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The BFSS matrix model can therefore be used as a prototype for a correct formulation of M-theory and a tool for investigating the properties of M-theory in a relatively simple setting. The BFSS matrix model is also considered the worldvolume theory of a large number of D0- branes in Type IIA string theory.
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits.
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix of two quantum mechanical systems and , to be separable. It is also called the PPT criterion, for positive partial transpose. In the 2×2 and 2×3 dimensional cases the condition is also sufficient.
In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble [1] of physical systems as quantum states (even if the ensemble contains only one system). It allows for the calculation of the probabilities of the outcomes of any measurements performed upon the systems of the ensemble using the Born rule .
In matrix form, operators allow real eigenvalues to be found, corresponding to measurements. Orthogonality allows a suitable basis set of vectors to represent the state of the quantum system. The eigenvalues of the operator are also evaluated in the same way as for the square matrix, by solving the characteristic polynomial :
where is the charge conjugation matrix, which matches the Dirac version defined above. The reason for making all gamma matrices imaginary is solely to obtain the particle physics metric (+, −, −, −), in which squared masses are positive. The Majorana representation, however, is real.
The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics , scattering theory and quantum field theory (QFT).