A Clifford Calculus for Physical Field Theories

Tucker, Robin

doi:10.1007/978-94-009-4728-3_16

Cited by 10 publications

(8 citation statements)

References 15 publications

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“…A choice of values for the dimensionless parameters { 0 , a, b, q, m 0 } can be used to solve (23) numerically for a collection of trajectories for charged particles, each arranged initially around the circumference of a circle in a plane orthogonal to the propagation axis of incident CM type electromagnetic pulses with different chirality. The resulting space-curves in 3-dimensions, displayed in figure 1 clearly exhibit the different responses of charged matter to CM pulses with distinct chirality values [10].…”

Section: Electromagnetic Pulses In Spacetime Vacuamentioning

confidence: 99%

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Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

Tucker,

Walton

2021

Preprint

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We review a technique for solving a class of classical linear partial differential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar Laplacian and a complexified Hertz potential. The complexification prescription ensures the existence of regular physical solutions with chirality and propagating, non-singular, pulselike characteristics that are bounded in all three spatial dimensions. The technique is applied to the source-free Maxwell, Bopp-Landé-Podolsky and linearised Einstein field systems, and particular solutions are used for constructing classical models describing single-cycle laser pulses and a mechanism is discussed for initiating astrophysical jets. Our article concludes with a brief introduction to spacetime Clifford algebra ideals that we use to represent spinor fields. We employ these to demonstrate how the same technique used for tensor fields enables one to construct new propagating, chiral, non-singular, pulse-like spinor solutions to the massless Dirac equation in Minkowski spacetime.

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Section: Electromagnetic Pulses In Spacetime Vacuamentioning

confidence: 99%

“…If follows that S Y also depends upon P, W and J ≡ ξ * . For other choices of involution, the reader may consult [5,23,24].…”

Section: Spinor Pre-potentialsmentioning

confidence: 99%

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

Tucker,

Walton

2021

Preprint

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“…This latter choice is precious for admitting a local equivalence between spinor fields and the sections of minimal left ideal bundle of the Clifford bundle. A good account of this tradition can be found in [11,12]. Throughout the text we assume a Riemannian spacetime [38] i.e.…”

Section: Introductionmentioning

confidence: 99%

On a Relation Between Twistors and Killing Spinors

Açık

2018

Cumhuriyet Science Journal

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Inspiring from the consequence of constructing conformal Killing-Yano forms out of Killing-Yano forms and closed conformal Killing-Yano forms, this work includes a method for building up twistors from Killing spinors which can be analogously interpreted as the quantum electrodynamical pair annihilation process in background gravitational fields. The former consequence is easily verified if one introduces a new defining differential equation for (possibly inhomogeneous) Killing-Yano forms which is free from auxiliary vector fields, as is done in this text. From this point of view a neat relation between the symmetry operators of massive and massless Dirac equation is also introduced. Some other physical interpretations are also included.

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“…This latter choice is precious for admitting a local equivalence between spinor fields and the sections of minimal left ideal bundle of the Clifford bundle. A good account of our tradition can be found in [12,13]. Throughout the text we assume a Riemannian spacetime [37] i.e.…”

Section: Introductionmentioning

confidence: 99%

Twistors from Killing Spinors alias Radiation from Pair Annihilation I: Theoretical Considerations

Açık

2017

Preprint

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This paper is intended to be a further step through our Killing spinor programme started with Class. Quantum Grav. 32, 175007 (2015), and we will advance our programme in accordance with the road map recently given in arXiv:1611.04424v2. In the latter reference many open problems were declared, one of which contained the uncovered relations between specific spinors in spacetime represented by an arrow diagram built upon them. This work deals with one of the arrows with almost all of its details and ends up with an important physical interpretation of this setup in terms of the quantum electrodynamical pair annihilation process. This method will shed light on the classification of pseudo-Riemannian manifolds admitting twistors in connection with the classification problem related to Killing spinors. Many physical interpretations are given during the text some of which include dynamics of brane immersions, quantum field theoretical considerations and black hole evaporation.

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A Clifford Calculus for Physical Field Theories

Cited by 10 publications

References 15 publications

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

On a Relation Between Twistors and Killing Spinors

Twistors from Killing Spinors alias Radiation from Pair Annihilation I: Theoretical Considerations

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