4,354 research outputs found
Two-spinor Formulation of First Order Gravity coupled to Dirac Fields
Two-spinor formalism for Einstein Lagrangian is developed. The gravitational
field is regarded as a composite object derived from soldering forms. Our
formalism is geometrically and globally well-defined and may be used in
virtually any 4m-dimensional manifold with arbitrary signature as well as
without any stringent topological requirement on space-time, such as
parallelizability. Interactions and feedbacks between gravity and spinor fields
are considered. As is well known, the Hilbert-Einstein Lagrangian is second
order also when expressed in terms of soldering forms. A covariant splitting is
then analysed leading to a first order Lagrangian which is recognized to play a
fundamental role in the theory of conserved quantities. The splitting and
thence the first order Lagrangian depend on a reference spin connection which
is physically interpreted as setting the zero level for conserved quantities. A
complete and detailed treatment of conserved quantities is then presented.Comment: 16 pages, Plain TE
Bose Symmetry and Chiral Decomposition of 2D Fermionic Determinants
We show in a precise way, either in the fermionic or its bosonized version,
that Bose symmetry provides a systematic way to carry out the chiral
decomposition of the two dimensional fermionic determinant. Interpreted
properly, we show that there is no obstruction of this decomposition to gauge
invariance, as is usually claimed. Finally, a new way of interpreting the
Polyakov-Wiegman identity is proposed.Comment: LaTex file, 17 pages, Ref.(5) corrected, final version to appear in
Nucl. Phys.
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