From the very beginning of quantum mechanics, the notion of the position of a particle has been much discussed. In the nonrelativistic case, the proo… - Arthur Wightman
" "From the very beginning of quantum mechanics, the notion of the position of a particle has been much discussed. In the nonrelativistic case, the proof of the equivalence of matrix and wave mechanics, the discovery of the uncertainty relations, and the development of the statistical interpretation of the theory led to an understanding which, within the inevitable limitations of the nonrelativistic theory, may be regarded as completely satisfactory.
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About Arthur Wightman
(March 30, 1922 – January 13, 2013) was an American mathematical physicist, known for the .
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Alternative Names:
Arthur Strong Wightman
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Additional quotes by Arthur Wightman
Vacuum expectation values of products of neutral scalar field operators are discussed. The properties of these distributions arising from , the absence of negative energy states and the positive definiteness of the scalar product are determined. The vacuum expectation values are shown to be boundary values of analytic functions. Local commutativity of the field is shown to be equivalent to a symmetry property of the analytic functions. The problem of determining a theory of a neutral scalar field given its vacuum expectation values is posed and solved.
… there are other things wrong with these models but the fundamental trouble is the non-uniqueness of the vacuum as was first shown by , , and STEINMANN … Actually, … has shown that the cluster decomposition property is not only necessary but sufficient for the uniqueness of the vacuum, if there is at least one cyclic vacuum. …
HEPP, K., JOST, R., RUELLE, D. and STEINMANN, O., Necessary condition on Wightman functions, Helv. Phys. Acta 34 (1961) 542.
BORCHERS, H.J., On the structure of the algebra of field observables, Nuovo Cim. 24 (1962) 214
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Why was the discovery of the ... so important for the physics of the 1920s and 30s? The answer is manifold. The Dirac equation provided a relativistic description of spin ½ particles and in particular of the electron. In doing so, it gave a relativistic description of spin and opened the way for the application of group theory to the description of particles of arbitrary spin. The reinterpretation of the Dirac equation as a field equation that followed from Dirac's theory of holes was decisive in the conceptual transformation of single particle theory to many particle (quantum field) theory. The resulting quantum electrodynamics of spin ½ particles, refined by two generations of theoretical work, is the best theory we have. Although it is an approximation since it does not include the effects of weak and strong interactions it has survived many stringent experimental tests when applied to electrons and s.
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