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https://hdl.handle.net/2142/30685
Description
Title
Quantum field theories on the light front
Author(s)
Root, Robert Gerald
Issue Date
1973
Director of Research (if dissertation) or Advisor (if thesis)
Chang, Shau-Jin
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
light fronts
quantum mechanics
quantum field theories
Language
en
Abstract
Several popular field theories are quantized on light fronts, that is O 3
surfaces defined by x + = x0 + x3 = constant. Schwinger's quantum ac tion principle is employed to deduce the correct canonical equal-x+(anti-) commutation relations. The formulations developed for free fields of spin-o,-t,-l, and -2 are equivalent to the equal-time formulations. However, in the new formulations it is easy to take the limit of vanishing mass in the massive spin-2 theory. Consistent formulations are found for self-interacting scalar fields and for scalar and Dirac fields interacting through simple couplings. The S-matrix elements are given by a x+-ordered
product rather than the usual time-ordered product. The Feynman rules for
these S-matrix elements are identical to the old rules in the case of the
self-interacting scalar theory, but they differ by noncovariant terms for
the interacting Dirac theory. A formal proof of the equivalence of the S-m3trix in the new formulation and the usual time-ordered expansion is given for renormalized interacting Dirac fields. A set of generalized Schwinger conditions for a quantum theory to be Lorentz invariant are verified in scalar and Dirac field theories; then the presence of c-number Schwinger terms in the equal-x+ stress tensor commutators is demonstrated. This new formulation is used to find spectral sum rules and leading singularities of both the Green's function and the product of field operators near the light front. The implications for current algebra sum rules are mentioned. Reduction formulas for scalar and Dirac particles are derived.
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