A Conformal Diagram of a Minkowski Spacetime

John D. Norton

First, here is the conformal diagram of a Minkowski spacetime. This is the complete spacetime. It includes all of the infinity of space and the infinity of time through which things persist.This diagram gives the simplest case in which we consider just one dimension of space.

Note the three types of infinities: timelike, lightlike and spacelike. They correspond to the different vanishing points in an ordinary perspective drawing.

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**The Quantum Theory of the Electron**

**Paul Dirac**

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In mathematical physics, the **gamma matrices**, {γ^{0},γ^{1},γ^{2},γ^{3}}, also known as the **Dirac matrices**, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra *C*ℓ(1,3). It is also possible to define higher-dimensional Gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of space time acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate space-time computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-½ particles.

In Dirac representation, the four contravariant gamma matrices are

Analogue sets of gamma matrices can be defined in any dimension and signature of the metric. For example the Pauli matrices are a set of “gamma” matrices in dimension 3 with metric of Euclidean signature (3,0).

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### Thoughts on Angel and Demons Plot

“For me, the most attractive way … would be to capture the antihydrogen in a neutral particle trap … The objective would be to then study the properties of a small number of [antihydrogen] atoms confined in the neutral trap for a long time.“Gerald Gabrielse, 1986 Erice Lecture (shortly after first trapping of antiprotons)

“Penning Traps, Masses and Antiprotons”, in Fundamental Symmetries,

edited by P. Bloch, P. Paulopoulos and R. Klapisch, p. 59 (Plenum, New York, 1987). See:Goals for ATRAP

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