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The Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space H.
Since ω x (1)=||x|| 2, ω x is a state if ||x||=1. If A is a C*-subalgebra of B(H) and M an operator system in A, then the restriction of ω x to M defines a positive linear functional on M. The states of M that arise in this manner, from unit vectors in H, are termed vector states of M.
These vacuum expectation values can take any value for which the potential function is a minimum. Consequently, when the potential function has continuous families of global minima, the space of vacua for the quantum field theory is a manifold (or orbifold), usually called the vacuum manifold. [2]
The standard model is a quantum field theory, meaning its fundamental objects are quantum fields, which are defined at all points in spacetime. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. These fields are
The theorem proves that there is a contradiction between two basic assumptions of the hidden-variable theories intended to reproduce the results of quantum mechanics: that all hidden variables corresponding to quantum-mechanical observables have definite values at any given time, and that the values of those variables are intrinsic and ...
The resulting plasmas are expected to generate at least twice as much energy as is required to sustain themselves at high temperatures (200 million K), [13] giving a fusion gain Q > 2, with an expected Q ≈ 11. [1] Construction site in May 2023
More recent motivation comes from quantum computing. In quantum mechanics the quantum state can evolve in two ways: by Schrödinger's equation (unitary transformations), or by their collapse. Logic operations for quantum computers, of which the Toffoli gate is an example, are unitary transformations and therefore evolve reversibly. [2]
In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops.They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops.