Reiji Sugano

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

On Consistency between Lagrange and Hamilton Formalisms in Quantum Mechanics Case of Non-Relativistic Velocity-Dependent Potential

. Hence the number of arbitrarily chosen primary gauge conditions

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

\chi_1^\alpha

On Classification of Interactions: Possibility of Existence of a New Boson coupled with Λ and µ

is the same as that of

Necessary and Sufficient Conditions of Reducibility of Gauge Degrees of Freedom without Using Gauge Conditions

\phi_\alpha^1

Necessary and sufficient conditions for the existence of a lagrangian. The case of quasi-linear field equations

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

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

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Pathological Dynamical System with Constraints

. If a canonical Hamiltonian (weakly) vanishes, χα must be explicitly time-dependent, otherwise we have the trivial result. Further, it is pointed out that the HE formalism has discrepancies with the HT formalism in...