Shinji Hamamoto

Higher Derivatives and Canonical Formalisms

Path integral expressions for three canonical formalisms -- Ostrogradskis one, constrained one and generalized one -- of higher-derivative theories are given. For each fomalism we consider both nonsingular and singular cases. It is shown that three formalisms share the same path integral expressions. In paticular it is pointed out that the generalized canonical formalism is connected with the constrained one by a canonical transformation.

Possible Nonlinear Completion of Massive Gravity

A possible nonlinear completion of massive gravity is presented. An additional scalar ghost contained in the linear theory condenses to give rise to positive energy excitations.

Gauge Theory of Massive Tensor Field

In order to construct a massive tensor theory with a smooth massless limit, we apply the Batalin-Fradkin algorithm to the ordinary massive tensor theory. By introducing an auxiliary vector field all second-class constraints are converted into first-class ones. We find a gauge-fixing condition which produces a massive tensor theory of desirable property.

MASSLESS LIMITS OF MASSIVE TENSOR FIELDS

In order to construct a massive tensor theory with a smooth massless limit, we apply two kinds of gauge-fixing procedures, Nakanishis one and the BRS one, to two models of massive tensor field. The first is of the Fierz-Pauli (FP) type, which describes a pure massive tensor field; the other is of the additional-scalar-ghost (ASG) type, which includes a scalar ghost in addition to an ordinary tensor field. It is shown that Nakanishis procedure can eliminate massless singularities in both two models, while the BRS procedure regularizes the ASG model only. The BRS-regularized ASG model is most promising in constructing a complete nonlinear theory.

Massless Limits of Massive Tensor Fields. II: Infrared Regularizaiton of the Fierz-Pauli Model

Izawas gauge-fixing procedure based on BRS symmetry is applied twice to the massive tensor field theory of Fierz-Pauli type. It is shown the second application can remove massless singularities which remain after the first application. Massless limit of the theory is discussed.

Gauge Theory of Massive Tensor Field. II Covariant Expressions

Covariant forms are given to a gauge theory of massive tensor field. This is accomplished by introducing another auxiliary field of scalar type to the system composed of a symmetric tensor field and an auxiliary field of vector type. The situation is compared to the case of the theory in which a tensor field describes a scalar ghost as well as an ordinary massive tensor. In this case only an auxiliary vector field is needed to give covariant expressions for the gauge theory.

Nonlinear completion of massive gravity of the Fierz-Pauli type

A possible nonlinear completion of massive gravity of the Fierz-Pauli type is proposed. The theory describes a system consisting of a massive tensor field of the Fierz-Pauli type and an additional massive vector field. Massless limit as well as flat-spacetime limit can be taken smoothly. Constructing a nonlinear version of the physical-state condition which drives an extra scalar ghost from physical states is still unsettled.

Path-Integral Measures in Higher-Derivative Gravitational Theories

A simple method of obtaining path-integral measures in higher-derivative gravitational theories is presented. The measures are identical to the generalized Lee-Yang terms.

Gauging Higher Derivatives

The usual prescription for constructing gauge-invariant Lagrangian is generalized to the case where a Lagrangian contains second derivatives of fields as well as first derivatives. Symmetric tensor fields in addition to the usual vector fields are introduced as gauge fields. Covariant derivatives and gauge-field strengths are determined.