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This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons , quarks , gauge bosons and the Higgs boson .
t. e. In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n -by- n invertible matrices, then the adjoint representation is the group ...
Rodrigues' rotation formula. In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO (3), the group ...
The general linear group GL(n, R) over the field of real numbers is a real Lie group of dimension n 2. To see this, note that the set of all n×n real matrices, M n (R), forms a real vector space of dimension n 2. The subset GL(n, R) consists of those matrices whose determinant is non-zero.
At the other extreme, if is a deterministic function of and is a deterministic function of then all information conveyed by is shared with : knowing determines the value of and vice versa. As a result, the mutual information is the same as the uncertainty contained in Y {\displaystyle Y} (or X {\displaystyle X} ) alone, namely the entropy of Y ...
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement.
Lagrangian. [edit] Instead of forces, Lagrangian mechanics uses the energies in the system. The central quantity of Lagrangian mechanics is the Lagrangian, a function which summarizes the dynamics of the entire system. Overall, the Lagrangian has units of energy, but no single expression for all physical systems.
The first general equation of motion developed was Newton's second law of motion. In its most general form it states the rate of change of momentum p = p(t) = mv(t) of an object equals the force F = F(x(t), v(t), t) acting on it, [13]: 1112. The force in the equation is not the force the object exerts.