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Register a new userSplit property for free massless finite helicity fields
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Added by
Karl-Henning Rehren
Publication date
2018
fields
Physics
and research's language is
English
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We prove the split property for any finite helicity free quantum fields. Finite helicity Poincare representations extend to the conformal group and the conformal covariance plays an essential role in the argument. The split property is ensured by the trace class condition: Tr (exp(-s L_0)) is finite for all s>0 where L_0 is the conformal Hamiltonian of the Mobius covariant restriction of the net on the time axis. We extend the argument for the scalar case presented in [7]. We provide the direct sum decomposition into irreducible representations of the conformal extension of any helicity-h representation to the subgroup of transformations fixing the time axis. Our analysis provides new relations among finite helicity representations and suggests a new construction for representations and free quantum fields with non-zero helicity.
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We show that the Schrodinger operator associated with a physical system over a local field can be approximated in a very strong sense by finite Schrodinger operators. Some striking numerical results are included at the end of the article.
A system of coupled kinetic transport equations for the Wigner distributions of a free variable mass Klein-Gordon field is derived. This set of equations is formally equivalent to the full wave equation for electromagnetic waves in nonlinear dispersive media, thus allowing for the description of broadband radiation-matter interactions and the associated instabilities. The standard results for the classical wave action are recovered in the short wavelength limit of the generalized Wigner-Moyal formalism for the wave equation.
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