Vacuum amplitudes and time-like causal unitary in the loop-tree duality by The LTD collaboration, Selomit Ramírez-Uribe, Andrés E. Rentería-Olivo, David F. Rentería-Estrada, Jorge J. Martínez de Lejarza, Prasanna K. Dhani, Leandro Cieri, Roger J. Hernández-Pinto, German F. R. Sborlini, William J. Torres Bobadilla, Germán Rodrigo

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