Toshiei Kimura

Antisymmetric Tensor Gauge Field in General Covariant Gauges

Recently, Townsend has shown that there exist similarity and dissimilarity between the mode counting of spin 3/2 field and that of antisymmetric tensor gauge field. 11 Especially, one cannot find a mechanism of introducing extra two modes in contrast to the case of spin 3/2 theory where an additional extra Majorana spinor ghost has been introduced by Nielsen. 21 Nielsen adopted the ordinary form of Faddeev-Popov (FP) ghosts c*(rD)c+N(rD)N. On the other hand, Rata iand Kugo 31 have proposed a new formalism of supergravity by adopting the unconventional form of FP ghost ic*(ro) (rD)c. Since the ghosts c and c* of Hata-Kugo obey the second order differential equations, all their components are independent and give rise to eight modes of FP ghosts. There should then exist eight unphysical modes of spin 3/2 field sector which compensate eight modes of FP ghosts. Such an unphysical sector is constructed by introducing the Lagrangian multiplier spinor field B which plays a role of fixing the gauge. The unphysical modes consist of four longitudinal components of cj; 11 and four components of B, and their number is equal to that of FP ghosts. Fronsdal and Hata41 have further shown that such a type of formalism is necessary to construct the interacting theory of higher spin fields so that the unitarity ,:of the physical S-matrix is assured. The present author 51 has also shown that the axial anomaly for the gravitino in the background curved space is obtained by B field not by ghost fields in Hata-Kugo formalism. It is, therefore, desirable to discuss the mode counting of the quantized antisymmetric tensor gauge field by introducing the Lagrangian multiplier fields. We shall start with the following Lagrangian :

A dynamical formalism of singular Lagrangian system with higher derivatives

The singular Lagrangian system with higher derivatives is analyzed with the aid of the Ostrogradski transformation and the Dirac formalism. The formulation of canonical theory is developed so that the equivalence between the Lagrange formalism and the Hamilton one is maintained. As a practical example, the acceleration‐dependent potentials appearing in the Lagrangian of two‐point particles interacting gravitationally are dealt with and the equivalence between the two Hamiltonians that follow from the two Lagrangians which are related by the coordinate transformations is shown. It is also shown, when the constraints are all first class, that a consistent generator of gauge transformation is constructed. Typical examples are given.

Gauge transformations and gauge-fixing conditions in constraint systems

Gauge transformations and gauge-fixing conditions in the total Hamiltonian (HT) and extended Hamiltonian (HE) formalisms are investigated. For gauge-fixing conditions χα, only the condition det({ϕα, χβ}) ≠ 0 is usually imposed, where ϕα are first class constraints. This condition is not sufficient and one should (i) employ HT and (ii) choose the gauge-fixing conditions χα to be stationary under HT. Gauge degrees of freedom in the Lagrangian formalism are equal in number to the primary first class constraints

Generator of Gauge Transformation in Phase Space and Velocity Phase Space

\phi_\alpha^1

Classification of gauge groups in terms of algebraic structure of first class constraints

. Hence the number of arbitrarily chosen primary gauge conditions

Coupling of Dirac Particle and Gravitational Field

\chi_1^\alpha

On the Consistency between Lagrangian and Hamiltonian Formalisms in Quantum Mechanics. III

is the same as that of

Pathological Dynamical System with Constraints

\phi_\alpha^1

Fixation of Physical Space-Time Coordinates and Equation of Motion of Two-Body Problem

. Secondary gauge-fixing conditions associated with secondary first class constraints should be determined by the stationarity conditions of

Derivation of many‐body potential among charged particles in the S‐matrix method

\chi_1^\alpha