9,376 research outputs found
Ginsparg-Wilson operators and a no-go theorem
If one uses a general class of Ginsparg-Wilson operators, it is known that CP
symmetry is spoiled in chiral gauge theory for a finite lattice spacing and the
Majorana fermion is not defined in the presence of chiral symmetric Yukawa
couplings. We summarize these properties in the form of a theorem for the
general Ginsparg-Wilson relation.Comment: 8 pages, Latex, references updated, version to appear in Phys. Lett.
Quantum and Classical Gauge Symmetries in a Modified Quantization Scheme
The use of the mass term as a gauge fixing term has been studied by
Zwanziger, Parrinello and Jona-Lasinio, which is related to the non-linear
gauge of Dirac and Nambu in the large mass limit. We have
recently shown that this modified quantization scheme is in fact identical to
the conventional {\em local} Faddeev-Popov formula {\em without} taking the
large mass limit, if one takes into account the variation of the gauge field
along the entire gauge orbit and if the Gribov complications can be ignored.
This suggests that the classical massive vector theory, for example, is
interpreted in a more flexible manner either as a gauge invariant theory with a
gauge fixing term added, or as a conventional massive non-gauge theory. As for
massive gauge particles, the Higgs mechanics, where the mass term is gauge
invariant, has a more intrinsic meaning.
It is suggested to extend the notion of quantum gauge symmetry (BRST
symmetry) not only to classical gauge theory but also to a wider class of
theories whose gauge symmetry is broken by some extra terms in the classical
action. We comment on the implications of this extended notion of quantum gauge
symmetry.Comment: 14 pages. Substantially revised and enlarged including the change of
the title. To appear in International Journal of Modern Physics
CP breaking in lattice chiral gauge theory
The CP symmetry is not manifestly implemented for the local and doubler-free
Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify
where the effects of this CP breaking appear.Comment: 3 pages, Lattice2002(chiral
A continuum limit of the chiral Jacobian in lattice gauge theory
We study the implications of the index theorem and chiral Jacobian in lattice
gauge theory, which have been formulated by Hasenfratz, Laliena and Niedermayer
and by L\"{u}scher, on the continuum formulation of the chiral Jacobian and
anomaly. We take a continuum limit of the lattice Jacobian factor without
referring to perturbative expansion and recover the result of continuum theory
by using only the general properties of the lattice Dirac operator. This
procedure is based on a set of well-defined rules and thus provides an
alternative approach to the conventional analysis of the chiral Jacobian and
related anomaly in continuum theory. By using an explicit form of the lattice
Dirac operator introduced by Neuberger, which satisfies the Ginsparg-Wilson
relation, we illustrate our calculation in some detail. We also briefly comment
on the index theorem with a finite cut-off from the present viewpoint.Comment: Some of the statements were made more precise, and a footnote was
added. To be published in Nuclear Physics B. 19 page
Finite temperature regularization
We present a non-perturbative regularization scheme for Quantum Field
Theories which amounts to an embedding of the originally unregularized theory
into a spacetime with an extra compactified dimensions of length L ~
Lambda^{-1} (with Lambda an ultraviolet cutoff), plus a doubling in the number
of fields, which satisfy different periodicity conditions and have opposite
Grassmann parity. The resulting regularized action may be interpreted, for the
fermionic case, as corresponding to a finite-temperature theory with a
supersymmetry, which is broken because of the boundary conditions. We test our
proposal in a perturbative calculation (the vacuum polarization graph for a
D-dimensional fermionic theory) and in a non-perturbative one (the chiral
anomaly).Comment: 17 pages, LaTeX fil
General chiral gauge theories
Only requiring that Dirac operators decribing massless fermions on the
lattice decompose into Weyl operators we arrive at a large class of them. After
deriving general relations from spectral representations we study correlation
functions of Weyl fermions for any value of the index, stressing the related
conditions for basis transformations and getting the precise behaviors under
gauge and CP transformations. Using the detailed structure of the chiral
projections we also obtain a form of the correlation functions with a
determinant in the general case.Comment: 3 pages, Lattice2003(chiral
Chiral Anomaly for a New Class of Lattice Dirac Operators
A new class of lattice Dirac operators which satisfy the index theorem have
been recently proposed on the basis of the algebraic relation
. Here stands for a non-negative integer and
corresponds to the ordinary Ginsparg-Wilson relation. We analyze the
chiral anomaly and index theorem for all these Dirac operators in an explicit
elementary manner. We show that the coefficient of anomaly is independent of a
small variation in the parameters and , which characterize these
Dirac operators, and the correct chiral anomaly is obtained in the (naive)
continuum limit .Comment: 23 pages. Corrected typos and misprints. Made several sentences more
precise, and references up-dated. (To appear in Nucl. Phys. B
Algebraic Generalization of the Ginsparg-Wilson Relation
A specific algebraic realization of the Ginsparg-Wilson relation in the form
is discussed, where stands for a
non-negative integer and corresponds to the commonly discussed
Ginsparg-Wilson relation. From a view point of algebra, a characteristic
property of our proposal is that we have a closed algebraic relation for one
unknown operator , although this relation itself is obtained from the
original proposal of Ginsparg and Wilson,
, by choosing as an
operator containing (and thus Dirac matrices). In this paper, it is shown
that we can construct the operator explicitly for any value of . We
first show that the instanton-related index of all these operators is
identical. We then illustrate in detail a generalization of Neuberger's overlap
Dirac operator to the case . On the basis of explicit construction, it is
shown that the chiral symmetry breaking term becomes more irrelevent for larger
in the sense of Wilsonian renormalization group. We thus have an infinite
tower of new lattice Dirac operators which are topologically proper, but a
large enough lattice is required to accomodate a Dirac operator with a large
value of .Comment: 17 pages. Rewrote the abstract and added footnotes to Page 1 and Page
2. Also expanded Section 5. To appear in Nucl. Phys.
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