198 research outputs found
Non-Commutative Differential Geometry and Standard Model
We incorporate Sogami's idea in the standard model into our previous
formulation of non-commutative differential geometry by extending the action of
the extra exterior derivative operator on spinors defined over the discrete
space-time; four dimensinal Minkovski space multiplyed by two point discrete
space. The extension consists in making it possible to require that the
operator become nilpotent when acting on the spinors. It is shown that the
generalized field strength leads to the most general, gauge-invariant
Yang-Mills-Higgs Lagrangian even if the extra exterior derivative operator is
not nilpotent, while the fermionic part remains intact. The proof is given for
a single Higgs model. The method is applied to reformulate the standard model
by putting left-handed fermion doublets on the upper sheet and right-handed
fermion singlets on the lower sheet with generation mixing among quarks being
taken into account. We also present a matrix calculus of the method without
referring to the discrete space-time.Comment: 27 page
Lagrangian Formulation of Connes' Gauge Theory
It is shown that Connes' generalized gauge field in non-commutative geometry
is derived by simply requiring that Dirac lagrangian be invariant under local
transformations of the unitary elements of the algebra, which define the gauge
group. The spontaneous breakdown of the gauge symmetry is guaranteed provided
the chiral fermions exist in more than one generations as first observed by
Connes-Lott. It is also pointed out that the most general gauge invariant
lagrangian in the bosonic sector has two more parameters than in the original
Connes-Lott scheme.Comment: 9 pages, PTPTEX.st
Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory
It is shown that the one-loop two-point amplitude in {\it Lorentz-invariant}
non-commutative (NC) theory is finite after subtraction in the
commutative limit and satisfies the usual cutting rule, thereby eliminating the
unitarity problem in Lorentz-non-invariant NC field theory in the approximation
considered.Comment: 14 page
Gauge Theories Coupled to Fermions in Generation
Gauge theories coupled to fermions in generation are reformulated in a
modified version of extended differential geometry with the symbol .
After discussing several toy models, we will reformulate in our framework the
standard model based on Connes' real structure. It is shown that for the most
general bosonic lagrangin which is required to also reconstruct N=2 super
Yang-Mills theory Higgs mechanism operates only for more than one generation as
first pointed out by Connes and Lott.Comment: 18 pages, ptptex.st
A Field-Theoretic Approach to Connes' Gauge Theory on
Connes' gauge theory on is reformulated in the Lagrangian
level. It is pointed out that the field strength in Connes' gauge theory is not
unique. We explicitly construct a field strength different from Connes' one and
prove that our definition leads to the generation-number independent Higgs
potential. It is also shown that the nonuniqueness is related to the assumption
that two different extensions of the differential geometry are possible when
the extra one-form basis is introduced to define the differential
geometry on . Our reformulation is applied to the standard model
based on Connes' color-flavor algebra. A connection between the unimodularity
condition and the electric charge quantization is then discussed in the
presence or absence of .Comment: LaTeX file, 16 page
The Role of Central Bank in the Recession in the Case of Japan's Recession
Japan's economy is expanding and expected to continue expanding moderately, according to Monthly Report of Recent Economic and Financial Developments released by the Bank of Japan in July 2007.The BOJ declared the change of policy stance at the Monetary Policy Meeting held on July 14, 2006. The BOJ had to tackle a recession which the Japanese economy had not experienced before. The economy was on the verge of financial panic, especially in 1997 and 1998, when major financial institutions had failed. It reminded us of the recurrence of the Great Depression in the 1930s. The article will clarify how the Japanese economy fell into a serious depression with a reflection on the role of the BOJ in the emergence of prolonged depression. We will also estimate the interest rate elasticity of money demand in order to identify whether or not the Japanese economy was in a liquidity trap in the prolonged recession. We will use the EGARCH model to quantify the financial anxieties. The conclusion will suggest that the BOJ should have paid more attention to the behavior of money stock at the early stage of depression.bubble, money stock, financial anxieties, liquidity trap
Lorentz-Invariant Non-Commutative Space-Time Based On DFR Algebra
It is argued that the familiar algebra of the non-commutative space-time with
-number is inconsistent from a theoretical point of view.
Consistent algebras are obtained by promoting to an
anti-symmetric tensor operator . The simplest among them
is Doplicher-Fredenhagen-Roberts (DFR) algebra in which the triple commutator
among the coordinate operators is assumed to vanish. This allows us to define
the Lorentz-covariant operator fields on the DFR algebra as operators diagonal
in the 6-dimensional -space of the hermitian operators,
. It is shown that we then recover Carlson-Carone-Zobin
(CCZ) formulation of the Lorentz-invariant non-commutative gauge theory with no
need of compactification of the extra 6 dimensions. It is also pointed out that
a general argument concerning the normalizability of the weight function in the
Lorentz metric leads to a division of the -space into two disjoint
spaces not connected by any Lorentz transformation so that the CCZ covariant
moment formula holds true in each space, separately. A non-commutative
generalization of Connes' two-sheeted Minkowski space-time is also proposed.
Two simple models of quantum field theory are reformulated on
obtained in the commutative limit.Comment: LaTeX file, 27 page
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