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One of the most widely used examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect. This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking. Examples are: The Higgs field has a vacuum ...
Then = is the non-vanishing vacuum expectation value of the Higgs field. v {\displaystyle v} has units of mass, and it is the only parameter in the Standard Model that is not dimensionless. It is also much smaller than the Planck scale and about twice the Higgs mass, setting the scale for the mass of all other particles in the Standard Model.
If this field has a vacuum expectation value, it points in some direction in field space. Without loss of generality, one can choose the z -axis in field space to be the direction that ϕ {\displaystyle \phi } is pointing, and then the vacuum expectation value of ϕ {\displaystyle \phi } is (0, 0, à ) , where à is a constant with dimensions ...
In quantum field theory, the quantum effective action is a modified expression for the classical action taking into account quantum corrections while ensuring that the principle of least action applies, meaning that extremizing the effective action yields the equations of motion for the vacuum expectation values of the quantum fields.
The expectation value of in the ground state (the vacuum expectation value or VEV) is then =, where = | |. The measured value of this parameter is ~ 246 GeV/ c 2 . [ 126 ] It has units of mass, and is the only free parameter of the Standard Model that is not a dimensionless number.
A vacuum can be viewed not as empty space but as the combination of all zero-point fields. In quantum field theory this combination of fields is called the vacuum state, its associated zero-point energy is called the vacuum energy and the average energy value is called the vacuum expectation value (VEV) also called its condensate.
The theorem is useful because, among other things, by relating the ground state of the interacting theory to its non-interacting ground state, it allows one to express Green's functions (which are defined as expectation values of Heisenberg-picture fields in the interacting vacuum) as expectation values of interaction picture fields in the non ...
where is the vacuum expectation value. The L y {\displaystyle \ {\mathcal {L}}_{y}\ } term describes the Yukawa interaction with the fermions, L y = − y u i j ϵ a b h b † Q ¯ i a u j c − y d i j h Q ¯ i d j c − y e i j h L ¯ i e j c + h . c .