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Tadafumi Ohsaku

Publications and source records attributed to Tadafumi Ohsaku.

At least 19 recordsLinked to original sources
arXiv2013

The Anomalous Nambu-Goldstone Theorem in Relativistic/Nonrelativistic Quantum Field Theory

The anomalous Nambu-Goldstone (NG) theorem which is found as a violation of counting law of the number of NG bosons of the normal NG theorem in nonrelativistic and Lorentz-symmetry-violated relativistic theories is studied in detail, with emphasis on its mathematical aspect from Lie algebras, geometry to number theory. The basis of counting law of NG bosons in the anomalous NG theorem is examined by Lie algebras (local) and Lie groups (global). A quasi-Heisenberg algebra is found generically in various symmetry breaking schema of the anomalous NG theorem, and it indicates that it causes a violation/modification of the Heisenberg uncertainty relation in an NG sector which can be experimentally confirmed. The formalism of effective potential is presented for understanding the mechanism of anomalous NG theorem with the aid of our result of Lie algebras. After an investigation on a bosonic kaon condensation model with a finite chemical potential as an explicit Lorentz-symmetry-breaking parameter, a model Lagrangian approach on the anomalous NG theorem is given for our general discussion. Not only the condition of the counting law of true NG bosons, but also the mechanism to generate a mass of massive NG boson is also found by our examination on the kaon condensation model. Furthermore, the generation of a massive mode in the NG sector is understood by the quantum uncertainty relation of the Heisenberg algebra, obtained from a symmetry breaking of a Lie algebra, which realizes in the effective potential of the kaon condensation model. Hence the relation between a symmetry breaking scheme, a Heisenberg algebra, a mode-mode coupling, and the mechanism of mass generation in an NG sector is established. Finally, some relations between the Riemann hypothesis and the anomalous NG theorem are presented.

physics.gen-ph↗
arXiv2010

Dynamical Mass Generations and Collective Excitations in the (Supersymmetric-)Nambu$-$Jona-Lasinio Model and a Gauge Theory with Left-Right-Asymmetric Majorana Mass Terms

The structure of effective potential surface of the Nambu$-$Jona-Lasinio (NJL) model with right-left asymmetric Majorana mass terms (corresponds to the single-flavor type-II seesaw situation of neutrino) is investigated. After the dynamical generation of Dirac mass, two collective modes appear similar to the case of ordinary NJL model, and the phase mode (phason), which corresponds to majoron or pion at vanishing Majorana mass parameter(s), has an excitation mass. The mechanism of generation of phason as a pseudo Nambu-Goldstone boson is examined by a mathematical manner, summarized into a theorem (claims as the generalized Nambu-Goldstone theorem). The mass of phason is also evaluated in a supersymmetric version of the NJL-type model, and phason mass takes the order of that of axion commonly accepted today. An $SU(2_{c})$-gauge model is constructed for the context of neutrino seesaw mechanism, and the Schwinger-Dyson equation of dynamical mass functions is examined. Several physical implications such as decay modes of phason, a non-linear sigma model for phason are given. It is proposed that the method/result of this paper can be applied to an understanding on the origin of the Kobayashi-Maskawa matrix.

hep-ph↗
arXiv2008

Generalized Seesaw Mechanism of Neutrino and Bose-Einstein Condensation in the Modified O'Raifeartaigh Model

The modified O'Raifeartaigh model from the context of the generalized seesaw mechanism of neutrino mass is investigated. In our evaluation of effective potentials of the theory, both the component field and the superspace formalisms to approach the problem are presented. In the component field formalism, we take into account the Bose-Einstein condensates in the scalar sector by the method of many-boson theory, i.e. we consider both the condensates and the Hartree-Fock-Bogoliubov-type self-energies of quantum fluctuations. The diagonalization of the mass matrix of the fermion sector gives the same functional forms of the mass eigenvalues in the generalized seesaw mechanism. The stability condition in the vicinity of the classical vacuum which shows the generalized seesaw situation is obtained by the examination of the mass eigenvalues of the scalar sector of the model. The superspace formalism will be devoted to a comparison between its result with that of the component field formalism.

hep-ph↗
arXiv2008

Relativistic BCS Theory in Quasi-(2+1)-Dimensions: Effects of an Inter-layer Transfer in the Honeycomb Lattice Symmetry

Motivated by recent huge interests on graphene sheet and graphite as "relativistic" systems, a BCS superconductivity in a quasi-(2+1)-dimensional relativistic model is investigated. The intra-layer particle dynamics is described by a (2+1)-dimensional Gross-Neveu-type four-body contact interaction model, while inter-layer particle motions will be caused by a hopping term with a transfer parameter $t$. Especially, we examine the effects of non-vanishing $t$, chemical potential $μ$, and a mass parameter $m$ which will give a gap at a conical intersection point of the relativistic band dispersion, in the BCS s-wave (scalar) superconducting gap function $Δ$.

cond-mat.supr-con↗
arXiv2008

Dynamical Dirac Mass Generation in the Supersymmetric Nambu--Jona-Lasinio Model with the Seesaw Mechanism of Neutrinos

The dynamical generation of Dirac mass in the supersymmetric Nambu$-$Jona-Lasinio (SNJL) model with the seesaw mechanism of neutrino is investigeted. The right and left handed Majorana mass parameters are introduced into the SNJL model; we regard them as external model parameters. The question on the origin of these Majorana masses are set aside, and we concentrate on the examination of the effect of the Majorana mass parameters on the dynamical generation of Dirac mass. The effective potential of the model and the gap equation for the self-consistent determination of Dirac mass are derived and solved. We use both the four-dimensional covariant and three-dimensional non-covariant cutoff schemes for the regularizations of the effective potential. We find there are cases of the first and second order phase transitions with respect to variation of the coupling constant of the Nambu$-$Jona-Lasinio-type four-body interaction of the SNJL model. In the case of second-order phase transition, the dynamically generated Dirac mass $|ϕ_{S}|$ can arbitrarily be small compared with the right-handed Majorana mass parameter $|M|$ and thus the seesaw condition $0<|ϕ_{S}|\ll|M|$ can be satisfied by a fine tuning of the coupling constant, while at the first-order case it seems very difficult and/or "unnatural" to satisfy the condition. The numerical results do not depend on the difference of the cutoff schemes qualitatively.

hep-ph↗
arXiv2008

Dynamical Chiral Symmetry Breaking and Superconductivity in the Supersymmetric Nambu$-$Jona-Lasinio Model at finite Temperature and Density

We investigate the dynamical chiral symmetry breaking (DCSB) and superconductivity in a supersymmetric model at finite temperature and density. We employ the ${\cal N}=1$ four-dimensional generalized supersymmetric Nambu$-$Jona-Lasinio model (${\cal N}=1$ generalized ${\rm SNJL}_{4}$) with a chemical potential as the model Lagrangian, and select the gauge freedom as U(1). In order to realize the DCSB and BCS-type superconductivity in this model, we introduce a SUSY soft mass term. Under the finite-temperature Matsubara formalism, the effective potential and the gap equations are derived in the flamework of the large-N expansion. The finite-density effect in the DCSB is shown by the critical coupling. The roles of both the boson and fermion sectors in the superconductivity are examined by the quasiparticle excitation spectra and the gap equations.

hep-ph↗
arXiv2008

Dynamical Chiral Symmetry Breaking, Color Superconductivity, and Bose-Einstein Condensation in an $SU(N_{c})\times U(N_{f})_{L}\times U(N_{f})_{R}$-invariant Supersymmetric Nambu$-$Jona-Lasinio Model

We investigate the phenomena of the dynamical chiral symmetry breaking (DCSB), color superconductivity (CSC), and Bose-Einstein condensation (BEC) in an ${\cal N}=1$ four-dimensional generalized SUSY Nambu$-$Jona-Lasinio model at finite temperature and density. Both the ${\cal N}=1$ four-dimensional and ${\cal N}=2$ three-dimensional cases are considered. The ${\cal N}=2$ three-dimensional theory is obtained by a simple dimensional reduction scheme of the four-dimensional counterpart. In order to realize the DCSB and BCS-type CSC in this model, we introduce a SUSY soft mass term. After adopting the method of SUSY auxiliary fields with the Fierz transformation in color and flavor spaces, we discuss several possible breaking schemes of the global symmetries of the model. The integrations of the auxiliary fields of composites in the effective potential are performed by using the steepest descent approximation. The roles of both the boson and fermion sectors in the BEC, DCSB and CSC are examined by the quasiparticle excitation spectra and the gap equations. The physical properties of the DCSB and the CSC are studied in detail, while that of the BEC is beyond scope of this paper. It is found that the BEC, DCSB and CSC can coexist under a condition of model parameters.

hep-ph↗
arXiv2008

Supersymmetric Nambu$-$Jona-Lasinio Model on ${\cal N}=1/2$ four-dimensional Non(anti)commutative Superspace

We construct the Lagrangian of the ${\cal N}=1$ four-dimensional generalized supersymmetric Nambu$-$Jona-Lasinio (SNJL) model, which has ${\cal N}=1/2$ supersymmetry (SUSY) on non(anti)commutative superspace. A special attention is paid to the examination on the nonperturbative quantum dynamics: The phenomenon of dynamical-symmetry-breaking/mass-generation on the deformed superspace is investigated. The model Lagrangian and the method of SUSY auxiliary fields of composites are examined in terms of component fields. We derive the effective action, examine it, and solve the gap equation for self-consistent mass parameters.

hep-th↗
arXiv2007

Dynamical Symmetry Breaking of a Relativistic Model in Quasi-(1+1)-Dimensions. I. Formulation

The dynamical symmetry breaking in a quasi-(1+1)-dimensional relativistic model is investigated. The motions of particles in intrachain are described as a relativistic electron-hole gas, while the interchain hopping term is introduced as a 0th-component of vector in (1+1)-dimensions, a kind of chemical potential of the system. The gauge symmetry of the model is chosen as U(1) suitable for a possible situation of a real substance in condensed matter physics. We consider the BCS-type contact interactions for the s-wave fermion-pair condensates, while employ the nonlocal interactions of the generalized BCS framework to generate the $p$-, $d$- and $f$-wave condensations in the system. Especially we examine the dynamical generation of a Dirac mass term and superconductivity in the model. The phenomenon is interpreted as metal-insulator/metal-superconductor phase transitions.

cond-mat.supr-con↗
arXiv2006

Algebra of Noncommutative Riemann Surfaces

We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into that of a complex coordinate system. The basis of noncommutative complex analysis is obtained thoroughly, and the considerations on functional analysis are also given before performing the examination of the conformal mapping and the Teichmüller theory. (Keywords; Complex Analysis, Riemann Surfaces and Teichmüller Space, Functional Analysis, Deformation Quantization, Non-Commutative Geometry, Quantum Groups)

math-ph↗
arXiv2004

Dynamical Chiral Symmetry Breaking and its Restoration for an Accelerated Observer

Based on the Hawking-Unruh thermalization theorem, we investigate the phenomenon of the dynamical chiral symmetry breaking and its restoration for a uniformly accelerated observer. We employ the Nambu$-$Jona-Lasinio model in Rindler coordinates, and calculate the effective potential and the gap equation. The critical coupling and the critical acceleration for symmetry restoration are obtained.

hep-th↗
arXiv2003

Relativistic Model of two-band Superconductivity in (2+1)-dimension

We investigate the relativistic model of superconductivity in (2+1)-dimension. We employ the massless Gross-Neveu model at finite temperature and density, to study the superconductivity and superconducting instability. Our investigation is related to the superconductivity in (2+1)-dimensional two-band systems like ${\rm MgB_{2}}$ or intercalated graphite.

cond-mat.supr-con↗
arXiv2003

Relativistic Model for two-band Superconductivity

To understand the superconductivity in MgB2, several two-band models of superconductivity were proposed. In this paper, by using the relativistic fermion model, we clearize the effect of the lower band in the superconductivity.

cond-mat.supr-con↗