Symbol tilde a_j
tilde is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
The precise, non-negotiable content of the ambiguity is the Bogoliubov transformation. Given two ways of splitting a free field into positive- and negative-frequency modes — two choices of “particle,” in the ordinary sense of excitations above a chosen vacuum — the annihilation operators of one decomposition mix the creation and annihilation operators of the other: . When any of the coefficients is nonzero, the vacuum of the a -decomposition is a many-particle state of the -decomposition, and vice versa: “how many particles are present” is a question whose answer depends on which set of modes was declared fundamental, not on the field configuration by…
Read the representative guide
Symbol k
k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol alpha_jk
alphk is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol a_k
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol a_k^dagger
agger is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Starting index or lower bound: k
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 1 · Evolutionary Physics
No Particle Without a Cosigner
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
The precise, non-negotiable content of the ambiguity is the Bogoliubov transformation. Given two ways of splitting a free field into positive- and negative-frequency modes — two choices of “particle,” in the ordinary sense of excitations above a chosen vacuum — the annihilation operators of one decomposition mix the creation and annihilation operators of the other: . When any of the coefficients is nonzero, the vacuum of the a -decomposition is a many-particle state of the -decomposition, and vice versa: “how many particles are present” is a question whose answer depends on which set of modes was declared fundamental, not on the field configuration by…