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What is special to two dimensions is that the scaling dimension of the free boson vanishes. This permits the presence of a non-vanishing background charge, and is at the origin of the theory's conformal symmetry. In probability theory, the free boson can be constructed as a Gaussian free field.
In theoretical condensed matter physics and quantum field theory, bosonization is a mathematical procedure by which a system of interacting fermions in (1+1) dimensions can be transformed to a system of massless, non-interacting bosons.
To produce simple poles on boson frequencies =, either of the following two types of Matsubara weighting functions can be chosen () = = = (+ ()),() = = (),depending on which half plane the convergence is to be controlled in. () controls the convergence in the left half plane (Re z < 0), while () controls the convergence in the right half plane (Re z > 0).
The massive neutral (Z) boson: = The massless neutral boson: = + The massive charged W bosons: = where θ W is the Weinberg angle. The A field is the photon , which corresponds classically to the well-known electromagnetic four-potential – i.e. the electric and magnetic fields.
The name boson was coined by Paul Dirac [3] [4] to commemorate the contribution of Satyendra Nath Bose, an Indian physicist. When Bose was a reader (later professor) at the University of Dhaka, Bengal (now in Bangladesh), [5] [6] he and Albert Einstein developed the theory characterising such particles, now known as Bose–Einstein statistics and Bose–Einstein condensate.
In quantum field theory, a bosonic field is a quantum field whose quanta are bosons; that is, they obey Bose–Einstein statistics.Bosonic fields obey canonical commutation relations, as distinct from the canonical anticommutation relations obeyed by fermionic fields.
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