Symbol T
T is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Why this formula appears here
Nothing about this phase disturbs conservation of energy or momentum, and it is worth saying explicitly why. [] does not come from a new term added to any Hamiltonian; it comes from how already-unitary translation and boost operators compose. Each operator in the product T()G()T(-)G(-) conserves probability on its own, and the product of unitaries is unitary regardless of whether the factors commute, so the loop as a whole still conserves probability and leaves every expectation value of energy and momentum exactly where an ordinary, non-extended calculation would put it. What changes is not a conserved quantity but the bookkeeping of…
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Symbol b
b is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Symbol G
G is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Symbol v
v is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Read this expression with the definitions, units, and assumptions supplied by the article.
Published contexts (1)
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Equation 50 · Evolutionary Physics
The Clock That Comes Back Wrong by Exactly Its Mass
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Nothing about this phase disturbs conservation of energy or momentum, and it is worth saying explicitly why. [] does not come from a new term added to any Hamiltonian; it comes from how already-unitary translation and boost operators compose. Each operator in the product T()G()T(-)G(-) conserves probability on its own, and the product of unitaries is unitary regardless of whether the factors commute, so the loop as a whole still conserves probability and leaves every expectation value of energy and momentum exactly where an ordinary, non-extended calculation would put it. What changes is not a conserved quantity but the bookkeeping of…
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