerge in an arbitrary sequence and there are an infinite number of ways they may be selected. The subset alphabets in addition to having mathematical interpretation as algebra can also be constrained to emerge in a minimal way which then has application as a foundational physical system. Each subset alphabet may itself be the basis of a rewrite system where rules that operate on symbols (representing characters) or collections of symbols manipulate the specific properties in a dynamic way.

cs.OH↗

arXiv2001

The group structure bases of a foundational approach to physics

Based on a fundamental symmetry between space, time, mass and charge, a series of group structures of physical interest is generated, ranging from C2 to E8. The most significant result of this analysis is a version of the Dirac equation combining quaternions and multivariate vectors, which is already second quantized and intrinsically supersymmetric, and which automatically leads to a symmetry breaking, with the creation of specific particle structures and a mass-generating mechanism.

physics.gen-ph↗

arXiv2001

The factor 2 in fundamental physics

A brief history is given of the factor 2, starting in the most elementary considerations of geometry and kinematics of uniform acceleration, and moving to relativity, quantum mechanics and particle physics. The basic argument is that in all the significant cases in which the factor 2 or 1/2 occurs in fundamental physics, whether classical, quantum or relativistic, the same physical operation is taking place.

physics.gen-ph↗

arXiv2001

QED using the nilpotent formalism

The nilpotent formalism for the Dirac equation, outlined in previous papers,is applied to QED. It is shown that what is usually described as 'renormalization' is effectively a statement of the fact that the nilpotent formulation is automatically second quantized and constrains the field into producing finite values for fundamental quantities.

quant-ph↗

arXiv2001

A foundational approach to physics

A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to explain certain physical facts and even to derive new mathematical theorems. Applications are made to classical mechanics, electromagnetic theory and quantum mechanics.

physics.class-ph↗

arXiv2001

The Dirac algebra and grand unification

A representation of the Dirac algebra, derived from first principles, can be related to the combinations of unit charges which determine particle structures. The algebraic structure derives from a broken symmetry between 4-vectors and quaternions which can be applied to the broken symmetry between the three nongravitational interactions. The significance of this relation for Grand Unification is derived by explicit calculation of the running values of the fine structure constants, with suggestions for the calculation of particle masses.

quant-ph↗

arXiv2001

Applications of the nilpotent Dirac state vector

The nilpotent version of the Dirac equation is applied to the baryon wavefunction, the strong interaction potential, electroweak mixing, and Dirac and Klein-Gordon propagators. The results are used to interpret a quaternion-vector model of particle structures.

quant-ph↗

arXiv2000

The Dirac algebra and its physical interpretation

A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free fermions, vector bosons, scalar bosons; Bose-Einstein condensates, and baryons;annihilation, creation and vacuum operators; the quantum field integrals; and C, P and T transformations; and to suggest new insights into the meaning of supersymmetry and renormalization.

quant-ph↗