143 research outputs found
Ginsparg-Wilson Relation and Admissibility Condition in Noncommutative Geometry
Ginsparg-Wilson relation and admissibility condition have the key role to
construct lattice chiral gauge theories. They are also useful to define the
chiral structure in finite noncommutative geometries or matrix models. We
discuss their usefulness briefly.Comment: Latex 4 pages, uses ptptex.cls. Talk given at Nishinomiya-Yukawa
Memorial Symposium on Theoretical Physics ``Noncommutative Geometry and
Quantum Spacetime in Physics", Japan, Nov.11-15, 2006. (To be published in
the Proceedings
Chiral Anomaly and Ginsparg-Wilson Relation on the Noncommutative Torus
We evaluate chiral anomaly on the noncommutative torus with the overlap Dirac
operator satisfying the Ginsparg-Wilson relation in arbitrary even dimensions.
Utilizing a topological argument we show that the chiral anomaly is combined
into a form of the Chern character with star products.Comment: 19 pages, uses ptptex.cls and ptp-prep.clo, references added, typo
corrected, the final version to appear in Prog.Theor.Phy
Formulation of Complex Action Theory
We formulate a complex action theory which includes operators of coordinate
and momentum and being replaced with non-hermitian
operators and , and their eigenstates and with complex eigenvalues and .
Introducing a philosophy of keeping the analyticity in path integration
variables, we define a modified set of complex conjugate, real and imaginary
parts, hermitian conjugates and bras, and explicitly construct ,
, and by formally
squeezing coherent states. We also pose a theorem on the relation between
functions on the phase space and the corresponding operators. Only in our
formalism can we describe a complex action theory or a real action theory with
complex saddle points in the tunneling effect etc. in terms of bras and kets in
the functional integral. Furthermore, in a system with a non-hermitian
diagonalizable bounded Hamiltonian, we show that the mechanism to obtain a
hermitian Hamiltonian after a long time development proposed in our letter
works also in the complex coordinate formalism. If the hermitian Hamiltonian is
given in a local form, a conserved probability current density can be
constructed with two kinds of wave functions.Comment: 29 pages, 2 figures, references added, presentation improved, typos
corrected. (v5)The definition of and are
corrected by replacing them with their hermitian conjugates. The errors and
typos mentioned in the errata of PTP are corrected. arXiv admin note:
substantial text overlap with arXiv:1009.044
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