arXiv subjects

Shoichi Ichinose

Publications and source records attributed to Shoichi Ichinose.

51 records · Page 3Linked to original sources

arXiv2001

A Solution of the Randall-Sundrum Model and the Mass Hierarchy Problem

A solution of the Randall-Sundrum model for a simplified case (one wall) is obtained. It is given by the $1/k^2$-expansion (thin wall expansion) where $1/k$ is the {\it thickness} of the domain wall. The vacuum setting is done by the 5D Higgs potential and the solution is for a {\it family} of the Higgs parameters. The mass hierarchy problem is examined. Some physical quantities in 4D world such as the Planck mass, the cosmological constant, and fermion masses are focussed. Similarity to the domain wall regularization used in the chiral fermion problem is explained. We examine the possibility that the 4D massless chiral fermion bound to the domain wall in the 5D world can be regarded as the real 4D fermions such as neutrinos, quarks and other leptons.

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arXiv1999

Heat-Kernel Approach to the Overlap Formalism

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arXiv1999

New Regularization Using Domain Wall

We present a new regularization method, for d dim (Euclidean) quantum field theories in the continuum formalism, based on the domain wall configuration in (1+d) dim space-time. It is inspired by the recent progress in the chiral fermions on the lattice. The wall "height" is given by 1/M, where M is a regularization mass parameter and appears as a 1+d dim Dirac fermion mass. The present approach gives a thermodynamic view to the domain wall or the overlap formalism in the lattice field theory. We will show qualitative correspondence between the present continuum results and those of the lattice. The extra dimension is regarded as the (inverse) temperature t. The domains are defined by the directions of the "system movement", not by the sign of M as in the original overlap formalism. Physically the parameter M controls both the chirality selection and the dimensional reduction to d dimension. From the point of regularization, the limit $Mt\ra 0$ regularize the infra-red behaviour whereas the condition on the momentum ($k^\m$) integral, $|k^\m|\leq M$, regularize the ultra-violet behaviour. To check the new regularization works correctly, we take the 4 dim QED and 2 dim chiral gauge theory as examples. Especially the consistent and covariant anomalies are correctly obtained. The choice of solutions of the higher dim Dirac equation characterize the two anomalies. The projective properties of the positive and negative energy free solutions are exploited in calculation. Some integral functions, the incomplete gamma functions and the generalized hypergeometric functions characteristically appear in the regularization procedure.

hep-th↗

arXiv1999

Temperature in Fermion Systems and the Chiral Fermion Determinant

We give an interpretation to the issue of the chiral determinant in the heat-kernel approach. The extra dimension (5-th dimension) is interpreted as (inverse) temperature. The 1+4 dim Dirac equation is naturally derived by the Wick rotation for the temperature. In order to define a ``good'' temperature, we choose those solutions of the Dirac equation which propagate in a fixed direction in the extra coordinate. This choice fixes the regularization of the fermion determinant. The 1+4 dimensional Dirac mass ($M$) is naturally introduced and the relation: $|$4 dim electron momentum$|$ $\ll$ $|M|$ $\ll$ ultraviolet cut-off, naturally appears. The chiral anomaly is explicitly derived for the 2 dim Abelian model. Typically two different regularizations appear depending on the choice of propagators. One corresponds to the chiral theory, the other to the non-chiral (hermitian) theory.

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arXiv1998

Weyl Anomaly in Higher Dimensions and Feynman Rules in Coordinate Space

An algorithm to obtain the Weyl anomaly in higher dimensions is presented. It is based on the heat-kernel method. Feynman rules, such as the vertex rule and the propagator rule, are given in (regularized) coordinate space. Graphical calculation is introduced. The 6 dimensional scalar-gravity theory is taken as an example, and its explicit result is obtained.

hep-th↗

arXiv1998

Weak Field Expansion of Gravity: Graphs, Matrices and Topology

We present some approaches to the perturbative analysis of the classical and quantum gravity. First we introduce a graphical representation for a global SO(n) tensor $(\pl)^d h_\ab$, which generally appears in the weak field expansion around the flat space: $g_\mn=\del_\mn+h_\mn$. Making use of this representation, we explain 1) Generating function of graphs (Feynman diagram approach), 2) Adjacency matrix (Matrix approach), 3) Graphical classification in terms of "topology indices" (Topology approach), 4) The Young tableau (Symmetric group approach). We systematically construct the global SO(n) invariants. How to show the independence and completeness of those invariants is the main theme. We explain it taking simple examples of $\pl\pl h-, {and} (\pl\pl h)^2-$ invariants in the text. The results are applied to the analysis of the independence of general invariants and (the leading order of) the Weyl anomalies of scalar-gravity theories in "diverse" dimensions (2,4,6,8,10 dimensions).

hep-th↗

arXiv1998

Conformal Anomaly in 4D Gravity-Matter Theories Non-minimally Coupled with Dilaton

The conformal anomaly for 4D gravity-matter theories, which are non-minimally coupled with the dilaton, is systematically studied. Special care is taken for: rescaling of fields, treatment of total derivatives, hermiticity of the system operator and choice of measure. Scalar, spinor and vector fields are taken as the matter quantum fields and their explicit conformal anomalies in the gravity-dilaton background are found. The cohomology analysis is done and some new conformal invariants and trivial terms, involving the dilaton, are obtained. The symmetry of the constant shift of the dilaton field plays an important role. The general structure of the conformal anomaly is examined. It is shown that the dilaton affects the conformal anomaly characteristically for each case: 1)[Scalar] The dilaton changes the conformal anomaly only by a new conformal invariant, $I_4$; 2)[Spinor] The dilaton does {\it not} change the conformal anomaly; 3)[Vector] The dilaton changes the conformal anomaly by three new (generalized) conformal invariants, $I_4,I_2,I_{1}$. We present some new anomaly formulae which are useful for practical calculations. Finally, the anomaly induced action is calculated for the dilatonic Wess-Zumino model. We point out that the coefficient of the total derivative term in the conformal anomaly for the 2D scalar coupled to a dilaton is ambiguous. This resolves the disagreement between calculations in refs.\cite{ENO,NO,SI97,KLV} and the result of Hawking-Bousso\cite{BH}.

hep-th↗

arXiv1998

General Structure of Conformal Anomaly and 4 Dimensional Photon-Dilaton Gravity

The general structure of the conformal anomaly and the dilaton's effect to it are analysed. First we give a new formal proof of the statement that the conformal anomaly, in the theory which is conformal invariant at the classical level, is conformal invariant. The heat-kernel regularization and Fujikawa's method are taken for the analysis. We present a new explicit result of the conformal anomaly in 4 dimensional photon-dilaton gravity. This result is examined from the point of the general structure.

hep-th↗

arXiv1998

Weyl Anomaly of 2D Dilaton-Scalar Gravity and Hermiticity of System Operator

Weyl Anomaly in the dilaton-scalar system in 2 dimensional gravity is examined. We take the heat-kernel regularization for the ultraviolet divergences. Generally the Weyl anomaly is determined by the 2nd order differential (elliptic) operator of the system and the definition of the measure. We have the freedom of the operator choice caused by the arbitrariness of total divergences (surface terms) in the action. We examine the Weyl anomaly in connection with such points and the hermiticity of the operator.

hep-th↗

arXiv1998

New Algorithm for Tensor Calculation in Field Theories

Tensor calculation of suffix-contraction is carried out by a C-program. Tensors are represented graphically, and the algorithm makes use of the topology of graphs. Classical and quantum gravity, in the weak-field perturbative approach, is a special interest. Examples of the leading order calculation of some general invariants such as $R_{\mn\ls}R^{\mn\ls}$ are given. Application to Weyl anomaly calculation is commented.

hep-th↗

arXiv1997

Graphical Classification of Global SO(n) Invariants and Independent General Invariants

This paper treats some basic points in general relativity and in its perturbative analysis. Firstly a systematic classification of global SO(n) invariants, which appear in the weak-field expansion of n-dimensional gravitational theories, is presented. Through the analysis, we explain the following points: a) a graphical representation is introduced to express invariants clearly; b) every graph of invariants is specified by a set of indices; c) a number, called weight, is assigned to each invariant. It expresses the symmetry with respect to the suffix-permutation within an invariant. Interesting relations among the weights of invariants are given. Those relations show the consistency and the completeness of the present classification; d) some reduction procedures are introduced in graphs for the purpose of classifying them. Secondly the above result is applied to the proof of the independence of general invariants with the mass-dimension $M^6$ for the general geometry in a general space dimension. We take a graphical representation for general invariants too. Finally all relations depending on each space-dimension are systematically obtained for 2, 4 and 6 dimensions.

hep-th↗

arXiv1996

Gauge Symmetry of the Heat-Kernel and Anomaly Formulas

We consider a gauge symmetry in a quantum Hilbert space. The symmetry leads to that of the heat-kernel and of the anomaly formulae which were previously obtained by the authors. This greatly simplifies and clarifies the structure of the formulae. We explicitly obtain the anomaly formulae in two and four dimensions, which ``unify'' all kinds of anomaly. The symmetry corresponds to that of the counterterm formulae in the background field method. As an example, the non-abelian anomaly is considered.

hep-th↗

arXiv1996

Weak Field Expansion of Gravity and Graphical Representation

We introduce a graphical representation for a global SO(n) tensor $\pl_\m\pl_\n h_\ab$, which generally appears in the perturbative approach of gravity around the flat space: $g_\mn=\del_\mn+h_\mn$. We systematically construct global SO(n) invariants. Independence and completeness of those invariants are shown by taking examples of $\pl\pl h$-, and $ (\pl\pl h)^2$- invariants. They are classified graphically. Indices which characterize all independent invariants (or graphs) are given. We apply the results to general invariants with dimension $(Mass)^4$ and the Gauss-Bonnet identity in 4-dim gravity.

hep-th↗

arXiv1995

New Formulation of Anomaly,Anomaly Formula and Graphical Representation

A general approach to anomaly in quantum field theory is newly formulated by use of the propagator theory in solving the heat-kernel equation. We regard the heat-kernel as a sort of the point-splitting regularization in the space(-time) manifold. Fujikawa's general standpoint that the anomalies come from the path-integral measure is taken. We obtain some useful formulae which are valid for general anomaly calculation. They turn out to be the same as the 1-loop counter-term formulae except some important total derivative terms. Various anomalies in 2 and 4 dimensional theories are systematically calculated. Some important relations between them are concretely shown. As for the representation of general (global SO(n)) tensors, we introduce a graphical one. It makes the tensor structure of invariants very transparent and makes the tensor calculation so simple.

hep-th↗

arXiv1993

Graphical Representation of Invariants and Covariants in General Relativity

We present a grapical way to describe invariants and covariants in the (4 dim) general relativity. This makes us free from the complexity of suffixes . Two new off-shell relations between (mass)$\ast\ast 6$\ invariants are obtained. These are important for 2-loop off-shell calculation in the perturbative quantum gravity. We list up all independent invarians with dimensions of (mass)$\ast\ast 4$\ and (mass)$\ast\ast 6$. Furthermore the explicit form of 6 dim Gauss-Bonnet identity is obtained.

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