Boundary terms for massless fermionic fields

Details Boundary terms for massless fermionic fields Boundary terms for massless fermionic fields

Jun 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994fophl...7..303e&link_type=abstract

Foundations of Physics Letters, Volume 7, Issue 3, pp.303-308

Physics

2

Variational Problems, Weyl-Equation, Quantum Cosmology

Scientific paper

Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal e n A/A' to the boundary and a pair of independent spinor fields ψ A andtilde ψ ^{A'} . This paper studies the corresponding classical properties, i.e., the classical boundary-value problem and boundary terms in the variational problem. Ifsqrt 2 _e n_A^{A'} tilde ψ ^{A'} mp tilde ψ ^{A'} equiv Φ ^{A'} is set to zero on a 3-sphere bounding flat Euclidean 4-space, the modes of the massless spin-1/2 field multiplying harmonics having positive eigenvalues for the intrinsic 3-dimensional Dirac operator on S 3 should vanish on S 3. Remarkably, this coincides with the property of the classical boundary-value problem when spectral boundary conditions are imposed on S 3 in the massless case. Moreover, the boundary term in the action functional is proportional to the integral on the boundary of Φ A' e n AA' ψ A .

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