Boundary terms for massless fermionic fields |
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Authors: | Giampiero Esposito Hugo Morales-Técotl Giuseppe Pollifrone |
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Institution: | (1) Istituto Nazionale di Fisica Nucleare, Mostra d'Oltremare Padiglione 20, 80125 Napoli, Italy;(2) Dipartimento di Scienze Fisiche, Mostra d'Oltremare Padiglione 19, 80125 Napoli, Italy;(3) Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34013 Trieste, Italy |
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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 fields
A
and
. This paper studies the corresponding classical properties, i.e., the classical boundary-value problem and boundary terms in the variational problem. If
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
A
e
n
AA
A
. |
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Keywords: | variational problems Weyl-equation quantum cosmology |
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