The paper introduces a novel approach to nonadiabatic field (NaF) dynamics using triangle window functions (TWFs) and the constraint coordinate-momentum phase space (CPS) formulation. The CPS-TW representation is applied to discrete electronic degrees of freedom (DOFs) and integrated with the NaF strategy to form a more consistent trajectory-based approach for studying nonadiabatic transition dynamics. The key contributions include: 1. **CPS-TW Representation**: The CPS-TW representation is derived from the U(F)/U(F-1) CPS and triangle window functions, providing an exact expression for the population–population correlation function in the two-state system and a reasonable approximation for multistate systems. This representation ensures that the population dynamics is always positive semidefinite. 2. **NaF-TW Approach**: The NaF-TW approach is proposed, which uses the CPS-TW representation for electronic DOFs and the infinite Wigner coordinate-momentum phase space for nuclear DOFs. This approach is applied to nonadiabatic dynamics, offering a more accurate description of both nuclear motion and electronic coherence/dissipation. 3. **Numerical Tests**: Extensive benchmark tests on various model systems, including condensed phase and gas phase systems, demonstrate the superior performance of NaF-TW compared to conventional methods like Ehrenfest dynamics, fewest-switches surface hopping (FSSH), and symmetrical quasi-classical (SQC) methods. NaF-TW consistently captures the dynamical interplay between electronic and nuclear DOFs, even in regions where states remain coupled or where bifurcation characteristics are important. 4. **Advantages**: The CPS-TW representation ensures that the population dynamics is always positive semidefinite, addressing the negative population problem in phase space mapping dynamics methods. This property, combined with the accurate representation of electronic dynamics, makes NaF-TW a robust and accurate method for nonadiabatic dynamics. Overall, the CPS-TW representation and NaF-TW approach provide a powerful tool for studying nonadiabatic transition dynamics in complex molecular systems, offering a more consistent and accurate description of both electronic and nuclear dynamics.The paper introduces a novel approach to nonadiabatic field (NaF) dynamics using triangle window functions (TWFs) and the constraint coordinate-momentum phase space (CPS) formulation. The CPS-TW representation is applied to discrete electronic degrees of freedom (DOFs) and integrated with the NaF strategy to form a more consistent trajectory-based approach for studying nonadiabatic transition dynamics. The key contributions include: 1. **CPS-TW Representation**: The CPS-TW representation is derived from the U(F)/U(F-1) CPS and triangle window functions, providing an exact expression for the population–population correlation function in the two-state system and a reasonable approximation for multistate systems. This representation ensures that the population dynamics is always positive semidefinite. 2. **NaF-TW Approach**: The NaF-TW approach is proposed, which uses the CPS-TW representation for electronic DOFs and the infinite Wigner coordinate-momentum phase space for nuclear DOFs. This approach is applied to nonadiabatic dynamics, offering a more accurate description of both nuclear motion and electronic coherence/dissipation. 3. **Numerical Tests**: Extensive benchmark tests on various model systems, including condensed phase and gas phase systems, demonstrate the superior performance of NaF-TW compared to conventional methods like Ehrenfest dynamics, fewest-switches surface hopping (FSSH), and symmetrical quasi-classical (SQC) methods. NaF-TW consistently captures the dynamical interplay between electronic and nuclear DOFs, even in regions where states remain coupled or where bifurcation characteristics are important. 4. **Advantages**: The CPS-TW representation ensures that the population dynamics is always positive semidefinite, addressing the negative population problem in phase space mapping dynamics methods. This property, combined with the accurate representation of electronic dynamics, makes NaF-TW a robust and accurate method for nonadiabatic dynamics. Overall, the CPS-TW representation and NaF-TW approach provide a powerful tool for studying nonadiabatic transition dynamics in complex molecular systems, offering a more consistent and accurate description of both electronic and nuclear dynamics.