ISSN:
1572-9524
Keywords:
variational problems
;
Weyl-equation
;
quantum cosmology
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract 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 fieldsψ A and $$\tilde \psi ^{{\rm A}'} $$ . This paper studies the corresponding classical properties, i.e., the classical boundary-value problem and boundary terms in the variational problem. If $$\sqrt 2 _e n_{\rm A}^{{\rm A}'} \tilde \psi ^{{\rm A}'} \mp \tilde \psi ^{{\rm A}'} \equiv \Phi ^{{\rm A}'} $$ 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 onS 3 should vanish onS 3. Remarkably, this coincides with the property of the classical boundary-value problem when spectral boundary conditions are imposed onS 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 .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02275257
