arXiv subjects

Takehisa Fujita

Publications and source records attributed to Takehisa Fujita.

31 records · Page 2Linked to original sources

arXiv2003

No Goldstone boson in NJL and Thirring models

We present an intuitive picture of the chiral symmetry breaking in the NJL and Thirring models. For the current current interaction model with the massless fermion, the vacuum is realized with the chiral symmetry broken phase, and the fermion acquires the induced mass. With this finite fermion mass, we calculate the boson mass, and find that the boson is always massive, and there exists no Goldstone boson in the Nambu-Jona-Lasinio (NJL) model.

hep-th↗

arXiv2003

No massless boson in chiral symmetry breaking in NJL and Thirring models

We show that the chiral symmetry breaking occurs in the vacuum of the massless Nambu-Jona-Lasinio (NJL) and Thirring models without a Goldstone boson. The basic reason of non-existence of the massless boson is due to the fact that the new vacuum after the symmetry breaking acquires nonzero fermion mass which inevitably leads to massive bosons. The new vacuum has a finite condensate of $<\bar ψψ>$ with the chiral current conservation. Thus, it contradicts the Goldstone theorem, and we show that the proof of the Goldstone theorem cannot be justified any more for fermion field theory models with regularizations.

hep-th↗

arXiv2003

New spectrum and condensate in two dimensional QCD

The boson mass and the condensate in two dimensional QCD with $SU(N_c)$ colors are numerically evaluated with the Bogoliubov vacuum. It is found that the boson mass is finite at the massless limit, and it is well described by the phenomenological expression $ {\cal M}_{N_c}={2\over 3}\sqrt{N_cg^2\over{3π}} $ for large $N_c$. Also, the condensate values agree very well with the prediction by the $1/N_c$ expansion. The validity of the naive light cone method is examined, and it turns out that the light cone prescription of the boson mass with the trivial vacuum is accidentally good for QED$_2$. But it is not valid for QCD$_2$. Further, at the massless fermion limit, the chiral symmetry is spontaneouly broken without anomaly, and the Goldstone theorem does not hold for QCD$_2$.

hep-th↗

arXiv2002

Bound State Spectrum of Massive Thirring Model in Rest Frame

The bound state spectrum of the massive Thirring model is studied in the framework of the canonical quantization in the rest frame. First, we quantize the field with the massless free fermion basis states. Then, we make a Bogoliubov transformation. This leads to the natural mass renormalization. The bound state spectrum is analytically solved by the $q\bar{q}$ Fock space. It is found that the spectrum has the right behaviors both for the weak and for the strong coupling limits after the appropriate wave function regularization. This regularization is quite clear and the treatment is self-consistent for the bound state problem compared to other regularizations. Further, we show that the interaction between $q\bar{q}$ bosons is always repulsive and therefore there is no bound state in the four fermion ($qq \bar q \bar q$) Fock space. This confirms that there is only one bound state in the massive Thirring model.

hep-th↗

arXiv2002

Possible Suppression of Neutron EDM

Employing generalized Schiff's transformation on electric dipole moments (EDM) in quantum field theory, we show that the chromoelectric EDM lagrangian density is transformed into the electric EDM term with a new coefficient. Under the new constraint on the EDM operators, the neutron EDM can be described by a unique combination of electric EDM $d_f$ and chromoelectric EDM ${\tilde d}_f $ of quarks. If the special relation of $\displaystyle{d_f={e_f\over{2g_s}}{\tilde d}_f}$ holds, then the neutron EDM is suppressed significantly.

hep-ph↗

arXiv1998

Violation of S-matrix factorization in massive Thirring model

We present a counter example which shows the violation of the S-matrix factorization in the massive Thirring model. This is done by solving the PBC equations of the massive Thirring model exactly but numerically. The violation of the S-matrix factorization is related to the fact that the crossing symmetry and the factorization do not commute with each other. This confirms that the soliton antisoliton S-matrix factorization picture of the sine-Gordon model is semiclassical and does not lead to a full quantization procedure of the massive Thirring model.

hep-th↗

arXiv1998

Hyperfine Anomaly of Be Isotopes and Anomalous Large Anomaly in $^{11}$Be

A new result of investigations of the hyperfine structure (hfs) anomaly in Be isotopes is presented. The hfs constant for $^{11}$Be is obtained by using the core plus neutron type wave function: $ |2s_{1\over 2}>+|1d_{5\over2}\times 2^+ ; {1/2}^{+}> $. A large hfs anomaly of $^{11}$Be is found, which is mainly due to a large radius of the halo single particle state.

nucl-th↗

arXiv1998

g-factor of a tightly bound electron

We study the hyperfine splitting of an electron in hydrogen-like $^{209}Bi ^{82+} $. It is found that the hfs energy splitting can be explained well by considering the g-factor reduction due to the binding effect of a bound electron. We determine for the first time the experimental value of the magnetic moment of a tightly bound electron.

nucl-th↗

arXiv1997

Reexamination of standard solar model to the solar neutrino problems

We examine the calculation of the solar neutrino flux based on the standard solar model (SSM). It is found that the solar neutrino data (KAMIOKANDE experiment) can be well described by the SSM with careful employment of nuclear data of $^7Be (p,γ) ^{8} B$. The main point is that the simple-minded product ansatz of Coulomb plus nuclear parts should have a few percent uncertainties which induce the large reduction of the neutrino flux from $^8 B$. Also, if the electron capture of $^7 Be$ inside the sun is suppressed, then the GALLEX experiment can be understood by the SSM calculation.

astro-ph↗

arXiv1997

Finite size corrections in massive Thirring model

We calculate for the first time the finite size corrections in the massive Thirring model. This is done by numerically solving the equations of periodic boundary conditions of the Bethe ansatz solution. It is found that the corresponding central charge extracted from the $1/L$ term is around 0.4 for the coupling constant of ${g_0}=-{π\over 4} $ and decreases down to zero when ${g_0}=-{π\over{3}}$. This is quite different from the predicted central charge of the sine-Gordon model.

hep-th↗

arXiv1997

Hyperfine Structure Constants for Eu Isotopes: Is The Empirical Formula of HFS Anomaly Universal ?

We calculate the hyperfine structure constant for the Eu isotopes with shell model wave functions. The calculated results are compared with those predicted by the Moskowitz-Lombardi (M-L) empirical formula. It turns out that the two approaches give the very different behaviors of the hfs constants in the isotope dependence. This should be easily measured by experiment, which may lead to the universality check of the M-L formula.

nucl-th↗

arXiv1996

Bound states of 1+1 dimensional field theories

We discuss the bound states of the massive Thirring model. Here, the periodic boundary condition equations for the Bethe ansatz solutions are numerically solved. It is found that the massive Thirring model has only one bound state and the bound state spectrum as the function of the coupling constant agrees with that of infinite momentum frame prescription by Fujita and Ogura. Boson boson states (2p$-$2h states) appear only as the continuum spectrum without making any bound states. Further, the finite size correction to the vacuum energy is estimated. The evaluated central charge is found to be close to unity.

hep-th↗

arXiv1996

A new interpretation of Bethe ansatz solutions for massive Thirring model

We reexamine Bethe ansatz solutions of the massive Thirring model. We solve equations of periodic boundary conditions numerically without referring to the density of states. It is found that there is only one bound state in the massive Thirring model. The bound state spectrum obtained here is consistent with Fujita-Ogura's solutions of the infinite momentum frame prescription. Further, it turns out that there exist no solutions for string-like configurations. Instead, we find boson boson scattering states in 2-particle 2-hole configurations where all the rapidity variables turn out to be real.

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