General Wigner Rotations in D Dimensions
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摘要
We construct general Wigner rotations for both massive and massless particles in D-dimensional spacetime.We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between the electromagnetic gauge invariance and the non-uniqueness of Wigner rotation.
We construct general Wigner rotations for both massive and massless particles in D-dimensional spacetime.We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between the electromagnetic gauge invariance and the non-uniqueness of Wigner rotation.
We construct general Wigner rotations for both massive and massless particles in D-dimensional spacetime.We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between the electromagnetic gauge invariance and the non-uniqueness of Wigner rotation.
引文
[1]E.P.Wigner,Ann.Math.40(1939)149.
[2]S.Weinberg,“The Quantum Theory of Fields,”Vol.1,Cambridge University Press,New York(1995).
[3]E.P.Wigner,“Gruppentheorie und ihre Anwendungen auf die Quantenmechanik der Atomspektren”,Braunschweig,Vieweg Verlag(1931),Translated into English by J.J.Griffin,“Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra”,Academic Press,New York(1959).
?For a particle of unit mass, k~μ=(0, 0,..., 0, 1); For a massless particle, k~μ=(0,..., 0, 1, 1), with “1” standing for unit energy.
§In this paper, Lorentz transformations without the subscript “S”, such as L(p),Λ, R, and W(Λ, p)are in the vector representation.
?If D≤4, it is relatively easy to work out the explicit expression ofΛSfor a given generalΛ.(See Subsec. 2.2)
∥For a massless particle of unit energy, ■.
**That is, the gauge field of helicity±1 satisfies the equation of motion ?ν?_νA_μ(x)=0.
??In Chapter 2 of Ref.[2], the generators T~1and T~2 are denoted as A and B, respectively.
[2]S.Weinberg,“The Quantum Theory of Fields,”Vol.1,Cambridge University Press,New York(1995).
[3]E.P.Wigner,“Gruppentheorie und ihre Anwendungen auf die Quantenmechanik der Atomspektren”,Braunschweig,Vieweg Verlag(1931),Translated into English by J.J.Griffin,“Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra”,Academic Press,New York(1959).
?For a particle of unit mass, k~μ=(0, 0,..., 0, 1); For a massless particle, k~μ=(0,..., 0, 1, 1), with “1” standing for unit energy.
§In this paper, Lorentz transformations without the subscript “S”, such as L(p),Λ, R, and W(Λ, p)are in the vector representation.
?If D≤4, it is relatively easy to work out the explicit expression ofΛSfor a given generalΛ.(See Subsec. 2.2)
∥For a massless particle of unit energy, ■.
**That is, the gauge field of helicity±1 satisfies the equation of motion ?ν?_νA_μ(x)=0.
??In Chapter 2 of Ref.[2], the generators T~1and T~2 are denoted as A and B, respectively.