States and operators in the spacetime algebra

Journal Article · Wed Sep 01 00:00:00 EDT 1993 · Foundations of Physics; (United States)

DOI:https://doi.org/10.1007/BF01883678· OSTI ID:5541471

Doran, C ^[1]; Lasenby, A; Gull, S ^[2]

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1. DAMTP, Cambridge (United Kingdom)
2. MRAO, Cavendish Lab., Cambridge (United Kingdom)

The spacetime algebra (STA) is the natural, representation-free language for Dirac's theory of the electron. Conventional Pauli, Dirac, Weyl, and Majorana spinors are replaced by spacetime multivectors, and the quantum [sigma]- and [gamma]-matrices are replaced by two-sided multivector operations. The STA is defined over the reals, and the role of the scalar unit imaginary of quantum mechanics is played by a fixed spacetime bivector. The extension to multiparticle systems involves a separate copy of the STA for each particle, and it is shown that the standard unit imaginary induces correlations between these particle spaces. In the STA, spinors and operators can be manipulated without introducing any matrix representation or coordinate system. Furthermore, the formalism provides simple expressions for the spinor bilinear covariants which dispense with the need for the Fierz identities. A reduction to 2+1 dimensions is given, and applications beyond the Dirac theory are discussed. 35 refs.

• OSTI ID: 5541471
• Journal Information: Foundations of Physics; (United States), Journal Name: Foundations of Physics; (United States) Vol. 23:9; ISSN 0015-9018; ISSN FNDPA4
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ANGULAR MOMENTUM OPERATORS
CORRELATIONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FIERZ-PAULI THEORY
LEPTONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MATRICES
MECHANICS
MINKOWSKI SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PAULI SPIN OPERATORS
QUANTUM MECHANICS
QUANTUM OPERATORS
SPACE
SPACE-TIME
SPINORS
WAVE EQUATIONS