arXiv subjects

Shoichi Ichinose

Publications and source records attributed to Shoichi Ichinose.

At least 19 recordsLinked to original sources

arXiv2015

Velocity-Field Theory, Boltzmann's Transport Equation, Geometry and Emergent Time

Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The properties of the fluid matter (fluid particles) appear as the density and the viscosity. {\it Statistical fluctuation} is examined, and is clearly discriminated from the quantum effect. The time variable is {\it emergently} introduced through the computational process step. Besides the ordinary potential, the general velocity potential is introduced. The collision term, for the Higgs-type velocity potential, is explicitly obtained and the (statistical) fluctuation is closely explained. The system is generally {\it non-equilibrium}. The present field theory model does {\it not} conserve energy and is an open-system model. One dimensional Navier-Stokes equation, i.e., Burgers equation, appears. In the latter part of the text, we present a way to directly define the distribution function by use of the geometry, appearing in the energy expression, and Feynman's path-integral.

hep-th↗

arXiv2015

Non-equilibrium Statistical Approach to Friction Models

A geometric approach to the friction phenomena is presented. It is based on the holographic view which has recently been popular in the theoretical physics community. We see the system in one-dimension-higher space. The heat-producing phenomena are most widely treated by using the non-equilibrium statistical physics. We take 2 models of the earthquake. The dissipative systems are here formulated from the geometric standpoint. The statistical fluctuation is taken into account by using the (generalized) Feynman's path-integral.

cond-mat.stat-mech↗

arXiv2013

New Approach to Cosmological Fluctuation using the Background Field Method and CMB Power Spectrum

A new field theory formulation is presented for the analysis of the CMB power spectrum distribution in the cosmology. The background-field formalism is fully used. Stimulated by the recent idea of the {\it emergent} gravity, the gravitational (metric) field $g_\mn$ is not taken as the quantum-field, but as the background field. The statistical fluctuation effect of the metric field is taken into account by the path (hyper-surface)-integral over the space-time. Using a simple scalar model on the curved (dS$_4$) space-time, we explain the above things with the following additional points: 1) Clear separate treatment of the classical effect, the statistical effect and the quantum effect; 2) The cosmological fluctuation comes not from the 'quantum' gravity but from the unkown 'microscopic' movement; 3) IR parameter ($\ell$) is introduced for the time axis as the periodicity. Time reversal(Z$_2$)-symmetry is introduced in order to treat the problem separately with respect to the Z$_2$ parity. This procedure much helps both UV and IR regularization to work well.

hep-th↗

arXiv2013

Velocity-Field Theory, Boltzmann's Transport Equation and Geometry

Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. {\it Fluctuation} is examined, and is clearly discriminated from the quantum effect. The time variable is {\it emergently} introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does {\it not} conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.

hep-th↗

arXiv2013

Renormalization Group Approach to Dissipative System

In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a new method which has the following characteristic points: 1) the geometrical approach to the statistical mechanical system; 2) the continuum approach using Feynman's path integral (generalized version); 3) the holographic (higher-dimensional) approach; 4) the renormalization phenomenon takes place in order to treat the statistical fluctuation.

hep-th↗

arXiv2012

Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance

Electromagnetism in substance is characterized by permittivity (dielectric constant) and permeability (magnetic permeability). They describe the substance property {\it effectively}. We present a {\it geometric} approach to it. Some models are presented, where the two quantities are geometrically defined. Fluctuation due to the micro dynamics (such as dipole-dipole interaction) is taken into account by the (generalized) path-integral. Free energy formula (Lifshitz 1954), for the material composed of three regions with different permittivities, is explained. Casimir energy is obtained by a new regularization using the path-integral. Attractive force or repulsive one is determined by the sign of the {\it renormalization-group} $β$-function.

cond-mat.mes-hall↗

arXiv2012

Casimir Energy of the Universe and the Dark Energy Problem

We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function ($\be$-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.

hep-th↗

arXiv2011

Geometric Approach to Quantum Statistical Mechanics and Minimal Area Principle

A geometric approach to some quantum statistical systems (including the harmonic oscillator) is presented. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$τ$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {\it Euclidean time} variable ($τ$). Introducing a path (line or hypersurface) in this space (X$^i$,$τ$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {\it mechanical} system. It is inspired by the {\it extra dimensional model}, appearing in the unified theory of forces including gravity, using the bulk-boundary configuration. The system Hamiltonian appears as the {\it area}. We show quantization is realized by the {\it minimal area principle} in the present geometric approach. When we take a {\it line} as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a {\it hyper-surface} as the path, the system Hamiltonian is given by the {\it area} of the {\it hyper-surface} which is defined as a {\it closed-string configuration} in the bulk space. In this case, the system becomes a O(N) non-linear model. The two choices,\ (1) the {\it line element} in the bulk ($X^i,τ$) and (2) the Hamiltonian(defined as the damping functional in the path-integral) specify the system dynamics. After explaining this new approach, we apply it to a topic in the 5 dimensional quantum gravity. We present a {\it new standpoint} about the quantum gravity: (a)\ The metric (gravitational) field is treated as the background (fixed) one;\ (b)\ The space-time coordinates are not merely position-labels but are quantum (statistical) variables by themselves. We show the recently-proposed 5 dimensional Casimir energy is valid.

hep-th↗

arXiv2011

Renormalization Group Flow and the Dark Energy Problem

Casimir energy is calculated for 5D scalar theory in the {\it warped} geometry. A new regularization, called {\it sphere lattice regularization}, is taken. The regularized configuration is {\it closed-string like}. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, extra space UV-boundary parameter) and $T$(extra space IR-boundary parameter) dependence of Casimir energy. 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} $\om$ suffers from the {\it renormalization effect}. Regarding Casimir energy as the main contribution to the cosmological term, we examine the dark energy problem.

hep-th↗

arXiv2010

Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$τ$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {\it Euclidean time} variable ($τ$). Introducing paths (lines or hypersurfaces) in this space (X$^i$,$τ$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {\it mechanical} system. The system Hamiltonian appears as the {\it area}. We show quantization is realized by the {\it minimal area principle} in the present geometric approach. When we take a {\it line} as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a {\it hyper-surface} as the path, the system Hamiltonian is given by the {\it area} of the {\it hyper-surface} which is defined as a {\it closed-string configuration} in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.

hep-th↗

arXiv2010

New Regularization in Extra Dimensional Model and Renormalization Group Flow of the Cosmological Constant

Casimir energy is calculated for 5D scalar theory in the {\it warped} geometry. A new regularization, called {\it sphere lattice regularization}, is taken. The regularized configuration is {\it closed-string like}. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of Casimir energy. 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} $\om$ suffers from the {\it renormalization effect}. We examine the cosmological constant problem.

hep-th↗

arXiv2010

Casimir Energy of 5D Warped System and Sphere Lattice Regularization

Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory in the {\it warped} geometry. It is compared with the flat case(arXiv:0801.3064). A new regularization, called {\it sphere lattice regularization}, is taken. In the integration over the 5D space, we introduce two boundary curves (IR-surface and UV-surface) based on the {\it minimal area principle}. It is a {\it direct} realization of the geometrical approach to the {\it renormalization group}. The regularized configuration is {\it closed-string like}. We do {\it not} take the KK-expansion approach. Instead, the position/momentum propagator is exploited, combined with the {\it heat-kernel method}. All expressions are closed-form (not KK-expanded form). The {\it generalized} P/M propagators are introduced. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of the Casimir energy. We present two {\it new ideas} in order to define the 5D QFT: 1) the summation (integral) region over the 5D space is {\it restricted} by two minimal surfaces (IR-surface, UV-surface) ; or 2) we introduce a {\it weight function} and require the dominant contribution is given by the {\it minimal surface}. Based on these, 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} $\om$ suffers from the {\it renormalization effect}. We examine the meaning of the weight function and reach a {\it new definition} of the Casimir energy where {\it the 4D momenta(or coordinates) are quantized} with the extra coordinate as the Euclidean time (inverse temperature). We comment on the cosmological constant term and present an answer to the problem at the end. Dirac's large number naturally appears.

hep-th↗

arXiv2010

Casimir Energy of the Universe and New Regularization of Higher Dimensional Quantum Field Theories

Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory in the {\it warped} geometry. It is compared with the flat case. A new regularization, called {\it sphere lattice regularization}, is taken. In the integration over the 5D space, we introduce two boundary curves (IR-surface and UV-surface) based on the {\it minimal area principle}. It is a {\it direct} realization of the geometrical approach to the {\it renormalization group}. The regularized configuration is {\it closed-string like}. We do {\it not} take the KK-expansion approach. Instead, the position/momentum propagator is exploited, combined with the {\it heat-kernel method}. All expressions are closed-form (not KK-expanded form). The {\it generalized} P/M propagators are introduced. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of the Casimir energy. We present two {\it new ideas} in order to define the 5D QFT: 1) the summation (integral) region over the 5D space is {\it restricted} by two minimal surfaces (IR-surface, UV-surface) ; or 2) we introduce a {\it weight function} and require the dominant contribution, in the summation, is given by the {\it minimal surface}. Based on these, 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} $\om$ suffers from the {\it renormalization effect}. The IR parameter $T$ does not. We examine the meaning of the weight function and finally reach a {\it new definition} of the Casimir energy where {\it the 4D momenta(or coordinates) are quantized} with the extra coordinate as the Euclidean time (inverse temperature). We examine the cosmological constant problem and present an answer at the end. Dirac's large number naturally appears.

hep-th↗

arXiv2009

Casimir Energy of 5D Electromagnetism and New Regularization Based on Minimal Area Principle

We examine the Casimir energy of 5D electromagnetism in the recent standpoint. The bulk geometry is flat. Z$_2$ symmetry and the periodic property, for the extra coordinate, are taken into account. After confirming the consistency with the past result, we do new things based on a {\it new regularization}. In the treatment of the divergences, we introduce IR and UV cut-offs and {\it restrict} the (4D momentum, extra coordinate)-integral region. The regularized configuration is the {\it sphere lattice}, in the 4D continuum space, which changes along the extra coordinate. The change (renormalization flow) is specified by the {\it minimal area principle}, hence this regularization configuration is string-like. We do the analysis not in the Kaluza-Klein expanded form but in a {\it closed} form. We do {\it not} use any perturbation. The formalism is based on the heat-kernel approach using the {\it position/momentum propagator}. Interesting relations between the heat-kernels and the P/M propagators are obtained, where we introduce the {\it generalized} P/M propagators. A useful expression of the Casimir energy, in terms of the P/M propagator, is obtained. The restricted-region approach is replaced by the weight-function approach in the latter-half description. Its meaning, in relation to the {\it space-time quantization}, is argued. {\it Finite} Casimir energy is numerically obtained. The compactification-size parameter (periodicity) suffers from the renormalization effect. Numerical evaluation is exploited. Especially the minimal surface lines in the 5D flat space are obtained both numerically using the Runge-Kutta method and analytically using the general solution.

hep-th↗

arXiv2008

Casimir Energy of 5D Electro-Magnetism and Sphere Lattice Regularization

Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called {\it sphere lattice regularization}, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do {\it not} take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warpedness parameter) and $T$(extra space IR parameter) dependence.

hep-th↗

arXiv2007

Casimir and Vacuum Energy of 5D Warped System and Sphere Lattice Regularization

We examine the Casimir energy of 5D electro-magnetism in the recent standpoint. Z$_2$ symmetry is taken into account. After confirming the consistency with the past result, we do new things based on a new regularization. The regularization is based on the minimal area principle and the regularized configuration is the {\it sphere lattice}. We do it not in the Kaluza-Klein expanded form but in the closed form. The formalism is based on the heat-kernel approach using the position/momentum propagator. A useful expression of the Casimir energy, in terms of the P/M propagator, is obtained. Renormalization flow is realized as the change along the extra-axis.

hep-th↗

arXiv2007

Graphical Representation of SUSY and Application to QFT

We present a graphical representation of the supersymmetry and the graphical calculation. Calculation is demonstrated for 4D Wess-Zumino model and for Super QED. The chiral operators are graphically expressed in an illuminating way. The tedious part of SUSY calculation, due to manipulating chiral suffixes, reduces considerably. The application is diverse.

hep-th↗

arXiv2007

CP Violation from a Higher Dimensional Model

It is shown that Randall-Sundrum model has the EDM term which violates the CP-symmetry. The comparison with the case of Kaluza-Klein theory is done. The chiral property, localization, anomaly phenomena are examined. We evaluate the bulk quantum effect using the method of the induced effective action. This is a new origin of the CP-violation.

hep-th↗