By David Lurie
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Extra info for Particles And Fields
The important difference in the meaning of spin for massive and massless particles is that when m + 0 one can refer the particle to a rest frame in which the spin can point in any direction, whereas for massless particles there is no rest frame and the spin can only point in the direction of motion. Note that along the direction of motion the orbital angular momentum is zero, so that the projection of the spin along k may be identified with the projection of the total angular momentum. Outlook Despite their generality, the Bargmann-Wigner equations are difficult to handle, especially from the point of view of Lagrangian field theory (see Chapter 2).
1959) (with G. C. Wick) Ann. 7,404 Klein, O. (1926) Z. Phys- 37, 895 Kusaka, S. (1941) Phys. Reu. ffi,61 Lee, T. D. (1957) (with C. N. Yang) Phys. K. (1942) Physica 9, 310 Moldauer, P. A. (1956) (with K. M. Case) Phys. 102,279 Pauli, W. (1934) (with V. Weisskopf) Helu. Phys. ActaT,lW Rarita, W. (1941) (with J. Schwinger) Phys. Reu. 60,61 Salam, A. (1965) (with R. Delbourgo and J. Strathdee) Proc. Roy. Soc. A 2U,146 2 Lagrangian Field Theory 2-1 Hamilton's action principle Canonical Coordinates for a Field To lay the basis for field quantization, we now reformulate classical field theories in the canonical language of Lagrangian and Hamiltonian mechanics.
K, 0 0 1(e8) : Let us assume that m * 0 and go to the rest frame k : 0. Adopting the representation 1(28) in which y+ is diagonal with diagonal elements l. (O,m) is non-zero only when all indices r B . are restricted to the values 1 and 2. This is just the generalization of the result \a9a). Taking into account the requirement that w,fl... must be completely symmetric in all indices, we can construct the following complete set of linearly independent solutions for Eu : *. ,: *Lh)r. ,: 6ny6p16yr ..