Calculation of zero-norm states and reduction of stringy scattering amplitudes

Jen-Chi Lee*

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Scopus citations


We give a simplified method to generate two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. Zero-norm states up to the fourth massive level and general formulas of some zero-norm tensor states at arbitrary mass levels are calculated. On-shell Ward identities generated by zero-norm states and the factorization property of stringy vertex operators can then be used to argue that the string-tree scattering amplitudes of the degenerate lower spin propagating states are fixed by those of higher spin propagating states at each fixed mass level. This decoupling phenomenon is, in contrast to Gross's high-energy symmetries, valid to all energies. As examples, we explicitly demonstrate this stringy phenomenon up to the fourth massive level (spin-five), which justifies the calculation of two other previous approaches based on the massive worldsheet sigma-model and Witten's string field theory (WSFT).

Original languageEnglish
Pages (from-to)259-273
Number of pages15
JournalProgress of Theoretical Physics
Issue number1
StatePublished - 1 Jul 2005

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