The wave-particle duality,as a manifestation of Bohr’s complementarity,is usually quantified in terms of path predictability and interference visibility.Various characterizations of the wave-particle duality have bee...The wave-particle duality,as a manifestation of Bohr’s complementarity,is usually quantified in terms of path predictability and interference visibility.Various characterizations of the wave-particle duality have been proposed from an operational perspective,most of them are in forms of inequalities,and some of them are expressed in forms of equalities by incorporating entanglement or coherence.In this work,we shed different insights into the nature of the wave-particle duality by casting it into a form of information conservation in a multi-path interferometer,with uncertainty as a unified theme.More specifically,by employing the simple yet fundamental concept of variance,we establish a resolution of unity,which can be interpreted as a complementarity relation among wave feature,particle feature,and mixedness of a quantum state.This refines or reinterprets some conventional approaches to wave-particle duality,and highlights informational aspects of the issue.The key idea of our approach lies in that a quantum state,as a Hermitian operator,can also be naturally regarded as an observable,with measurement uncertainty(in a state)and state uncertainty(in a measurement)being exploited to quantify particle feature and wave feature of a quantum state,respectively.These two kinds of uncertainties,although both are defined via variance,have fundamentally different properties and capture different features of a state.Together with the mixedness,which is a kind of uncertainty intrinsic to a quantum state,they add up to unity,and thus lead to a characterization of the waveparticle-mixedness complementarity.This triality relation is further illustrated by examples and compared with some popular wave-particle duality or triality relations.展开更多
It is proved that there exists a vector representation of Dirac＇s spinor field and. in one sense it is equivalent to biquaternion （i.e. complexified quaternion） representation. This can be considered as a generaliz...It is proved that there exists a vector representation of Dirac＇s spinor field and. in one sense it is equivalent to biquaternion （i.e. complexified quaternion） representation. This can be considered as a generalization of Cartan＇s idea of triality to Dirac＇s spinors. In the vector representation the first-order Dirac Lagrangian is dual-equivalent to the two-order Lagrangian of topologically massive gauge field. The potential field which corresponds to the Dirac field is obta/ned by using master （or parent） action approach. The novel gauge field is self-dual and contains both anti-symmetric Lee and symmetric Jordan structure.展开更多
The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4 + 4)-space. Split octonionic representation of SO(4, 4) and Spin(4, 4) groups and the trilinear inva...The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4 + 4)-space. Split octonionic representation of SO(4, 4) and Spin(4, 4) groups and the trilinear invariant form are explicitly written and compared with Clifford algebraic matrix representation. It is noted that the complete algebra of split octonionic basis units can be recovered from the Moufang and Malcev relations for the three vector-like elements. Lagrangians on split octonionic fields that generalize Dirac and Maxwell systems are constructed using group invariant forms. It is shown that corresponding equations are related to split octonionic analyticity conditions.展开更多
基金supported by the National Key R&D Program of China,Grant No.2020YFA0712700the Fundamental Research Funds for the Central Universities,Grant No.FRFTP-19-012A3the National Natural Science Foundation of China,Grant Nos.11875317 and 61833010。
文摘The wave-particle duality,as a manifestation of Bohr’s complementarity,is usually quantified in terms of path predictability and interference visibility.Various characterizations of the wave-particle duality have been proposed from an operational perspective,most of them are in forms of inequalities,and some of them are expressed in forms of equalities by incorporating entanglement or coherence.In this work,we shed different insights into the nature of the wave-particle duality by casting it into a form of information conservation in a multi-path interferometer,with uncertainty as a unified theme.More specifically,by employing the simple yet fundamental concept of variance,we establish a resolution of unity,which can be interpreted as a complementarity relation among wave feature,particle feature,and mixedness of a quantum state.This refines or reinterprets some conventional approaches to wave-particle duality,and highlights informational aspects of the issue.The key idea of our approach lies in that a quantum state,as a Hermitian operator,can also be naturally regarded as an observable,with measurement uncertainty(in a state)and state uncertainty(in a measurement)being exploited to quantify particle feature and wave feature of a quantum state,respectively.These two kinds of uncertainties,although both are defined via variance,have fundamentally different properties and capture different features of a state.Together with the mixedness,which is a kind of uncertainty intrinsic to a quantum state,they add up to unity,and thus lead to a characterization of the waveparticle-mixedness complementarity.This triality relation is further illustrated by examples and compared with some popular wave-particle duality or triality relations.
文摘It is proved that there exists a vector representation of Dirac＇s spinor field and. in one sense it is equivalent to biquaternion （i.e. complexified quaternion） representation. This can be considered as a generalization of Cartan＇s idea of triality to Dirac＇s spinors. In the vector representation the first-order Dirac Lagrangian is dual-equivalent to the two-order Lagrangian of topologically massive gauge field. The potential field which corresponds to the Dirac field is obta/ned by using master （or parent） action approach. The novel gauge field is self-dual and contains both anti-symmetric Lee and symmetric Jordan structure.
文摘The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4 + 4)-space. Split octonionic representation of SO(4, 4) and Spin(4, 4) groups and the trilinear invariant form are explicitly written and compared with Clifford algebraic matrix representation. It is noted that the complete algebra of split octonionic basis units can be recovered from the Moufang and Malcev relations for the three vector-like elements. Lagrangians on split octonionic fields that generalize Dirac and Maxwell systems are constructed using group invariant forms. It is shown that corresponding equations are related to split octonionic analyticity conditions.
