arXiv subjects

Kazuo Fujikawa

Publications and source records attributed to Kazuo Fujikawa.

136 records · Page 8Linked to original sources

arXiv1996

Phase operator problem and an index theorem for Q-deformed oscillator

The notion of index is applied to analyze the phase operator problem associated with the photon. We clarify the absence of the hermitian phase operator on the basis of an index consideration. We point out an interesting analogy between the phase operator problem and the chiral anomaly in gauge theory, and an appearance of a new class of quantum anomaly is noted. The notion of index, which is invariant under a wide class of continuous deformation, is also shown to be useful to characterize the representations of Q-deformed oscillator algebra.

hep-th↗

arXiv1995

Gribov Problem and BRST Symmetry

After a brief historical comment on the study of BRS(or BRST) symmetry , we discuss the quantization of gauge theories with Gribov copies. A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very specific way if the functional correspondence between $τ$ and the gauge parameter $ω$ defined by $τ(x) = f( A_μ^ω(x))$ is ``globally single valued'', where $f( A_μ^ω(x)) = 0 $ specifies the gauge condition. As an example of the theory which satisfies this criterion, we comment on a soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren. We also comment on a possible connection of the dynamical instability of BRST symmetry with the Gribov problem on the basis of an index notion.

hep-th↗

arXiv1995

BRST Symmetric Formulation of a Theory with Gribov-type Copies

A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very specific way if the functional correspondence between $τ$ and the gauge parameter $ω$ defined by $τ(x) = f( A_μ^ω)$ is ``globally single valued'', where $f( A_μ^ω) = 0 $ specifies the gauge condition. A soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren satisfies this criterion. A detailed BRST analysis of the soluble model proposed by the above authors is presented. The BRST symmetry, if it is consistently implemented, ensures the gauge independence of physical quantities. In particular, the vacuum (ground) state and the perturbative corrections to the ground state energy in the above model are analysed from a view point of BRST symmetry and $R_ξ$-gauge. Implications of the present analysis on some aspects of the Gribov problem in non-Abelian gauge theory, such as the $1/N$ expansion in QCD and also the dynamical instability of BRST symmetry, are briefly discussed.

hep-th↗

arXiv1995

Phase operator for the photon, an index theorem, and quantum anomaly

An index relation $dim\ ker\ a - dim\ ker\ a^{\dagger} = 1$ is satisfied by the creation and annihilation operators $a^{\dagger}$ and $a$ of a harmonic oscillator. Implications of this analytic index on the possible form of the phase operator are discussed. A close analogy between the present phase operator problem and chiral anomaly in gauge theory, which is associated with Atiyah-Singer index theorem, is emphasized.

hep-th↗

arXiv1995

Q-Deformed Oscillator Algebra and an Index Theorem for the Photon Phase Operator

The quantum deformation of the oscillator algebra and its implications on the phase operator are studied from a view point of an index theorem by using an explicit matrix representation. For a positive deformation parameter $q$ or $q=exp(2πiθ)$ with an irrational $θ$, one obtains an index condition $\dml a - \dml a^{\dagger} = 1$ which allows only a non-hermitian phase operator with $\dml \expon^{i φ} - \dml (\expon^{iφ})^{\dagger} = 1$. For $q=exp(2πiθ)$ with a rational $θ$ , one formally obtains the singular situation $\dml a =\infty$ and $ \dml a^{\dagger} = \infty$, which allows a hermitian phase operator with $\dml \expon^{i Φ} - \dml (\expon^{iΦ})^{\dagger} = 0$ as well as the non-hermitian one with $\dml \expon^{i φ} - \dml (\expon^{iφ})^{\dagger} = 1$. Implications of this interpretation of the quantum deformation are discussed. We also show how to overcome the problem of negative norm for $q=exp(2πiθ)$.

hep-th↗

arXiv1995

Analytic index and chiral fermions

A recent application of an index relation of the form, $dim\ ker\ M - dim\ ker\ M^{\dagger} = ν$, to the generation of chiral fermions in a vector-like gauge theory is reviewed. In this scheme the chiral structure arises from a mass term with a non-trivial index.The essence of the generalized Pauli-Villars regularization of chiral gauge theory, which is based on this mechanism, is also clarified.

hep-th↗

arXiv1995

Phase Operator for the Photon Field and an Index Theorem

An index relation $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 1$ is satisfied by the creation and annihilation operators $a^{\dagger}$ and $a$ of a harmonic oscillator. A hermitian phase operator, which inevitably leads to $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 0$, cannot be consistently defined. If one considers an $s+1$ dimensional truncated theory, a hermitian phase operator of Pegg and Barnett which carries a vanishing index can be defined. However, for arbitrarily large $s$, we show that the vanishing index of the hermitian phase operator of Pegg and Barnett causes a substantial deviation from minimum uncertainty in a characteristically quantum domain with small average photon numbers. We also mention an interesting analogy between the present problem and the chiral anomaly in gauge theory which is related to the Atiyah-Singer index theorem. It is suggested that the phase operator problem related to the above analytic index may be regarded as a new class of quantum anomaly. From an anomaly view point ,it is not surprising that the phase operator of Susskind and Glogower, which carries a unit index, leads to an anomalous identity and an anomalous commutator.

hep-th↗

arXiv1994

A Vector-like Extension of the Standard Model

A vector-like extension of the standard model for heavier quarks and leptons with $SU(2)\times U(1)$ gauge symmetry and only one Higgs doublet is examined. This scheme incorporates infinitely many fermions and avoids the appearance of a strongly interacting sector. The model is perturbatively well controllable, and constraints such as $b\rightarrow sγ$ and GIM suppression in general are naturally satisfied if the on-set of heavier fermion mass scale is chosen at a few TeV. In this scheme, the physical Higgs particle generally mediates leptonic as well as quark flavor-changing processes at a rate below the present experimental limit. Vector-like models, if suitably defined, provide a viable and interesting scheme for physics beyond 1 TeV.

hep-ph↗

arXiv1994

Generalized Pauli-Villars Regularization and the Covariant Form of Anomalies

In the generalized Pauli-Villars regularization of chiral gauge theory proposed by Frolov and Slavnov , it is important to specify how to sum the contributions from an infinite number of regulator fields. It is shown that an explicit sum of contributions from an infinite number of fields in anomaly-free gauge theory essentially results in a specific choice of regulator in the past formulation of covariant anomalies. We show this correspondence by reformulating the generalized Pauli- Villars regularization as a regularization of composite current operators. We thus naturally understand why the covariant fermion number anomaly in the Weinberg-Salam theory is reproduced in the generalized Pauli-Villars regularization. A salient feature of the covariant regularization,which is not implemented in the lagrangian level in general but works for any chiral theory and gives rise to covariant anomalies , is that it spoils the Bose symmetry in anomalous theory. The covariant regularization however preserves the Bose symmetry as well as gauge invariance in anomaly-free gauge theory.

hep-th↗

arXiv1993

Constraints on left-right symmetric models from the process $b \rightarrow s γ$

In left-right symmetric models, large contributions to the decay amplitude $b \rightarrow s+ γ$ can arise from the mixing of the $W_L$ and $W_R$ gauge bosons as well as from the charged Higgs boson. These amplitudes are enhanced by the factor $\mt/\mb$ compared to the contributions in the standard model. We use the recent CLEO results on the radiative $B$ decay to place constraints on the $W_L-W_R$ mixing angle $ζ$ and the mass of the charged Higgs boson $m_{H^\pm}$. Significant departures from the standard model predictions occur when $|ζ| > 0.003$ and/or when $m_{H^\pm} < $ a few TeV.

hep-ph↗