Group Theoretical Properties of Dual Resonance Models

One of the remarkable things about duality is that it leads to the formulation of very esthetic theoretical ideas although it has its roots in the structure of strong-interaction data. Surely this marriage of conceptual beauty with experimental observation is no accident. The first steps towards the construction of amplitudes that were “dual” have been excellently described in several review articlesi; in these lectures we would rather like to show the emergence of a very fundamental group theoretical structure that seems to underlie all dual resonance models (DRM) built to date. Since no DRM duplicates the data closely enough, we would like to understand how to add the missing ingredients without affecting the properties we like about the more primitive models (like factorization, crossing, Regge behavior, etc. )....

Note:

Lectures presented at the 1971 Boulder Summer School.

DUALITY
dual resonance model
SCATTERING AMPLITUDE: ANALYTIC PROPERTIES
GROUP THEORY
MODEL: VENEZIANO
MODEL: N-POINT FUNCTION
INVARIANCE: GAUGE
SYMMETRY: CROSSING
EXCITED STATE
QUANTUM NUMBER

References(24)

Figures(0)

[1]

See, for example Lectures at the Erice Summer School

G. Veneziano

[2]

Nucl. Phys. Bs, 517

Z. Koba
,
H. Nielsen

[3]

SU(1,1) Analysis of Dual Resonance Models

L. Clavelli
(
- Fermilab
)
,
Pierre Ramond
(
- Fermilab
)

- Phys.Rev.D 2 (1970) 973
•
DOI:
- 10.1103/PhysRevD.2.973

[4]

op.cit

L. Clavelli
,
P. Ramond

[5]

A general treatment of factorization in dual resonance models

- Phys.Lett.B 29 (1969) 679-682
•
DOI:
- 10.1016/0370-2693(69)90109-9

[5]

University of Chicago Report no. EFI 69-64 (unpublished)

Y. Nambu

[14]

Duality in operator formalism

S. Fubini
(
- MIT, LNS
)
,
G. Veneziano
(
- MIT, LNS
)

- Nuovo Cim.A 67 (1970) 29-47
•
DOI:
- 10.1007/BF02728411

[7]

Nuovo Cimento Letters IV, 689

A. Della Selva
,
S. Saito

[7]

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P. Ramond

[7]

Phys. Rev. z, 2493

K. Bardacki
,
M.B. Halpern

[8]

This procedure is used throughout Ref. 3

[9]

Phys. Rev. g, 2933

M.A. Virasoro

[10]

This algebra was first derived by Phys. (N. Y. ) 63, 12 without the c-number. Its existencewas pointed out independently by J. Weiss and L. Clavelli An independent derivation is found in Y. Nambu University of Chicago Preprint #EFI-70-07 (unpublished). -37-

S. Fubini
,
G. Veneziano in Ann

[11]

Phys. Rev. E 987

L. Clavelli
,
P. Ramond

[12]

This was first shown by Ref. 3, for scalar external legs

L. Clavelli
,
P. Ramond

[13]

The author wishes to thank Bardacki for a discussion on this point

K.

[14]

Duality in operator formalism

S. Fubini
(
- MIT, LNS
)
,
G. Veneziano
(
- MIT, LNS
)

- Nuovo Cim.A 67 (1970) 29-47
•
DOI:
- 10.1007/BF02728411

[14]

Ref. 3

L. Clavelli
,
P. Ramond

[15]

This ambiguity may be avoided by considering representations of SL( 2, R)

[15]

thanks are due to Dr for this remark

I. Bars

[16]

See the appendix of Ref. 2

[17]

Nucl. Phys. E, 323

D.B. Fairlie
,
K. Jones

[18]

See Ref. 10. l9 MIT Preprint 167

E. Del Giudice
,
P. Di Vecchia

[18]

Pomeron form-factors and dual Regge cuts

C. Lovelace
(
- Rutgers U., Piscataway
)

- Phys.Lett.B 34 (1971) 500-506
•
DOI:
- 10.1016/0370-2693(71)90665-4