학술논문
Boundary conditions for constraint systems in variational principle.
Document Type
Journal
Author
Izumi, Keisuke (J-NAGO-OPU) AMS Author Profile; Shimada, Keigo (J-TOKYTE-P) AMS Author Profile; Tomonari, Kyosuke (J-TOKYTE-P) AMS Author Profile; Yamaguchi, Masahide (J-TOKYTE-P) AMS Author Profile
Source
Subject
83 Relativity and gravitational theory -- 83D Relativistic gravitational theories other than Einstein's, including asymmetric field theories
83D05Relativistic gravitational theories other than Einstein's, including asymmetric field theories
83D05
Language
English
Abstract
Summary: ``We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match that of physical degrees of freedom , which implies that, even in theories with up to first-order derivatives, the minimal (or extremal) value of the action with the boundary terms is not a solution of the equation of motion in the Dirac procedure of constrained systems. We propose specific and concrete steps to solve this problem. These steps utilize the Hamilton formalism, which allows us to separate the physical degrees of freedom from the constraints. This reveals the physical degrees of freedom that are necessary to be fixed on boundaries, and also enables us to specify the variables to be fixed and the surface terms.''