Tensorial Aspects of Quantum Physics

Yannick Meurice

David Daniel O’Regan

Max Born

Yannick Meurice

In most lattice simulations, the variables of integration are compact and character expansion (for instance Fourier analysis for U(1) models) can be used to rewrite the partition function and average observables as discrete sums of contracted tensors. These reformulations have been used for RG blocking but they also naturally fit the needs of quantum computing. We discuss FAQ about tensorial reformulations: effects of truncations on symmetries, boundary conditions, Grassmann variables, and other recent aspects of quantum computing in the same context.

Max Born

Enrique Ordaz Romay

The analytic physics, when it is development from aprioristic form, constructs all the laws from the Hamilton principle, also called action principle. According to this principle all systems are characterized by a magnitude called action which variation is equal to zero for the real evolution of the systems. At first, do not exist restrictions for the mathematical form of the action function, nonetheless, as in the a posteriori developer of the analytic physics, the traditional equations of the physics lead up to a scalar action, it is always sure that the action may be a scalar function. In this article we propose the existence of a tensorial function like origin of the traditional scalar action. First because it permits, without other argumens, to justify the own action principle and second because it permits connect the complementary principle of the Quantum physics with the analytic expressions of the nonquantum physics, including the General Relativity. We call tensorial action to this original function and their components are connecting, directly, with the tensorial (spinorial) componets of the wave function of the particles with spin higher than zero. For this reason we can understand why in the nonquantum physics only has significance a scalar action.