TY - CHAP

T1 - Introduction and some problems encountered in the construction of a relativistic quantum theory

AU - Horwitz, Lawrence P.

N1 - Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.

PY - 2015

Y1 - 2015

N2 - One of the deepest and most difficult problems of theoretical physics in the past century has been the construction of a simple, well-defined one-particle theory which unites the ideas of quantum mechanics and relativity. Early attempts, such as the construction of the Klein-Gordon equation and the Dirac equation were inadequate to provide such a theory since, as shown by Newton and Wigner (1949), they are intrinsically non-local, in the sense that the solutions of these equations cannot provide a well-defined local probability distribution. This result will be discussed in detail below. Relativistic quantum field theories, such as quantum electrodynamics, provide a manifestly covariant framework for important questions such as the Lamb shift and other level shifts, the anomalous moment of the electron and scattering theory, but the discussion of quantum mechanical interference phenomena and associated local manifestations of the quantum theory are not within their scope; the one particle sector of such theories display the same problem pointed out by Newton and Wigner since they satisfy the same one-particle field equations.

AB - One of the deepest and most difficult problems of theoretical physics in the past century has been the construction of a simple, well-defined one-particle theory which unites the ideas of quantum mechanics and relativity. Early attempts, such as the construction of the Klein-Gordon equation and the Dirac equation were inadequate to provide such a theory since, as shown by Newton and Wigner (1949), they are intrinsically non-local, in the sense that the solutions of these equations cannot provide a well-defined local probability distribution. This result will be discussed in detail below. Relativistic quantum field theories, such as quantum electrodynamics, provide a manifestly covariant framework for important questions such as the Lamb shift and other level shifts, the anomalous moment of the electron and scattering theory, but the discussion of quantum mechanical interference phenomena and associated local manifestations of the quantum theory are not within their scope; the one particle sector of such theories display the same problem pointed out by Newton and Wigner since they satisfy the same one-particle field equations.

KW - Dirac equation

KW - Lamb shift

KW - Particle sector

KW - Relativistic wave equation

KW - Wave function

UR - http://www.scopus.com/inward/record.url?scp=85091445678&partnerID=8YFLogxK

U2 - 10.1007/978-94-017-7261-7_1

DO - 10.1007/978-94-017-7261-7_1

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AN - SCOPUS:85091445678

SN - 978-94-017-7260-0

SN - 978-94-017-7956-2

T3 - Fundamental Theories of Physics

SP - 1

EP - 7

BT - Relativistic Quantum Mechanics

PB - Springer Netherlands

CY - Dordrecht

ER -