densitized造句

• The densitized triads can be used to reconstruct the spatial metric via
• Also there were also serious difficulties promoting the densitized Hamiltonian to a quantum operator.
• The \ Gamma _ a ^ i have a complicated relationship with the densitized triads and causes serious problems upon quantization.
• These require that the densitized triad be real and that the real part of the Ashtekar connection equals the compatible spin connection.
• The densitized triads are not unique, and in fact one can perform a local in space rotation with respect to the internal indices i.
• The densitized drei-bein can be used to re construct the metric as discussed above and the connection can be used to reconstruct the extrinsic curvature.
• In the connection representation the configuration variable is A _ a ^ i and its conjugate momentum is the ( densitized ) triad \ tilde { E } _ i ^ a.
• The densitized drei-bein is the conjugate momentum variable of this three-dimensional SU ( 2 ) gauge field ( or connection ) A ^ j _ b, in that it satisfies the Poisson bracket relation
• Also the Hamiltonian constraint Ashtekar worked with was the densitized version instead of the original Hamiltonian, that is, he worked with \ tilde { H } = \ sqrt { det ( q ) } H.
• For example, the Hamiltonian constraint Ashtekar worked with was the densitized version instead of the original Hamiltonian, that is, he worked with \ tilde { H } = \ sqrt { \ operatorname { det } ( q ) } H.
• In Ashtekar formulation the gauge field A _ a ^ i ( x ) is the configuration variable ( the configuration variable being analogous to q in ordinary mechanics ) and its conjugate momentum is the ( densitized ) triad ( electrical field ) \ tilde { E } ^ a _ i ( x ).
• To recover the real theory, one has to impose what are known as the " reality conditions . " These require that the densitized triad be real and that the real part of the Ashtekar connection equals the compatible spin connection ( the compatibility condition being \ nabla _ a e _ b ^ I = 0 ) determined by the densitized triad.
• To recover the real theory, one has to impose what are known as the " reality conditions . " These require that the densitized triad be real and that the real part of the Ashtekar connection equals the compatible spin connection ( the compatibility condition being \ nabla _ a e _ b ^ I = 0 ) determined by the densitized triad.
• (where \ delta ^ { ij } is the flat space metric, and the above equation expresses that q ^ { ab }, when written in terms of the basis E _ i ^ a, is locally flat ) . ( Formulating general relativity with triads instead of metrics was not new . ) The densitized triads are not unique, and in fact one can perform a local in space rotation with respect to the internal indices i.